Eduardo Fernandes Montesuma

Rafael Pereira Eufrazio, Eduardo Fernandes Montesuma, Charles Casimiro Cavalcante

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.

Eduardo Fernandes Montesuma, Yassir Bendou, Mike Gartrell

Wasserstein barycenters provide a powerful tool for aggregating probability measures, while leveraging the geometry of their ambient space. Existing discrete methods suffer from poor scalability, as they require access to the complete set of samples from input measures. We address this issue by recasting the original barycenter problem as a gradient flow in the Wasserstein space. Our approach offers two advantages. First, we achieve scalability by sampling mini-batches from the input measures. Second, we incorporate functionals over probability measures, which regularize the barycenter problem through internal, potential, and interaction energies. We present two algorithms for empirical and Gaussian mixture measures, providing convergence guarantees under the Polyak-Łojasiewicz inequality. Experimental validation on toy datasets and domain adaptation benchmarks show that our methods outperform previous discrete and neural net-based methods for computing Wasserstein barycenters.