A generalized Weisfeiler-Lehman graph kernel

After more than one decade, Weisfeiler-Lehman graph kernels are still among the most prevalent graph kernels due to their remarkable predictive performance and time complexity. They are based on a fast iterative partitioning of vertices, originally designed for deciding graph isomorphism with one-sided error. The Weisfeiler-Lehman graph kernels retain this idea and compare such labels with respect to equality. This binary valued comparison is, however, arguably too rigid for defining suitable graph kernels for certain graph classes. To overcome this limitation, we propose a generalization of Weisfeiler-Lehman graph kernels which takes into account a more natural and finer grade of similarity between Weisfeiler-Lehman labels than equality. We show that the proposed similarity can be calculated efficiently by means of the Wasserstein distance between certain vectors representing Weisfeiler-Lehman labels. This and other facts give rise to the natural choice of partitioning the vertices with the Wasserstein k-means algorithm. We empirically demonstrate on the Weisfeiler-Lehman subtree kernel, which is one of the most prominent Weisfeiler-Lehman graph kernels, that our generalization significantly outperforms this and other state-of-the-art graph kernels in terms of predictive performance on datasets which contain structurally more complex graphs beyond the typically considered molecular graphs.

Automated summary

Weisfeiler-Lehman graph kernels are still one of the most prevalent graph kernels after more than a decade, thanks to their impressive predictive performance and time complexity. However, their binary comparison based on label equality may be too rigid for certain graph classes. To address this limitation, we propose a generalization of the Weisfeiler-Lehman graph kernels that considers a more natural and fine-grained similarity between labels. We demonstrate that this similarity can be efficiently calculated using the Wasserstein distance between vectors representing the labels. Our generalization outperforms other state-of-the-art graph kernels in terms of predictive performance on datasets with structurally complex graphs.