Hyper-network curvature: A new representation method for high-order brain network analysis

Abstract

Human brain is a complex system and contains abundant high-order interactions among multiple brain regions, which can be described by brain hyper-network. In brain hyper-networks, nodes represent brain regions of interest (ROIs), while edges describe the interactions of multiple ROIs, providing important high-order information for brain disease analysis and diagnosis. However, most of the existing hyper-network studies focused on the hyper-connection (i.e. hyper-edge) analysis and ignored the local topological information on nodes. To address this problem, we propose a new representation method (i.e., hyper-network curvature) for brain hyper-network analysis. Compared with the existing hyper-network representation methods, the proposed hyper-network curvature can be used to analyze the local topologies of nodes in brain hyper-networks. Based on hyper-network curvature, we further propose a novel graph kernel called brain hyper-network curvature kernel to measure the similarity of a pair of brain hyper-networks. We have proved that the proposed hyper-network curvature is bounded and brain hyper-network curvature kernel is positive definite. To evaluate the effectiveness of our proposed method, we perform the classification experiments on functional magnetic resonance imaging data of brain diseases. The experimental results demonstrate that our proposed method can significantly improve classification accuracy compared to the state-of-the-art graph kernels and graph neural networks for classifying brain diseases.