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A novel Gromov-Wasserstein learning framework is proposed to jointly match(align) graphs and learn embedding vectors for the associated graph nodes.Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between twographs and find their correspondence, according to the learned optimaltransport. The node embeddings associated with the two graphs are learned underthe guidance of the optimal transport, the distance of which not only reflectsthe topological structure of each graph but also yields the correspondenceacross the graphs. These two learning steps are mutually-beneficial, and areunified here by minimizing the Gromov-Wasserstein discrepancy with structuralregularizers. This framework leads to an optimization problem that is solved bya proximal point method. We apply the proposed method to matching problems inreal-world networks, and demonstrate its superior performance compared toalternative approaches.

Gromov-Wasserstein Learning for Graph Matching and Node Embedding