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Message Passing Graph Kernels

arXiv.org Machine Learning

Graph kernels have recently emerged as a promising approach for tackling the graph similarity and learning tasks at the same time. In this paper, we propose a general framework for designing graph kernels. The proposed framework capitalizes on the well-known message passing scheme on graphs. The kernels derived from the framework consist of two components. The first component is a kernel between vertices, while the second component is a kernel between graphs. The main idea behind the proposed framework is that the representations of the vertices are implicitly updated using an iterative procedure. Then, these representations serve as the building blocks of a kernel that compares pairs of graphs. We derive four instances of the proposed framework, and show through extensive experiments that these instances are competitive with state-of-the-art methods in various tasks.


Wasserstein Weisfeiler-Lehman Graph Kernels

Neural Information Processing Systems

Most graph kernels are an instance of the class of 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.