Multi-Hypergraph Learning-Based Brain Functional Connectivity Analysis in fMRI Data.

Recently, a hypergraph constructed from functional magnetic resonance imaging (fMRI) was utilized to explore brain functional connectivity networks (FCNs) for the classification of neurodegenerative diseases. Each edge of a hypergraph (called hyperedge) can connect any number of brain regions-of-interest (ROIs) instead of only two ROIs, and thus characterizes high-order relations among multiple ROIs that cannot be uncovered by a simple graph in the traditional graph based FCN construction methods. Unlike the existing hypergraph based methods where all hyperedges are assumed to have equal weights and only certain topological features are extracted from the hypergraphs, we propose a hypergraph learning based method for FCN construction in this paper. Specifically, we first generate hyperedges from fMRI time series based on sparse representation, then employ hypergraph learning to adaptively learn hyperedge weights, and finally define a hypergraph similarity matrix to represent the FCN. In our proposed method, weighting hyperedges results in better discriminative FCNs across subjects, and the defined hypergraph similarity matrix can better reveal the overall structure of brain network than using those hypergraph topological features. Moreover, we propose a multi-hypergraph learning based method by integrating multi-paradigm fMRI data, where the hyperedge weights associated with each fMRI paradigm are jointly learned and then a unified hypergraph similarity matrix is computed to represent the FCN. We validate the effectiveness of the proposed method on the Philadelphia Neurodevelopmental Cohort dataset for the classification of individuals' learning ability from three paradigms of fMRI data. Experimental results demonstrate that our proposed approach outperforms the traditional graph based methods (i.e., Pearson's correlation and partial correlation with the graphical Lasso) and the existing unweighted hypergraph based methods, which sheds light on how to optimize estimation of FCNs for cognitive and behavioral study.