Analysis of Topological Data Analysis Methods for Higher-Order Interpretation of Networks

Topological Data Analysis (TDA) is an emerging tool in the field of network analysis. Our group’s previous work applied persistent homology, a TDA method, to neural, quantum,

and machine learning datasets, focusing on analyzing Betti numbers and birth–death diagrams to characterize higher-order organization in natural systems. However, persistent homology is not the only method available for topological data analysis; methods such as Mapper (Madukpe, Ugoala, and Zulkepli, 2025) and (Sheaf Cohomology Curry, 2014) have the potential to provide fresh insights into network models. This presentation will explore other Topological Data Analysis methods for the analysis of neural, machine learning, and quantum network data. We examine the mathematics underlying these methods and, through application and low-level analysis, uncover the key features of TDA algorithm design. The goal of this work is to better understand how TDA can be applied to network data and to provide insight into the design of network-specialized TDA methods for interpreting neural, machine learning, and quantum network data.

References

Curry, J. (2014). Sheaves, cosheaves and applications. Retrieved from https://arxiv.org/abs/1303.3255

Madukpe, V. N., Ugoala, B. C., & Zulkepli, N. F. S. (2025). A comprehensive review of the mapper algorithm, a topological data analysis technique, and its applications across various fields (2007-2025). Retrieved from https://arxiv.org/abs/2504.09042