Multi-Dimensional Fused Gromov Wasserstein Discrepancy for Edge-Attributed Graphs

Graph dissimilarities provide a powerful and ubiquitous approach for applying machine learning algorithms to edge-attributed graphs. However, conventional optimal transport-based dissimilarities cannot handle edge-attributes. In this paper, we propose an optimal transport-based dissimilarity between graphs with edge-attributes. The proposed method, multi-dimensional fused Gromov-Wasserstein discrepancy (MFGW), naturally incorporates the mismatch of edge-attributes into the optimal transport theory. Unlike conventional optimal transport-based dissimilarities, MFGW can directly handle edge-attributes in addition to structural information of graphs. Furthermore, we propose an iterative algorithm, which can be computed on GPUs, to solve non-convex quadratic programming problems involved in MFGW. Experimentally, we demonstrate that MFGW outperforms the conventional optimal transport-based dissimilarity in several machine learning applications including supervised classification, subgraph matching, and graph barycenter calculation.