Topological Data Analysis of Human Brain Networks Through Order Statistics

Abstract

Understanding the topological characteristics of the 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 features 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 conclude a statistically significant topological difference between the male and female brain networks. Author summaryWe fit a random graph model to the brain network and compute the expected persistent barcodes using order statistics. This novel approach significantly simplifies the computation of expected persistent barcodes, which otherwise requires complex theoretical constructs. Subsequently, the proposed statistical framework is used to discriminate if two groups of brain networks are topologically different. The method is applied in determining the sexual dimorphism in the shape of resting-state functional magnetic resonance images.