  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.
