Weisfeiler and Leman Go Walking: Random Walk Kernels Revisited
This work provides a theoretical and practical unification of graph kernels, potentially benefiting researchers in graph machine learning, though it is incremental in nature.
The paper tackles the problem of graph learning by unifying random walk kernels and Weisfeiler-Leman kernels, showing that modified random walk kernels achieve comparable expressiveness and accuracy, with experimental verification on real-world classification tasks.
Random walk kernels have been introduced in seminal work on graph learning and were later largely superseded by kernels based on the Weisfeiler-Leman test for graph isomorphism.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.