Nils Kriege
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Random walk kernels have been introduced in seminal work on graph learning and were later largely superseded by kernels based on the Weisfeiler-Leman test for graph isomorphism.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 uni ed view on both classes of graph kernels. We study walk-based node re nement methods and formally relate them to several widely-used techniques, including Morgan's algorithm for molecule canonization and the Weisfeiler-Leman test. We de ne corresponding walk-based kernels on nodes that allow ne-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 modi cations regarding de nition and computation are as expressive as the widelyused 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 classi cation tasks.
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