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Glocalized Weisfeiler-Lehman Graph Kernels: Global-Local Feature Maps of Graphs

Christopher Morris; Kristian Kersting; Petra Mutzel
In: Vijay Raghavan; Srinivas Aluru; George Karypis; Lucio Miele; Xindong Wu (Hrsg.). 2017 IEEE International Conference on Data Mining. IEEE International Conference on Data Mining (ICDM-2017), November 18-21, New Orleans, LA, USA, Pages 327-336, IEEE Computer Society, 2017.


Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take global graph properties into account may not scale well to large graph databases. Here we propose to start exploring the space between local and global graph kernels, so called glocalized graph kernels, striking the balance between both worlds. Specifically, we introduce a novel graph kernel based on the k-dimensional Weisfeiler-Lehman algorithm. Unfortunately, the k-dimensional Weisfeiler-Lehman algorithm scales exponentially in k. Consequently, we devise a stochastic version of the kernel with provable approximation guarantees using conditional Rademacher averages. On bounded-degree graphs, it can even be computed in constant time. We support our theoretical results with experiments on several graph classification benchmarks, showing that our kernels often outperform the state-of-the-art in terms of classification accuracies.

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