Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transport
This work addresses multi-view representation learning for data with nonlinear distortions, offering a flexible framework, though it appears incremental as it builds on existing optimal transport methods.
The paper tackles the problem of integrating multi-view data with heterogeneous geometries by proposing two geometry-aware embedding strategies based on Gromov-Wasserstein optimal transport, showing that these methods effectively preserve intrinsic relational structure across views in experiments on synthetic and real-world datasets.
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.