Persistent homology (PH) characterizes the shape of brain networks through the persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space representation of persistence diagram (PD) through heat diffusion reparameterizes using the finite number of Fourier coefficients with respect to the Laplace-Beltrami (LB) eigenfunction expansion of the domain, which provides a powerful vectorized algebraic representation for group comparisons of PDs. In this study, we advance a transposition-based permutation test for comparing multiple groups of PDs through the heat-diffusion estimates of the PDs. We evaluate the empirical performance of the spectral transposition test in capturing within- and between-group similarity and dissimilarity with respect to statistical variation of topological noise and hole location. We also illustrate how the method extends naturally into a clustering scheme by subtyping individuals with post-stroke aphasia through the PDs of their resting-state functional brain networks.

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