Wasserstein Weisfeiler-Lehman Graph Kernels

TL;DR

This paper introduces a novel graph kernel method that uses Wasserstein distance and Weisfeiler-Lehman embeddings to better capture graph similarities, especially with continuous attributes, improving classification performance.

Contribution

It proposes a new graph kernel combining Wasserstein distance with Weisfeiler-Lehman embeddings for continuous attributed graphs, enhancing existing graph classification methods.

Findings

Improved classification accuracy on multiple graph datasets.

Effective handling of continuous node attributes and weighted edges.

Demonstrated superiority over traditional graph kernels.

Abstract

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of the final set of substructures, usually a sum or average, thereby potentially discarding valuable information about the distribution of individual components. Furthermore, only a limited instance of these approaches can be extended to continuously attributed graphs. We propose a novel method that relies on the Wasserstein distance between the node feature vector distributions of two graphs, which allows to find subtler differences in data sets by considering graphs as high-dimensional objects, rather than simple means. We further propose a Weisfeiler-Lehman inspired embedding scheme for graphs with continuous node attributes and weighted edges, enhance it with the computed Wasserstein distance, and thus improve the state-of-the-art prediction performance on several graph classification tasks.