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Must: Maximizing Latent Capacity of Spatial Transcriptomics Data (2401.07543v1)
Published 15 Jan 2024 in cs.CE and cs.AI
Abstract: Spatial transcriptomics (ST) technologies have revolutionized the study of gene expression patterns in tissues by providing multimodality data in transcriptomic, spatial, and morphological, offering opportunities for understanding tissue biology beyond transcriptomics. However, we identify the modality bias phenomenon in ST data species, i.e., the inconsistent contribution of different modalities to the labels leads to a tendency for the analysis methods to retain the information of the dominant modality. How to mitigate the adverse effects of modality bias to satisfy various downstream tasks remains a fundamental challenge. This paper introduces Multiple-modality Structure Transformation, named MuST, a novel methodology to tackle the challenge. MuST integrates the multi-modality information contained in the ST data effectively into a uniform latent space to provide a foundation for all the downstream tasks. It learns intrinsic local structures by topology discovery strategy and topology fusion loss function to solve the inconsistencies among different modalities. Thus, these topology-based and deep learning techniques provide a solid foundation for a variety of analytical tasks while coordinating different modalities. The effectiveness of MuST is assessed by performance metrics and biological significance. The results show that it outperforms existing state-of-the-art methods with clear advantages in the precision of identifying and preserving structures of tissues and biomarkers. MuST offers a versatile toolkit for the intricate analysis of complex biological systems.
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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Saliba, A.-E., Westermann, A. J., Gorski, S. A. & Vogel, J. Single-cell rna-seq: advances and future challenges. Nucleic acids research 42, 8845–8860 (2014). [3] Luecken, M. D. & Theis, F. J. Current best practices in single-cell rna-seq analysis: a tutorial. Molecular systems biology 15, e8746 (2019). [4] Erhard, F. et al. Time-resolved single-cell rna-seq using metabolic rna labelling. Nature Reviews Methods Primers 2, 77 (2022). [5] Satija, R., Farrell, J. A., Gennert, D., Schier, A. F. & Regev, A. Spatial reconstruction of single-cell gene expression data. Nature biotechnology 33, 495–502 (2015). [6] Williams, C. G., Lee, H. J., Asatsuma, T., Vento-Tormo, R. & Haque, A. An introduction to spatial transcriptomics for biomedical research. Genome Medicine 14, 1–18 (2022). [7] Hudson, W. H. & Sudmeier, L. J. Localization of t cell clonotypes using the visium spatial transcriptomics platform. STAR protocols 3, 101391 (2022). [8] Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Luecken, M. D. & Theis, F. J. Current best practices in single-cell rna-seq analysis: a tutorial. Molecular systems biology 15, e8746 (2019). [4] Erhard, F. et al. Time-resolved single-cell rna-seq using metabolic rna labelling. Nature Reviews Methods Primers 2, 77 (2022). [5] Satija, R., Farrell, J. A., Gennert, D., Schier, A. F. & Regev, A. Spatial reconstruction of single-cell gene expression data. Nature biotechnology 33, 495–502 (2015). [6] Williams, C. G., Lee, H. J., Asatsuma, T., Vento-Tormo, R. & Haque, A. An introduction to spatial transcriptomics for biomedical research. Genome Medicine 14, 1–18 (2022). [7] Hudson, W. H. & Sudmeier, L. J. Localization of t cell clonotypes using the visium spatial transcriptomics platform. STAR protocols 3, 101391 (2022). [8] Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Erhard, F. et al. 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Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. 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Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hudson, W. H. & Sudmeier, L. J. Localization of t cell clonotypes using the visium spatial transcriptomics platform. STAR protocols 3, 101391 (2022). [8] Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. 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Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. 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Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Williams, C. G., Lee, H. J., Asatsuma, T., Vento-Tormo, R. & Haque, A. An introduction to spatial transcriptomics for biomedical research. Genome Medicine 14, 1–18 (2022). [7] Hudson, W. H. & Sudmeier, L. J. Localization of t cell clonotypes using the visium spatial transcriptomics platform. STAR protocols 3, 101391 (2022). [8] Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. 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Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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[25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. 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Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. 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Localization of t cell clonotypes using the visium spatial transcriptomics platform. STAR protocols 3, 101391 (2022). [8] Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. 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Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. 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Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hudson, W. H. & Sudmeier, L. J. Localization of t cell clonotypes using the visium spatial transcriptomics platform. STAR protocols 3, 101391 (2022). [8] Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. 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[13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). 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Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Williams, C. G., Lee, H. J., Asatsuma, T., Vento-Tormo, R. & Haque, A. An introduction to spatial transcriptomics for biomedical research. Genome Medicine 14, 1–18 (2022). [7] Hudson, W. H. & Sudmeier, L. J. Localization of t cell clonotypes using the visium spatial transcriptomics platform. STAR protocols 3, 101391 (2022). [8] Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hudson, W. H. & Sudmeier, L. J. Localization of t cell clonotypes using the visium spatial transcriptomics platform. STAR protocols 3, 101391 (2022). [8] Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. 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Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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[51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. 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[38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). 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Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. 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Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. 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[44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. 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Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. 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Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. 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[23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hudson, W. H. & Sudmeier, L. J. Localization of t cell clonotypes using the visium spatial transcriptomics platform. STAR protocols 3, 101391 (2022). [8] Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019). [9] Stickels, R. R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2. Nature biotechnology 39, 313–319 (2021). [10] Chen, A. et al. Spatiotemporal transcriptomic atlas of mouse organogenesis using dna nanoball-patterned arrays. Cell 185, 1777–1792 (2022). [11] Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. 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Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. 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Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. 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[19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. 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Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. 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Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. 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A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. 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Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). 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Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. 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Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016). [12] Longo, S. K., Guo, M. G., Ji, A. L. & Khavari, P. A. Integrating single-cell and spatial transcriptomics to elucidate intercellular tissue dynamics. Nature Reviews Genetics 22, 627–644 (2021). [13] Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021). [14] Tian, L., Chen, F. & Macosko, E. Z. The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. 