Semi-relaxed Gromov-Wasserstein divergence with applications on graphs
This work addresses graph comparison tasks for machine learning applications, offering an incremental improvement over existing Gromov-Wasserstein methods.
The paper tackles the problem of comparing graphs by proposing a semi-relaxed Gromov-Wasserstein divergence, which relaxes the mass conservation property of Optimal Transport to improve tasks like graph dictionary learning, partitioning, clustering, and completion, showing computational benefits and empirical relevance.
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.