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.

通过使用拓扑数据分析（TDA）和利普希茨 - 基林曲率（LKCs）方法，本研究探索了在生物医学多组学问题的背景下，作为强大工具进行特征提取和分类的应用。我们调查了结合这两种方法以提高分类准确性的潜力，并通过使用生物医学图像数据集来展示 TDA 和 LKCs 可以有效提取拓扑和几何特征。这种特征的组合相对于单独使用每种方法可以获得更好的分类性能，该方法为各种生物医学应用的复杂生物学过程的研究提供了有前景的结果，并突显了在生物医学数据分析中整合拓扑和几何信息的价值。随着我们继续探索多组学问题的复杂性，这些洞察力的融合对于揭示潜在的生物学复杂性有着巨大的潜力。