Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest

TL;DR

This paper presents a novel topological data analysis method using Wasserstein distance to identify and analyze dynamic brain network states at rest, outperforming traditional clustering techniques and exploring genetic influences.

Contribution

Introduces a topological data analysis approach for brain network state estimation that effectively captures temporal dynamics without explicit models.

Findings

Topological features of brain networks are heritable.

The method outperforms k-means clustering in identifying brain states.

Dynamic topological changes may encode genetic information.

Abstract

We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure topological differences, enabling the clustering of brain networks into distinct topological states. This technique outperforms the commonly used k-means clustering in identifying brain network state spaces by effectively incorporating the temporal dynamics of the data without the need for explicit model specification. We further investigate the genetic underpinnings of these topological features using a twin study design, examining the heritability of such state changes. Our findings suggest that the topology of brain networks, particularly in their dynamic state changes, may hold significant hidden genetic information. MATLAB code for the method is available at https://github.com/laplcebeltrami/PH-STAT.