G$^2$CN: Graph Gaussian Convolution Networks with Concentrated Graph Filters

Mingjie Li, Xiaojun Guo, Yifei Wang, Yisen Wang, Zhouchen Lin
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:12782-12796, 2022.

Abstract

Recently, linear GCNs have shown competitive performance against non-linear ones with less computation cost, and the key lies in their propagation layers. Spectral analysis has been widely adopted in designing and analyzing existing graph propagations. Nevertheless, we notice that existing spectral analysis fails to explain why existing graph propagations with the same global tendency, such as low-pass or high-pass, still yield very different results. Motivated by this situation, we develop a new framework for spectral analysis in this paper called concentration analysis. In particular, we propose three attributes: concentration centre, maximum response, and bandwidth for our analysis. Through a dissection of the limitations of existing graph propagations via the above analysis, we propose a new kind of propagation layer, Graph Gaussian Convolution Networks (G^2CN), in which the three properties are decoupled and the whole structure becomes more flexible and applicable to different kinds of graphs. Extensive experiments show that we can obtain state-of-the-art performance on heterophily and homophily datasets with our proposed G^2CN.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-li22h, title = {{G}$^2${CN}: Graph {G}aussian Convolution Networks with Concentrated Graph Filters}, author = {Li, Mingjie and Guo, Xiaojun and Wang, Yifei and Wang, Yisen and Lin, Zhouchen}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {12782--12796}, 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/li22h/li22h.pdf}, url = {https://proceedings.mlr.press/v162/li22h.html}, abstract = {Recently, linear GCNs have shown competitive performance against non-linear ones with less computation cost, and the key lies in their propagation layers. Spectral analysis has been widely adopted in designing and analyzing existing graph propagations. Nevertheless, we notice that existing spectral analysis fails to explain why existing graph propagations with the same global tendency, such as low-pass or high-pass, still yield very different results. Motivated by this situation, we develop a new framework for spectral analysis in this paper called concentration analysis. In particular, we propose three attributes: concentration centre, maximum response, and bandwidth for our analysis. Through a dissection of the limitations of existing graph propagations via the above analysis, we propose a new kind of propagation layer, Graph Gaussian Convolution Networks (G^2CN), in which the three properties are decoupled and the whole structure becomes more flexible and applicable to different kinds of graphs. Extensive experiments show that we can obtain state-of-the-art performance on heterophily and homophily datasets with our proposed G^2CN.} }
Endnote
%0 Conference Paper %T G$^2$CN: Graph Gaussian Convolution Networks with Concentrated Graph Filters %A Mingjie Li %A Xiaojun Guo %A Yifei Wang %A Yisen Wang %A Zhouchen Lin %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-li22h %I PMLR %P 12782--12796 %U https://proceedings.mlr.press/v162/li22h.html %V 162 %X Recently, linear GCNs have shown competitive performance against non-linear ones with less computation cost, and the key lies in their propagation layers. Spectral analysis has been widely adopted in designing and analyzing existing graph propagations. Nevertheless, we notice that existing spectral analysis fails to explain why existing graph propagations with the same global tendency, such as low-pass or high-pass, still yield very different results. Motivated by this situation, we develop a new framework for spectral analysis in this paper called concentration analysis. In particular, we propose three attributes: concentration centre, maximum response, and bandwidth for our analysis. Through a dissection of the limitations of existing graph propagations via the above analysis, we propose a new kind of propagation layer, Graph Gaussian Convolution Networks (G^2CN), in which the three properties are decoupled and the whole structure becomes more flexible and applicable to different kinds of graphs. Extensive experiments show that we can obtain state-of-the-art performance on heterophily and homophily datasets with our proposed G^2CN.
APA
Li, M., Guo, X., Wang, Y., Wang, Y. & Lin, Z.. (2022). G$^2$CN: Graph Gaussian Convolution Networks with Concentrated Graph Filters. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:12782-12796 Available from https://proceedings.mlr.press/v162/li22h.html.

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