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Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. 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Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. 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Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. 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Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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[25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. 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Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. 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Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. 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Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. 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Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). 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[25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. 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E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). 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Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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[25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. 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Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. 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Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. 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Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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[44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. 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A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. 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Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. 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Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). 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Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. 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Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. 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Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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[27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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[44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. 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A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. 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Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. 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The expanding vistas of spatial transcriptomics. Nature Biotechnology 41, 773–782 (2023). [15] Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications 14, 1155 (2023). [16] Bao, F. et al. Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. 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[19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. 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Integrative spatial analysis of cell morphologies and transcriptional states with muse. Nature biotechnology 40, 1200–1209 (2022). [17] Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). 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[51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). 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[51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. 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Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dries, R. et al. Giotto, a pipeline for integrative analysis and visualization of single-cell spatial transcriptomic data. BioRxiv 701680 (2019). [18] Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. 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G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. 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E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. 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G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. 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Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. 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Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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[32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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[44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. 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A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, Y. et al. Structure-preserving visualization for single-cell rna-seq profiles using deep manifold transformation with batch-correction. Communications Biology 6, 369 (2023). [19] Kleshchevnikov, V. et al. Cell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology 40, 661–671 (2022). [20] Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. 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Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. 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[25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). 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Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. 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[25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). 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Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nature biotechnology 40, 1349–1359 (2022). [21] Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. 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Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. 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Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. 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E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. 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Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). 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Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dumitrascu, B., Villar, S., Mixon, D. G. & Engelhardt, B. E. Optimal marker gene selection for cell type discrimination in single cell analyses. Nature communications 12, 1186 (2021). [22] Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). 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Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. 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Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. 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Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. 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Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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[34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). 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Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. 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[61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). 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Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Wolf, F. A. et al. Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome biology 20, 1–9 (2019). [23] Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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[34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). 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Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. 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[61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). 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[27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). 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Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). 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[60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Pedregosa, F. et al. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Gat, I., Schwartz, I., Schwing, A. & Hazan, T. Removing bias in multi-modal classifiers: Regularization by maximizing functional entropies. Advances in Neural Information Processing Systems 33, 3197–3208 (2020). [24] Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Guo, Y. et al. On modality bias recognition and reduction. ACM Transactions on Multimedia Computing, Communications and Applications 19, 1–22 (2023). [25] Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Dong, K. & Zhang, S. Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder. Nature communications 13, 1739 (2022). [26] Ren, H., Walker, B. L., Cang, Z. & Nie, Q. Identifying multicellular spatiotemporal organization of cells with spaceflow. Nature communications 13, 4076 (2022). [27] Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. 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Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. 