Fast subtree kernels on graphs

Part of Advances in Neural Information Processing Systems 22 (NIPS 2009)

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Nino Shervashidze, Karsten Borgwardt


In this article, we propose fast subtree kernels on graphs. On graphs with n nodes and m edges and maximum degree d, these kernels comparing subtrees of height h can be computed in O(mh), whereas the classic subtree kernel by Ramon & G¨artner scales as O(n24dh). Key to this efficiency is the observation that the Weisfeiler-Lehman test of isomorphism from graph theory elegantly computes a subtree kernel as a byproduct. Our fast subtree kernels can deal with labeled graphs, scale up easily to large graphs and outperform state-of-the-art graph ker- nels on several classification benchmark datasets in terms of accuracy and runtime.