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

2026-04-26

AI Summary

This work addresses the challenge of learning a unified low-dimensional representation from multi-view relational data, where inconsistent underlying geometric structures across views hinder effective integration. To overcome this, the authors propose a consensus embedding framework based on the Gromov–Wasserstein (GW) distance, which operates directly on pairwise distance matrices to preserve relational structures shared across views. By fusing intrinsic distances from multiple views and incorporating a clustering-oriented low-support representation, they introduce two novel algorithms—Bary-GWMDS and Mean-GWMDS-C—that robustly handle nonlinear distortions and yield geometrically consistent embeddings. Experimental results on both synthetic and real-world datasets demonstrate that the proposed methods produce representations with clear geometric interpretability and achieve superior clustering performance.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Representation Learning for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Web data integration and cleaning

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.

Problem

• multi-view
• relational embedding
• Gromov-Wasserstein
• clustering
• geometric discrepancy

Innovation

• Gromov-Wasserstein
• multi-view embedding
• relational data
• distance matrix
• clustering