Finding Global Homophily in Graph Neural Networks When Meeting Heterophily

TL;DR

This paper introduces GloGNN and GloGNN++, innovative graph neural network models that leverage global node information and learn correlation matrices to effectively handle heterophily, outperforming existing methods.

Contribution

The paper proposes two novel models, GloGNN and GloGNN++, that utilize global node aggregation and learn correlation matrices for improved heterophily handling in GNNs, with theoretical and empirical validation.

Findings

Outperform 11 competitors on 15 datasets

Achieve superior accuracy and efficiency

Theoretically proven grouping effect of the models

Abstract

We investigate graph neural networks on graphs with heterophily. Some existing methods amplify a node's neighborhood with multi-hop neighbors to include more nodes with homophily. However, it is a significant challenge to set personalized neighborhood sizes for different nodes. Further, for other homophilous nodes excluded in the neighborhood, they are ignored for information aggregation. To address these problems, we propose two models GloGNN and GloGNN++, which generate a node's embedding by aggregating information from global nodes in the graph. In each layer, both models learn a coefficient matrix to capture the correlations between nodes, based on which neighborhood aggregation is performed. The coefficient matrix allows signed values and is derived from an optimization problem that has a closed-form solution. We further accelerate neighborhood aggregation and derive a linear time complexity. We theoretically explain the models' effectiveness by proving that both the coefficient matrix and the generated node embedding matrix have the desired grouping effect. We conduct extensive experiments to compare our models against 11 other competitors on 15 benchmark datasets in a wide range of domains, scales and graph heterophilies. Experimental results show that our methods achieve superior performance and are also very efficient.