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

TL;DR

This paper introduces two geometry-aware multi-view embedding methods based on Gromov-Wasserstein optimal transport, effectively preserving intrinsic relational structures across heterogeneous views.

Contribution

The work presents novel GW-based multi-view embedding strategies that handle heterogeneous geometries without relying on feature concatenation or strict alignment assumptions.

Findings

Methods effectively preserve intrinsic relational structure across views.

Experiments on synthetic and real datasets demonstrate improved embedding quality.

GW-based approaches offer a flexible framework for multi-view representation learning.

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.