Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clustering

TL;DR

This paper introduces Bary-GWMDS, a Gromov-Wasserstein-based method for multi-view relational data embedding that preserves shared structure despite nonlinear distortions, and a clustering extension called Mean-GWMDS-C.

Contribution

It presents a novel Gromov-Wasserstein approach operating on distance matrices for multi-view embedding and clustering, handling nonlinear geometric differences across views.

Findings

The method produces stable, meaningful embeddings on synthetic and real data.

It effectively handles nonlinear distortions across different views.

The clustering formulation improves grouping quality in multi-view data.

Abstract

Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to learn a consensus embedding preserving shared relational structure. By leveraging intrinsic distances, the approach naturally handles nonlinear distortions across views. We also introduce Mean-GWMDS-C, a clustering-oriented formulation that averages distance matrices and learns reduced-support representations via a consensus Gromov-Wasserstein transport. Experiments on synthetic and real-world datasets show that the proposed framework yields stable and geometrically meaningful embeddings.