Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
184 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models (2401.00688v2)

Published 1 Jan 2024 in cs.SI and cs.LG

Abstract: Hypergraphs represent complex systems involving interactions among more than two entities and allow the investigation of higher-order structure and dynamics in complex systems. Node attribute data, which often accompanies network data, can enhance the inference of community structure in complex systems. While mixed-membership stochastic block models have been employed to infer community structure in hypergraphs, they complicate the visualization and interpretation of inferred community structure by assuming that nodes may possess soft community memberships. In this study, we propose a framework, HyperNEO, that combines mixed-membership stochastic block models for hypergraphs with dimensionality reduction methods. Our approach generates a node layout that largely preserves the community memberships of nodes. We evaluate our framework on both synthetic and empirical hypergraphs with node attributes. We expect our framework will broaden the investigation and understanding of higher-order community structure in complex systems.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (84)
  1. UMAP: Uniform manifold approximation and projection for dimension reduction. https://umap-learn.readthedocs.io/en/latest/. Accessed November 2023.
  2. Learning latent block structure in weighted networks. Journal of Complex Networks, 3:221–248, 2014.
  3. Mixed membership stochastic blockmodels. Journal of Machine Learning Research, 9:1981–2014, 2008.
  4. Evolutionary dynamics of higher-order interactions in social networks. Nature Human Behaviour, 5:586–595, 2021.
  5. Clustering in graphs and hypergraphs with categorical edge labels. In Proceedings of The Web Conference 2020, page 706–717, 2020.
  6. Hypergraphs with node attributes: structure and inference. arXiv preprint arXiv:2311.03857, 2023.
  7. Efficient and principled method for detecting communities in networks. Physical Review E, 84:036103, 2011.
  8. Dynamical Processes on Complex Networks. Cambridge University Press, Cambridge, UK, 2008.
  9. Mapping nonlocal relationships between metadata and network structure with metadata-dependent encoding of random walks. Science Advances, 8:eabn7558, 2022.
  10. Networks beyond pairwise interactions: Structure and dynamics. Physics Reports, 874:1–92, 2020.
  11. The physics of higher-order interactions in complex systems. Nature Physics, 17:1093–1098, 2021.
  12. Dimensionality reduction for visualizing single-cell data using umap. Nature Biotechnology, 37:38–44, 2019.
  13. Laplacian eigenmaps and spectral techniques for embedding and clustering. In T. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems, volume 14, 2001.
  14. On the stability of citation networks. Physica A: Statistical Mechanics and its Applications, 610:128399, 2023.
  15. Austin R. Benson. https://www.cs.cornell.edu/~arb/data/. Accessed September 2023.
  16. A social perspective on perceived distances reveals deep community structure. Proceedings of the National Academy of Sciences of the United States of America, 119:e2003634119, 2022.
  17. Ginestra Bianconi. Higher-Order Networks. Elements in the Structure and Dynamics of Complex Networks. Cambridge University Press, 2021.
  18. What are higher-order networks? SIAM Review, 65:686–731, 2023.
  19. The structure and dynamics of networks with higher order interactions. Physics Reports, 1018:1–64, 2023.
  20. Complex networks: Structure and dynamics. Physics Reports, 424:175–308, 2006.
  21. Random walks and community detection in hypergraphs. Journal of Physics: Complexity, 2:015011, 2021.
  22. Community detection in hypergraphs: Optimal statistical limit and efficient algorithms. In Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, volume 84, pages 871–879, 2018.
  23. Generative hypergraph clustering: From blockmodels to modularity. Science Advances, 7:eabh1303, 2021.
  24. Petr Chunaev. Community detection in node-attributed social networks: A survey. Computer Science Review, 37:100286, 2020.
  25. Inference of hyperedges and overlapping communities in hypergraphs. Nature Communications, 13:7229, 2022.
  26. Community detection with node attributes in multilayer networks. Scientific Reports, 10:15736, 2020.
  27. Community detection, link prediction, and layer interdependence in multilayer networks. Physical Review E, 95:042317, 2017.
  28. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39:1–22, 1977.
  29. How choosing random-walk model and network representation matters for flow-based community detection in hypergraphs. Communications Physics, 4:133, 2021.
  30. Santo Fortunato. Community detection in graphs. Physics Reports, 486:75–174, 2010.
  31. Community detection in networks: A user guide. Physics Reports, 659:1–44, 2016.
  32. Santo Fortunato and Mark E. J. Newman. 20 years of network community detection. Nature Physics, 18:848–850, 2022.
  33. Thomas M. J. Fruchterman and Edward M. Reingold. Graph drawing by force-directed placement. Software: Practice and Experience, 21:1129–1164, 1991.
  34. Mitigation of infectious disease at school: targeted class closure vs school closure. BMC Infectious Diseases, 14:695, 2014.
  35. Data on face-to-face contacts in an office building suggest a low-cost vaccination strategy based on community linkers. Network Science, 3:326–347, 2015.
  36. Evaluating overfit and underfit in models of network community structure. IEEE Transactions on Knowledge and Data Engineering, 32:1722–1735, 2020.
  37. Efficient discovery of overlapping communities in massive networks. Proceedings of the National Academy of Sciences of the United States of America, 110:14534–14539, 2013.
  38. Stochastic blockmodels: First steps. Social Networks, 5:109–137, 1983.
  39. Network structure, metadata, and the prediction of missing nodes and annotations. Physical Review X, 6:031038, 2016.
  40. Stochastic blockmodels and community structure in networks. Physical Review E, 83:016107, 2011.
  41. Community detection for hypergraph networks via regularized tensor power iteration. arXiv preprint arXiv:1909.06503, 2019.
