Weisfeiler and Leman Go Walking: Random Walk Kernels Revisited

TL;DR

This paper unifies and compares random walk kernels and Weisfeiler-Leman kernels, showing that walk-based kernels can match or surpass Weisfeiler-Leman in expressiveness and accuracy for graph classification.

Contribution

It provides a unified framework for walk-based and Weisfeiler-Leman kernels, demonstrating that classical random walk kernels can be as expressive and effective as Weisfeiler-Leman kernels.

Findings

Walk-based kernels are as expressive as Weisfeiler-Leman kernels.

Modified random walk kernels can outperform Weisfeiler-Leman kernels in classification.

Walk-based kernels support non-strict neighborhood comparison.

Abstract

Random walk kernels have been introduced in seminal work on graph learning and were later largely superseded by kernels based on the Weisfeiler-Leman test for graph isomorphism. We give a unified view on both classes of graph kernels. We study walk-based node refinement methods and formally relate them to several widely-used techniques, including Morgan's algorithm for molecule canonization and the Weisfeiler-Leman test. We define corresponding walk-based kernels on nodes that allow fine-grained parameterized neighborhood comparison, reach Weisfeiler-Leman expressiveness, and are computed using the kernel trick. From this we show that classical random walk kernels with only minor modifications regarding definition and computation are as expressive as the widely-used Weisfeiler-Leman subtree kernel but support non-strict neighborhood comparison. We verify experimentally that walk-based kernels reach or even surpass the accuracy of Weisfeiler-Leman kernels in real-world classification tasks.