Wasserstein Weisfeiler-Lehman Graph Kernels
This addresses the issue of limited expressiveness in graph kernels for researchers in machine learning, offering an incremental improvement over existing methods.
The paper tackles the problem of graph kernels discarding distributional information by proposing a method using Wasserstein distance between node feature vector distributions, which improves state-of-the-art prediction performance on several graph classification tasks.
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.