Towards Better Graph Representation Learning with Parameterized Decomposition & Filtering

Mingqi Yang, Wenjie Feng, Yanming Shen, Bryan Hooi
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:39234-39251, 2023.

Abstract

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-yang23c, title = {Towards Better Graph Representation Learning with Parameterized Decomposition & Filtering}, author = {Yang, Mingqi and Feng, Wenjie and Shen, Yanming and Hooi, Bryan}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {39234--39251}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/yang23c/yang23c.pdf}, url = {https://proceedings.mlr.press/v202/yang23c.html}, abstract = {Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.} }
Endnote
%0 Conference Paper %T Towards Better Graph Representation Learning with Parameterized Decomposition & Filtering %A Mingqi Yang %A Wenjie Feng %A Yanming Shen %A Bryan Hooi %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-yang23c %I PMLR %P 39234--39251 %U https://proceedings.mlr.press/v202/yang23c.html %V 202 %X Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.
APA
Yang, M., Feng, W., Shen, Y. & Hooi, B.. (2023). Towards Better Graph Representation Learning with Parameterized Decomposition & Filtering. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:39234-39251 Available from https://proceedings.mlr.press/v202/yang23c.html.

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