Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transport

• URL: http://arxiv.org/abs/2604.02610v1
• Date: Fri, 03 Apr 2026 00:58:19 GMT
• Title: Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transport
• Abstract summary: We propose two geometry-aware multi-view embedding strategies grounded in Gromov-Wasserstein (GW) optimal transport.<n>The first, termed Mean-GWMDS, aggregates view-specific relational information by averaging distance matrices.<n>The second strategy, referred to as Multi-GWMDS, adopts a selection-based paradigm in which multiple geometry-consistent candidate embeddings are generated.
• Score: 7.216399430290167
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multi-view data analysis seeks to integrate multiple representations of the same samples in order to recover a coherent low-dimensional structure. Classical approaches often rely on feature concatenation or explicit alignment assumptions, which become restrictive under heterogeneous geometries or nonlinear distortions. In this work, we propose two geometry-aware multi-view embedding strategies grounded in Gromov-Wasserstein (GW) optimal transport. The first, termed Mean-GWMDS, aggregates view-specific relational information by averaging distance matrices and applying GW-based multidimensional scaling to obtain a representative embedding. The second strategy, referred to as Multi-GWMDS, adopts a selection-based paradigm in which multiple geometry-consistent candidate embeddings are generated via GW-based alignment and a representative embedding is selected. Experiments on synthetic manifolds and real-world datasets show that the proposed methods effectively preserve intrinsic relational structure across views. These results highlight GW-based approaches as a flexible and principled framework for multi-view representation learning.

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