Semi-relaxed Gromov-Wasserstein divergence with applications on graphs

TL;DR

This paper introduces a semi-relaxed Gromov-Wasserstein divergence that relaxes the mass conservation constraint in optimal transport, enabling more efficient graph comparison and learning for tasks like partitioning, clustering, and completion.

Contribution

It proposes a novel semi-relaxed GW divergence that improves computational efficiency and applicability in graph learning tasks, addressing limitations of the original GW distance.

Findings

Enhanced graph partitioning and clustering performance

Efficient graph dictionary learning algorithm

Effective graph completion results

Abstract

Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has proven to be successful in handling the specific nature of the associated objects. More specifically, through the nodes connectivity relations, GW operates on graphs, seen as probability measures over specific spaces. At the core of OT is the idea of conservation of mass, which imposes a coupling between all the nodes from the two considered graphs. We argue in this paper that this property can be detrimental for tasks such as graph dictionary or partition learning, and we relax it by proposing a new semi-relaxed Gromov-Wasserstein divergence. Aside from immediate computational benefits, we discuss its properties, and show that it can lead to an efficient graph dictionary learning algorithm. We empirically demonstrate its relevance for complex tasks on graphs such as partitioning, clustering and completion.