  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 two
graphs and find their correspondence, according to the learned optimal
transport. The node embeddings associated with the two graphs are learned under
the guidance of the optimal transport, the distance of which not only reflects
the topological structure of each graph but also yields the correspondence
across the graphs. These two learning steps are mutually-beneficial, and are
unified here by minimizing the Gromov-Wasserstein discrepancy with structural
regularizers. This framework leads to an optimization problem that is solved by
a proximal point method. We apply the proposed method to matching problems in
real-world networks, and demonstrate its superior performance compared to
alternative approaches.
