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

arXiv: https://arxiv.org/abs/2604.02610 · HTML: https://mlsanity.com/paper/2604.02610/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance](https://mlsanity.com/paper/2405.15959/) (2024)
- [Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein](https://mlsanity.com/paper/2402.02239/) (2024)
- [Multidimensional Scaling on Multiple Input Distance Matrices](https://mlsanity.com/paper/1605.00286/) (2016)
- [A dimensionality reduction technique based on the Gromov-Wasserstein distance](https://mlsanity.com/paper/2501.13732/) (2025)

## Built on by (most cited first, 2 of 2)

- [Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clustering](https://mlsanity.com/paper/2604.23912/) (2026)
- [Gromov-Wasserstein Distillation for Inductive Multi-View Embedding](https://mlsanity.com/paper/2609.40047/) (2026)

## Abstract (arXiv)

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.