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
