Topological Learning for Brain Networks

TL;DR

This paper introduces a topological learning framework using persistent homology to compare and analyze brain networks of varying sizes and topologies, overcoming computational challenges in network matching.

Contribution

It presents a new topological loss function that efficiently integrates networks of different sizes and topologies, enabling advanced analysis of brain networks.

Findings

Effective discrimination of networks with different topologies in simulations

Successful application to twin brain imaging data

Determined genetic heritability of brain networks

Abstract

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient topological loss. The use of the proposed loss bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations to assess its effectiveness when discriminating networks with different topology. The method is further demonstrated in a twin brain imaging study where we determine if brain networks are genetically heritable. The challenge here is due to the difficulty of overlaying the topologically different functional brain networks obtained from resting-state functional MRI onto the template structural brain network obtained through diffusion MRI.