Higher-order Organization in the Human Brain from Matrix-Based R\'enyi's Entropy

TL;DR

This study introduces a matrix-based Rényi's entropy approach to quantify higher-order interactions in the human brain using multivariate mutual information metrics, revealing increased synergy during resting state.

Contribution

The paper applies matrix-based Rényi's entropy to estimate higher-order brain interactions, providing a direct, assumption-free method to analyze multivariate dependencies in fMRI data.

Findings

Higher-order interactions increase with interaction order.

Correlation between Total and Dual Total Correlation grows with order.

Brain exhibits synergy dominance during resting state.

Abstract

Pairwise metrics are often employed to estimate statistical dependencies between brain regions, however they do not capture higher-order information interactions. It is critical to explore higher-order interactions that go beyond paired brain areas in order to better understand information processing in the human brain. To address this problem, we applied multivariate mutual information, specifically, Total Correlation and Dual Total Correlation to reveal higher-order information in the brain. In this paper, we estimate these metrics using matrix-based R\'enyi's entropy, which offers a direct and easily interpretable approach that is not limited by direct assumptions about probability distribution functions of multivariate time series. We applied these metrics to resting-state fMRI data in order to examine higher-order interactions in the brain. Our results showed that the higher-order information interactions captured increase gradually as the interaction order increases. Furthermore, we observed a gradual increase in the correlation between the Total Correlation and Dual Total Correlation as the interaction order increased. In addition, the significance of Dual Total Correlation values compared to Total Correlation values also indicate that the human brain exhibits synergy dominance during the resting state.