A Persistent Weisfeiler–Lehman Procedure for Graph Classification

The Weisfeiler–Lehman graph kernel exhibits competitive performance in many graph classification tasks. However, its subtree features are not able to capture connected components and cycles, topological features known for characterising graphs. To extract such features, we leverage propagated node label information and transform unweighted graphs into metric ones. This permits us to augment the subtree features with topological information obtained using persistent homology, a concept from topological data analysis. Our method, which we formalise as a generalisation of Weisfeiler–Lehman subtree features, exhibits favourable classification accuracy and its improvements in predictive performance are mainly driven by including cycle information.

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Results from the Paper

 Ranked #1 on Graph Classification on MUTAG (Mean Accuracy metric)

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Task Dataset Model Metric Name Metric Value Global Rank Benchmark
Graph Classification MUTAG P-WL-C Mean Accuracy 90.51 # 1
Graph Property Prediction ogbg-molhiv P-WL Test ROC-AUC 0.8039 ± 0.0040 # 15
Validation ROC-AUC 0.8279 ± 0.0059 # 21
Number of params 4600000 # 5
Ext. data No # 1
Graph Classification PROTEINS P-WL-UC Accuracy 75.36% # 44


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