Title: Topological data analysis of brain networks through order statistics
Author: Das, S., Anand, D.V., Chung, M.K.
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.
The codes perform the validation study published in https://arxiv.org/pdf/2204.02527.pdf. Run VALIDATION_....m for generating each corresponding validation table. EXAMPLE_Figure_5.m generates Figure 5 in the paper.
(C) 2022 The codes are written by Das, S. of University of Wisconsin-Madison.