TOPOLOGICAL INFERENCE ON BRAIN NETWORKS WITH APPLICATION TO LESION SYMPTOM MAPPING

• 成果类型: Article
• 署名作者: Wang, Yuan; Yin, Jian; Riccardi, Nicholas; Den Ouden, Dirk-bart; Fridriksson, Julius; Desai, Rutvik H.
• 署名单位: University of South Carolina System; University of South Carolina Columbia; City University of Hong Kong; University of South Carolina System; University of South Carolina Columbia; University of South Carolina System; University of South Carolina Columbia
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157; 1941-7330
• DOI: 10.1214/26-AOAS2169
• 发表日期: 2026-06
• 页码: 1516-1540
• 关键词: Topological data analysis; Persistent Homology; Permutation Test; brain network; lesion symptom mapping; persistence

摘要

Persistent homology (PH) characterizes the shape of brain networks through 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 a finite number of Fourier coefficients with respect to the Laplace-Beltrami (LB) eigenfunction expansion of the domain, thus providing 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 using their 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 under statistical variation in topological noise and cycle location. In application, we introduce a topological lesion symptom mapping (TLSM) method based on the proposed topological inference framework. The method is applied to resting-state functional brain networks from individuals with post-stroke aphasia to identify characteristic cycles associated with varying degrees of speech-language impairment, as measured by behavioral test scores.