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

TL;DR

This paper introduces a novel heterogeneous graph convolutional neural network using Hodge-Laplacian operators for analyzing complex brain fMRI data, demonstrating superior performance and interpretability in predicting intelligence.

Contribution

It proposes a new spectral filtering framework on heterogeneous graphs with Hodge-Laplacian operators and a topological pooling method, advancing neural network analysis of brain connectivity data.

Findings

HL-edge network outperforms HL-node network in functional connectivity analysis.

HL-HGCNN surpasses existing GNNs like GAT and BrainNetCNN in accuracy.

Learned features are meaningful for interpreting neural circuits related to intelligence.

Abstract

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