GeoTop: Advancing Image Classification with Geometric-Topological Analysis

Abstract: In this study, we explore the application of Topological Data Analysis (TDA) and Lipschitz-Killing Curvatures (LKCs) as powerful tools for feature extraction and classification in the context of biomedical multiomics problems. TDA allows us to capture topological features and patterns within complex datasets, while LKCs provide essential geometric insights. We investigate the potential of combining both methods to improve classification accuracy. Using a dataset of biomedical images, we demonstrate that TDA and LKCs can effectively extract topological and geometrical features, respectively. The combination of these features results in enhanced classification performance compared to using each method individually. This approach offers promising results and has the potential to advance our understanding of complex biological processes in various biomedical applications. Our findings highlight the value of integrating topological and geometrical information in biomedical data analysis. As we continue to delve into the intricacies of multiomics problems, the fusion of these insights holds great promise for unraveling the underlying biological complexities.