Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching

TL;DR

This paper introduces a scalable Gromov-Wasserstein learning method that unifies graph partitioning and matching for large-scale graph analysis, providing theoretical support and improved efficiency over existing methods.

Contribution

It presents the first scalable approach to apply Gromov-Wasserstein discrepancy to large graphs, unifying graph partitioning and matching in a single framework with a novel algorithm.

Findings

Outperforms state-of-the-art methods in accuracy and efficiency

Achieves a time complexity of O(K(E+V)log_K V) for large graphs

Successfully extends to multi-graph partitioning and matching

Abstract

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 has isolated but self-connected nodes ($i.e.$, a disconnected graph), the optimal transport indicates the clustering structure of the other graph and achieves graph partitioning. Using this concept, we extend our method to multi-graph partitioning and matching by learning a Gromov-Wasserstein barycenter graph for multiple observed graphs; the barycenter graph plays the role of the disconnected graph, and since it is learned, so is the clustering. Our method combines a recursive $K$-partition mechanism with a regularized proximal gradient algorithm, whose time complexity is $\mathcal{O}(K(E+V)\log_K V)$ for graphs with $V$ nodes and $E$ edges. To our knowledge, our method is the first attempt to make Gromov-Wasserstein discrepancy applicable to large-scale graph analysis and unify graph partitioning and matching into the same framework. It outperforms state-of-the-art graph partitioning and matching methods, achieving a trade-off between accuracy and efficiency.