Unified Topological Inference for Brain Networks in Temporal Lobe Epilepsy Using the Wasserstein Distance

Persistent homology can extract hidden topological signals present in brain networks. Persistent homology summarizes the changes of topological structures over multiple different scales called filtrations. Doing so detect hidden topological signals that persist over multiple scales. However, a key obstacle of applying persistent homology to brain network studies has always been the lack of coherent statistical inference framework. To address this problem, we present a unified topological inference framework based on the Wasserstein distance. Our approach has no explicit models and distributional assumptions. The inference is performed in a completely data driven fashion. The method is applied to the resting-state functional magnetic resonance images (rs-fMRI) of the temporal lobe epilepsy patients collected at two different sites: University of Wisconsin-Madison and the Medical College of Wisconsin. However, the topological method is robust to variations due to sex and acquisition, and thus there is no need to account for sex and site as categorical nuisance covariates. We are able to localize brain regions that contribute the most to topological differences. We made MATLAB package available at https://github.com/laplcebeltrami/dynamicTDA that was used to perform all the analysis in this study.