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

arXiv cs.LG / 4/28/2026

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Key Points

The paper addresses the challenge of learning shared low-dimensional representations from multi-view relational data when each view has different underlying geometry.
It introduces Bary-GWMDS, a Gromov-Wasserstein-distance-matrix method that learns a consensus embedding by preserving relational structure common across views.
The approach uses intrinsic distances to better tolerate nonlinear distortions between views, improving the geometric faithfulness of the resulting embedding.
The authors also propose Mean-GWMDS-C, a clustering-focused variant that averages distance matrices and learns reduced-support representations via a consensus Gromov-Wasserstein transport.
Experiments on both synthetic and real-world datasets indicate the method produces stable, geometrically meaningful embeddings and supports clustering objectives.

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.