Global Weisfeiler-Lehman Graph Kernels

TL;DR

This paper introduces a new graph kernel based on the Weisfeiler-Lehman algorithm that balances local and global graph properties, with scalable stochastic approximations and strong empirical performance.

Contribution

It proposes a novel $k$-dimensional Weisfeiler-Lehman graph kernel and a stochastic approximation method with theoretical guarantees, improving scalability and accuracy.

Findings

Outperforms state-of-the-art kernels on classification benchmarks.

Provides a scalable stochastic kernel with approximation guarantees.

Achieves constant-time computation on bounded-degree graphs.

Abstract

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 propertiesinto account may not scale well to large graph databases. Here we propose to start exploring the space between local and global 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.