Entropic Hyper-Connectomes Computation and Analysis

TL;DR

This paper introduces the hyper-connectome, a hypergraph model based on joint information entropy and total correlation, demonstrating its superior predictive power for schizophrenia from fMRI data compared to traditional connectomes.

Contribution

It defines a novel hypergraph model for brain connectivity, provides computation methods, and proves its theoretical and practical advantages in prediction tasks.

Findings

Hyper-connectome outperforms connectome in schizophrenia prediction accuracy.

The hyper-connectome achieves up to 56% better accuracy and 0.52 higher F1 score.

Statistical significance confirmed with p-value = 0.00074.

Abstract

Brain function and connectivity is a pressing mystery in medicine related to many diseases. Neural connectomes have been studied as graphs with graph theory methods including topological methods. Work has started on hypergraph models and methods where the geometry and topology is significantly different. We define a hypergraph called the hyper-connectome with joint information entropy and total correlation. We give the pseudocode for computation from finite samples. We give the theoretic importance of this generalization's topology and geometry with respect to random variables and then prove the hypergraph can be necessary for prediction and classification. We confirm with a simulation study and computation. We prove the approximation for continuous random variables with finite samples. We compare connectome versus hyper-connectome for predicting schizophrenia in subjects based on a fMRI dataset using a linear support vector machine. The hyper-connectome achieves better performance in accuracy (up to 56\%) and F1 score (up to 0.52) than the connectome. We reject null hypothesis at 95\% with p-value = 0.00074.