Finding Global Homophily in Graph Neural Networks When Meeting Heterophily

Xiang Li, Renyu Zhu, Yao Cheng, Caihua Shan, Siqiang Luo, Dongsheng Li, Weining Qian
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:13242-13256, 2022.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-li22ad, title = {Finding Global Homophily in Graph Neural Networks When Meeting Heterophily}, author = {Li, Xiang and Zhu, Renyu and Cheng, Yao and Shan, Caihua and Luo, Siqiang and Li, Dongsheng and Qian, Weining}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {13242--13256}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/li22ad/li22ad.pdf}, url = {https://proceedings.mlr.press/v162/li22ad.html}, 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.} }
Endnote
%0 Conference Paper %T Finding Global Homophily in Graph Neural Networks When Meeting Heterophily %A Xiang Li %A Renyu Zhu %A Yao Cheng %A Caihua Shan %A Siqiang Luo %A Dongsheng Li %A Weining Qian %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-li22ad %I PMLR %P 13242--13256 %U https://proceedings.mlr.press/v162/li22ad.html %V 162 %X 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.
APA
Li, X., Zhu, R., Cheng, Y., Shan, C., Luo, S., Li, D. & Qian, W.. (2022). Finding Global Homophily in Graph Neural Networks When Meeting Heterophily. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:13242-13256 Available from https://proceedings.mlr.press/v162/li22ad.html.

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