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Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. 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[34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). 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Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. 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Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. 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Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. 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Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. 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Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. 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Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. 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Zong, Y. et al. const: an interpretable multi-modal contrastive learning framework for spatial transcriptomics. bioRxiv 2022–01 (2022). [28] Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zeng, Y. et al. Identifying spatial domain by adapting transcriptomics with histology through contrastive learning. Briefings in Bioinformatics 24, bbad048 (2023). [29] Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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[44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. 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A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. 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The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Li, J., Chen, S., Pan, X., Yuan, Y. & Shen, H.-B. Cell clustering for spatial transcriptomics data with graph neural networks. Nature Computational Science 2, 399–408 (2022). [30] Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. 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[44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. 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A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Roth, A. E. The Shapley value: essays in honor of Lloyd S. 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Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Teng, H., Yuan, Y. & Bar-Joseph, Z. Clustering spatial transcriptomics data. Bioinformatics 38, 997–1004 (2022). [31] Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. 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Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Hu, J. et al. Spagcn: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network. Nature methods 18, 1342–1351 (2021). [32] Pham, D. et al. stlearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues. BioRxiv 2020–05 (2020). [33] Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. 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[39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). 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[56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. 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[58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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[44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. 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A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. 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Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, X., Wang, X., Shivashankar, G. & Uhler, C. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for alzheimer’s disease. Nature Communications 13, 7480 (2022). [34] Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. 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Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. 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Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Xu, C. et al. Deepst: identifying spatial domains in spatial transcriptomics by deep learning. Nucleic Acids Research 50, e131–e131 (2022). [35] Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Bergenstråhle, L. et al. Super-resolved spatial transcriptomics by deep data fusion. Nature biotechnology 40, 476–479 (2022). [36] Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Deep manifold embedding of attributed graphs. Neurocomputing 514, 83–93 (2022). [37] Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. 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Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. 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Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. 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The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. 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Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zang, Z. et al. Dlme: Deep local-flatness manifold embedding. European Conference on Computer Vision 576–592 (2022). [38] Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Kipf, T. N. & Welling, M. Semi-supervised classification with graph convolutional networks (2017). 1609.02907. [39] Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Mamoor, S. The alpha subunit of the gamma-aminobutyric acid receptor, gabra1, is differentially expressed in the brains of patients with schizophrenia. OSF Preprints https://doi.org/10.31219/osf.io/m93ya (2020). [40] Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Zhang, Y. et al. Association between nrgn gene polymorphism and resting-state hippocampal functional connectivity in schizophrenia. BMC psychiatry 19, 1–9 (2019). [41] Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Maynard, K. R. et al. Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature neuroscience 24, 425–436 (2021). [42] Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. 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Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. 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[51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. 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[61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Winter, E. The shapley value. Handbook of game theory with economic applications 3, 2025–2054 (2002). [43] Roth, A. E. The Shapley value: essays in honor of Lloyd S. Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. 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Shapley (Cambridge University Press, 1988). [44] Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. 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Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). [59] Peterson, L. E. K-nearest neighbor. Scholarpedia 4, 1883 (2009). [60] Van der Maaten, L. & Hinton, G. Visualizing data using t-sne. Journal of machine learning research 9 (2008). [61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Scrucca, L., Fop, M., Murphy, T. B. & Raftery, A. E. mclust 5: clustering, classification and density estimation using gaussian finite mixture models. The R journal 8, 289 (2016). [45] Zang, Z. et al. Evnet: An explainable deep network for dimension reduction. IEEE Transactions on Visualization and Computer Graphics (2022). [46] Becht, E. et al. 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[61] Pedregosa, F. et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research 12, 2825–2830 (2011). Becht, E. et al. Dimensionality reduction for visualizing single-cell data using umap. Nature biotechnology 37, 38–44 (2019). [47] Saltelli, A. Sensitivity analysis for importance assessment. Risk analysis 22, 579–590 (2002). [48] Zou, H. The adaptive lasso and its oracle properties. Journal of the American statistical association 101, 1418–1429 (2006). [49] 10xgenomics. 10x genomics. https://www.10xgenomics.com/resources/datasets/ (2023). [50] Sunkin, S. M. et al. Allen brain atlas: an integrated spatio-temporal portal for exploring the central nervous system. Nucleic acids research 41, D996–D1008 (2012). [51] Fu, H. et al. Unsupervised spatially embedded deep representation of spatial transcriptomics. Biorxiv 2021–06 (2021). [52] Zacharias, D. A. & Kappen, C. Developmental expression of the four plasma membrane calcium atpase (pmca) genes in the mouse. Biochimica et Biophysica Acta (BBA)-General Subjects 1428, 397–405 (1999). [53] Gilmore, E. C. & Herrup, K. Cortical development: layers of complexity. Current Biology 7, R231–R234 (1997). [54] Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: large-scale single-cell gene expression data analysis. Genome biology 19, 1–5 (2018). [55] Svensson, V., Teichmann, S. A. & Stegle, O. Spatialde: identification of spatially variable genes. Nature methods 15, 343–346 (2018). [56] He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proceedings of the IEEE conference on computer vision and pattern recognition 770–778 (2016). [57] Hggstrm, O. & Mossel, E. Nearest-neighbor walks with low predictability profile and percolation in backslash epsilon dimensions. The Annals of Probability 26, 1212–1231 (1998). [58] Tang, J., Deng, C. & Huang, G.-B. Extreme learning machine for multilayer perceptron. IEEE transactions on neural networks and learning systems 27, 809–821 (2015). 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