The PWLR graph Representation: A Persistent Weisfeiler-Lehman Scheme with Random Walks for Graph Classification

Sun Woo Park, Yun Young Choi, Dosang Joe, U Jin Choi, Youngho Woo
Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, PMLR 196:287-297, 2022.

Abstract

This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs with discrete and continuous node features. The proposed scheme effectively incorporates normalized Weisfeiler-Lehman procedure, random walks on graphs, and persistent homology. We thereby integrate three distinct properties of graphs, which are local topological features, node degrees, and global topological invariants, while preserving stability from graph perturbations. This generalizes many variants of Weisfeiler-Lehman procedures, which are primarily used to embed graphs with discrete node labels. Empirical results suggest that these representations can be efficiently utilized to produce comparable results to state-of-the-art techniques in classifying graphs with discrete node labels, and enhanced performances in classifying those with continuous node features.

Cite this Paper

BibTeX
@InProceedings{pmlr-v196-park22a, title = {The PWLR graph Representation: A Persistent Weisfeiler-Lehman Scheme with Random Walks for Graph Classification}, author = {Park, Sun Woo and Choi, Yun Young and Joe, Dosang and Choi, U Jin and Woo, Youngho}, booktitle = {Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022}, pages = {287--297}, year = {2022}, editor = {Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Kaul, Manohar and Ktena, Ira and Kvinge, Henry and Miolane, Nina and Rieck, Bastian and Tymochko, Sarah and Wolf, Guy}, volume = {196}, series = {Proceedings of Machine Learning Research}, month = {25 Feb--22 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v196/park22a/park22a.pdf}, url = {https://proceedings.mlr.press/v196/park22a.html}, abstract = {This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs with discrete and continuous node features. The proposed scheme effectively incorporates normalized Weisfeiler-Lehman procedure, random walks on graphs, and persistent homology. We thereby integrate three distinct properties of graphs, which are local topological features, node degrees, and global topological invariants, while preserving stability from graph perturbations. This generalizes many variants of Weisfeiler-Lehman procedures, which are primarily used to embed graphs with discrete node labels. Empirical results suggest that these representations can be efficiently utilized to produce comparable results to state-of-the-art techniques in classifying graphs with discrete node labels, and enhanced performances in classifying those with continuous node features. } }
Endnote
%0 Conference Paper %T The PWLR graph Representation: A Persistent Weisfeiler-Lehman Scheme with Random Walks for Graph Classification %A Sun Woo Park %A Yun Young Choi %A Dosang Joe %A U Jin Choi %A Youngho Woo %B Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022 %C Proceedings of Machine Learning Research %D 2022 %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Manohar Kaul %E Ira Ktena %E Henry Kvinge %E Nina Miolane %E Bastian Rieck %E Sarah Tymochko %E Guy Wolf %F pmlr-v196-park22a %I PMLR %P 287--297 %U https://proceedings.mlr.press/v196/park22a.html %V 196 %X This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs with discrete and continuous node features. The proposed scheme effectively incorporates normalized Weisfeiler-Lehman procedure, random walks on graphs, and persistent homology. We thereby integrate three distinct properties of graphs, which are local topological features, node degrees, and global topological invariants, while preserving stability from graph perturbations. This generalizes many variants of Weisfeiler-Lehman procedures, which are primarily used to embed graphs with discrete node labels. Empirical results suggest that these representations can be efficiently utilized to produce comparable results to state-of-the-art techniques in classifying graphs with discrete node labels, and enhanced performances in classifying those with continuous node features.
APA
Park, S.W., Choi, Y.Y., Joe, D., Choi, U.J. & Woo, Y.. (2022). The PWLR graph Representation: A Persistent Weisfeiler-Lehman Scheme with Random Walks for Graph Classification. Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, in Proceedings of Machine Learning Research 196:287-297 Available from https://proceedings.mlr.press/v196/park22a.html.

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