Topological Data Analysis of Human Brain Networks Through Order Statistics

TL;DR

This paper introduces a robust statistical framework using persistent homology and order statistics to analyze human brain networks, revealing significant topological differences between genders.

Contribution

It develops a novel, computationally efficient method for group-level topological inference in brain graphs using order statistics and persistent homology.

Findings

Identified significant topological differences between male and female brain networks

Validated the method with simulation studies and real fMRI data

Provided a new approach for analyzing complex brain network data

Abstract

Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the topological properties of the brain network. The development of group-level statistical inference procedures in brain graphs while accounting for the heterogeneity and randomness still remains a difficult task. In this study, we develop a robust statistical framework based on persistent homology using the order statistics for analyzing brain networks. The use of order statistics greatly simplifies the computation of the persistent barcodes. We validate the proposed methods using comprehensive simulation studies and subsequently apply to the resting-state functional magnetic resonance images. We found a statistically significant topological difference between the male and female brain networks.