Finding Global Homophily in Graph Neural Networks When Meeting Heterophily
This addresses the problem of handling heterophily in graph neural networks for researchers and practitioners, though it appears incremental as it builds on existing methods by extending aggregation to global nodes.
The authors tackled the challenge of setting personalized neighborhood sizes for nodes in graph neural networks on heterophilic graphs, proposing GloGNN and GloGNN++ models that aggregate information from global nodes with linear time complexity, achieving superior performance over 11 competitors on 15 benchmark datasets.
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.