Gromov-Wasserstein Learning for Graph Matching and Node Embedding

TL;DR

This paper introduces a Gromov-Wasserstein learning framework that simultaneously aligns graphs and learns node embeddings, improving graph matching accuracy by leveraging optimal transport and structural regularization.

Contribution

The novel framework unifies graph matching and node embedding learning using Gromov-Wasserstein discrepancy, with an efficient optimization approach and demonstrated superior performance.

Findings

Outperforms alternative methods in real-world network matching tasks.

Effectively captures topological structures and cross-graph correspondences.

Provides a unified approach for graph alignment and node embedding learning.

Abstract

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.