Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clustering
This work addresses the challenge of multi-view learning when views have different underlying geometries, offering a geometrically meaningful approach for embedding and clustering.
Gromov-Wasserstein methods are proposed for multi-view relational embedding and clustering, operating directly on distance matrices to learn consensus embeddings that preserve shared structure across views with nonlinear distortions.
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.