A Generalized Weisfeiler-Lehman Graph Kernel
This addresses the problem of defining suitable similarity measures for complex graphs beyond molecular ones, offering an incremental improvement over existing graph kernels.
The authors tackled the rigidity of Weisfeiler-Lehman graph kernels by generalizing them to compare tree similarity instead of equality, using a fitted tree edit distance, and empirically showed significant outperformance over state-of-the-art methods on structurally complex graph datasets.
The Weisfeiler-Lehman graph kernels are among the most prevalent graph kernels due to their remarkable time complexity and predictive performance. Their key concept is based on an implicit comparison of neighborhood representing trees with respect to equality (i.e., isomorphism). This binary valued comparison is, however, arguably too rigid for defining suitable similarity measures over graphs. To overcome this limitation, we propose a generalization of Weisfeiler-Lehman graph kernels which takes into account the similarity between trees rather than equality. We achieve this using a specifically fitted variation of the well-known tree edit distance which can efficiently be calculated. We empirically show that our approach significantly outperforms state-of-the-art methods in terms of predictive performance on datasets containing structurally more complex graphs beyond the typically considered molecular graphs.