Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching

We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on graphs. Given two graphs, the optimal transport associated with their Gromov-Wasserstein discrepancy provides the correspondence between their nodes and achieves graph matching. When one of the graphs is a predefined graph with isolated but self-connected nodes ( i.e., disconnected graph), the optimal transport indicates the clustering structure of the other graph and achieves graph partitioning. Further, we extend our method to multi-graph partitioning and matching by learning a Gromov-Wasserstein barycenter graph for multiple observed graphs.