Global Weisfeiler-Lehman Graph Kernels
This addresses the scalability and accuracy trade-off in graph classification for machine learning applications, though it is incremental by building on existing Weisfeiler-Lehman methods.
The paper tackles the problem of graph kernels being either too local or too global, proposing a stochastic version of the k-dimensional Weisfeiler-Lehman kernel that balances both aspects and achieves state-of-the-art classification accuracies on benchmarks.
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.