Topological inference on brain networks across subtypes of post-stroke aphasia

TL;DR

This paper introduces a spectral transposition test for comparing brain network topologies using persistent homology, enabling effective group comparisons and subtyping in post-stroke aphasia based on topological features.

Contribution

It advances a permutation testing method utilizing heat-diffusion estimates of persistence diagrams for robust group comparisons and subtyping in brain network analysis.

Findings

Effective in capturing group similarities and differences.

Enables subtyping of post-stroke aphasia based on topological features.

Demonstrates robustness against topological noise.

Abstract

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.