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.

提出了GloGNN和GloGNN两种模型应用于具有异质性的图上，能够从全局节点中聚合信息生成节点嵌入，理论证明了这种方法的有效性并在15个基准数据集中进行实验证明其性能优异。

当遇到异质性时，在图神经网络中发现全局同质性