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

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