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.

该论文提出一种基于Gromov-Wasserstein方法的图对齐及嵌入学习框架，通过学习最优传输距离完成图的对齐，以及标记距离来引导嵌入向量的学习，并通过结构正则化减小Gromov-Wasserstein距离，使用近端点法求解这个优化问题。该方法在现实网络中的匹配问题上具有卓越的性能表现。

图匹配与节点嵌入的Gromov-Wasserstein学习