Topological inference on brain networks with application to lesion symptom mapping

2026-03-17

AI Summary

This study addresses the challenge of leveraging persistent homology features of brain networks for group comparisons, which is hindered by individual heterogeneity and a lack of sensitivity to topological differences in lesion–symptom mapping. To overcome this, the authors propose a novel framework that transforms persistence diagrams into vectorized representations via heat diffusion, expressed as Fourier coefficients in the Laplace–Beltrami eigenfunction basis. They further introduce a transposed permutation test to enable statistically rigorous inference on higher-order topological structures across multiple groups. This approach uniquely integrates heat-diffusion-based persistence diagram representations with transposed permutation testing, and demonstrates robust performance in identifying topological cycles significantly associated with language impairment severity in post-stroke aphasia patients, even in the presence of topological noise and variability in cycle locations.

Technology Category

• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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 diagrams (PDs) through heat diffusion reparameterizes them using a finite number of Fourier coefficients with respect to the Laplace--Beltrami (LB) eigenfunction expansion of the domain, providing a powerful vectorized algebraic representation for group comparisons. In this study, we develop a transposition-based permutation test for comparing multiple groups of PDs using heat-diffusion estimates. We evaluate the empirical performance of the spectral transposition test in capturing within- and between-group similarity and dissimilarity under varying levels of topological noise and cycle location variability. In application, we propose a topological lesion symptom mapping (TLSM) method based on the proposed framework. The method is applied to resting-state functional brain networks of individuals with post-stroke aphasia to identify characteristic cycles associated with varying levels of speech-language impairment.

Problem

• topological inference
• brain networks
• lesion symptom mapping
• persistent homology
• group comparison

Innovation

• persistent homology
• heat diffusion
• Laplace–Beltrami eigenfunction
• permutation test
• lesion symptom mapping