  42. Community detection in hypergraphs, spiked tensor models, and sum-of-squares. In 2017 International Conference on Sampling Theory and Applications (SampTA), pages 124–128, 2017.
  43. Efficiently inferring community structure in bipartite networks. Physical Review E, 90:012805, 2014.
  44. Complex Networks: Principles, Methods and Applications. Cambridge University Press, Cambridge, UK, 2017.
  45. A review of stochastic block models and extensions for graph clustering. Applied Network Science, 4(1):122, 2019.
  46. Community detection in attributed graphs: An embedding approach. Proceedings of the AAAI Conference on Artificial Intelligence, 32, 2018.
  47. Hypergraphx: a library for higher-order network analysis. Journal of Complex Networks, 11:cnad019, 2023.
  48. Higher-order motif analysis in hypergraphs. Communications Physics, 5(1), 2022.
  49. Hyperlink communities in higher-order networks. arXiv preprint arXiv:2303.01385, 2023.
  50. Dynamics on higher-order networks: A review. Journal of The Royal Society Interface, 19:20220043, 2022.
  51. Contact patterns in a high school: A comparison between data collected using wearable sensors, contact diaries and friendship surveys. PLOS ONE, 10:e0136497, 2015.
  52. UMAP: Uniform manifold approximation and projection. Journal of Open Source Software, 3:861, 2018.
  53. Unsupervised embedding of trajectories captures the latent structure of scientific migration. Proceedings of the National Academy of Sciences of the United States of America, 120:e2305414120, 2023.
  54. Quantifying gender imbalance in east asian academia: Research career and citation practice. Journal of Informetrics, 17:101460, 2023.
  55. Higher-order rich-club phenomenon in collaborative research grant networks. Scientometrics, 128(4):2429–2446, 2023.
  56. M. E. J. Newman. The structure of scientific collaboration networks. Proceedings of the National Academy of Sciences of the United States of America, 98:404–409, 2001.
  57. M. E. J. Newman. Networks. Second Edition. Oxford University Press, Oxford, UK, 2018.
  58. Structure and inference in annotated networks. Nature Communications, 7(1):11863, 2016.
  59. M. E. J. Newman and M. Girvan. Finding and evaluating community structure in networks. Physical Review E, 69:026113, 2004.
  60. Uncovering the overlapping community structure of complex networks in nature and society. Nature, 435:814–818, 2005.
  61. World citation and collaboration networks: uncovering the role of geography in science. Scientific Reports, 2:902, 2012.
  62. The shape of collaborations. EPJ Data Science, 6, 2017. Art. no. 18.
  63. The ground truth about metadata and community detection in networks. Science Advances, 3:e1602548, 2017.
  64. Efficient detection of online communities and social bot activity during electoral campaigns. Journal of Information Technology & Politics, 18:324–337, 2021.
  65. A framework to generate hypergraphs with community structure. arXiv preprint arXiv:2212.08593, 2023. DOI: 10.48550/arXiv.2212.08593.
  66. Community detection in large hypergraphs. Science Advances, 9:eadg9159, 2023.
  67. Hyperedge prediction and the statistical mechanisms of higher-order and lower-order interactions in complex networks. Proceedings of the National Academy of Sciences of the United States of America, 120:e2303887120, 2023.
  68. Stochastic block models with multiple continuous attributes. Applied Network Science, 4(1):54, 2019.
  69. High-resolution measurements of face-to-face contact patterns in a primary school. PLOS ONE, 6:e23176, 2011.
  70. A global geometric framework for nonlinear dimensionality reduction. Science, 290:2319–2323, 2000.
  71. The why, how, and when of representations for complex systems. SIAM Review, 63:435–485, 2021.
  72. Controlling nosocomial infection based on structure of hospital social networks. Journal of Theoretical Biology, 254:655–666, 2008.
  73. Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of Machine Learning Research, 9:2579–2605, 2008.
  74. Estimating potential infection transmission routes in hospital wards using wearable proximity sensors. PLOS ONE, 8:e73970, 2013.
  75. Semantic community identification in large attribute networks. Proceedings of the AAAI Conference on Artificial Intelligence, 30, 2016.
  76. C. F. Jeff Wu. On the convergence properties of the EM algorithm. The Annals of Statistics, 11:95–103, 1983.
  77. Community detection in networks with node attributes. In 2013 IEEE 13th International Conference on Data Mining, pages 1151–1156, 2013.
  78. Detecting cohesive and 2-mode communities indirected and undirected networks. In Proceedings of the 7th ACM International Conference on Web Search and Data Mining, page 323–332, 2014.
  79. Community detection in general hypergraph via graph embedding. Journal of the American Statistical Association, 118:1620–1629, 2023.
  80. Learning with hypergraphs: Clustering, classification, and embedding. In Advances in Neural Information Processing Systems, volume 19, 2006.
  81. Topological simplifications of hypergraphs. IEEE Transactions on Visualization and Computer Graphics, 29:3209–3225, 2023.
  82. spring_layout. networkx. https://networkx.org/documentation/stable/reference/generated/networkx.drawing.layout.spring_layout.html. Accessed November 2023.
  83. Networks beyond pairwise interactions: Structure and dynamics. Phys. Rep., 874:1–92, 2020.
  84. Community detection, link prediction, and layer interdependence in multilayer networks. Phys. Rev. E, 95:042317, 2017.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now