On a linear fused Gromov-Wasserstein distance for graph structured data

Abstract

We present a framework for embedding graph structured data into a vector space, taking into account node features and structures of graphs into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named LinearFGW, defined as the Euclidean distance between their embeddings. The advantages of the proposed distance are twofold: 1) it takes into account node features and structures of graphs for measuring the dissimilarity between graphs in a kernel-based framework, 2) it is more efficient for computing a kernel matrix than pairwise OT-based distances, particularly fused Gromov-Wasserstein [1], making it possible to deal with large-scale data sets. Our theoretical analysis and experimental results demonstrate that our proposed distance leads to an increase in performance compared to the existing state-of-the-art graph distances when evaluated on graph classification and clustering tasks.