Uncovering Treatment Response Patterns with Topological Clustering of Brain Networks

Topological data analysis (TDA) is a powerful tool for detecting hidden structures in complex data like biological signals and networks. A key TDA algorithm, persistent homology (PH), captures multi-scale topological features in data, which are robust to noise, as summarized by persistence diagrams (PDs). However, the non-Euclidean nature of PDs complicates traditional analysis. Recent topological inference methods use heat kernel (HK) expansion of PDs in multi-group permutation tests. Extending the topological inference methods, we develop a topological clustering framework based on the HK expansion of PDs. This flexible framework allows incorporation of Euclidean covariates into topological clustering, as well as an automated data-driven selection procedure for identifying the optimal number of topological clusters and most significant covariates associated with them. We demonstrate our method's effectiveness in cluster detection with varying degrees of topological dissimilarity through simulations of signals and point clouds in comparison to state-of-the-art functional and topological clustering methods, as well as applications to subtyping and treatment response in post-stroke aphasia. © 2025 IEEE.