Heterogeneous Graph Convolutional Neural Network via Hodge-Laplacian for Brain Functional Data

This study proposes a novel heterogeneous graph convolutional neural network (HGCNN) to handle complex brain fMRI data at regional and across-region levels. We introduce generic formulation of spectral filters on graphs by introducing the $$k-th$$ Hodge-Laplacian (HL) operator. In particular, we propose Laguerre polynomial approximations HL prove that their spatial localization is related order. Furthermore, based bijection property boundary operators simplex graphs, topological pooling (TGPool) method can be used any dimensional simplices. designs HL-node, HL-edge, HL-HGCNN networks learn signal representation node, edge levels, both, respectively. Our experiments employ from Adolescent Brain Cognitive Development (ABCD; n = 7693) predict general intelligence. results demonstrate advantage HL-edge over HL-node when functional connectivity considered as features. The outperforms state-of-the-art (GNNs) approaches, such GAT, BrainGNN, dGCN, BrainNetCNN, Hypergraph NN. features learned are meaningful in interpreting circuits