arXiv subjects

Rafael Pereira Eufrazio

Publications and source records attributed to Rafael Pereira Eufrazio.

4 recordsLinked to original sources

arXiv2026

Gromov-Wasserstein Distillation for Inductive Multi-View Embedding

Gromov-Wasserstein multidimensional scaling (GW-MDS) learns low-dimensional representations from relational data but remains transductive, providing no explicit mapping for unseen samples. We introduce an inductive framework based on barycentric distillation. A GW-MDS teacher learns a latent support and an optimal transport plan from the training data, and barycentric projection converts the resulting coupling into sample-aligned targets. A neural student then learns an explicit out-of-sample mapping, avoiding additional relational-matrix construction and GW optimization at inference. We formulate the approach for single-view data and extend it to Mean-GWMDS and Multi-GWMDS teachers through consensus and selected-projection targets learned by a multi-view student with view-specific encoders. We also investigate a direct neural baseline trained solely with a GW objective. Experiments on synthetic and real-world data using Euclidean, geodesic, and cosine relations show that the distilled models preserve the teacher geometry on unseen samples and consistently outperform direct neural GW training in sample-indexed relational preservation. These results establish barycentric projection as an effective bridge between transductive GW embeddings and inductive neural mappings.

cs.LG↗

arXiv2026

Multi-Domain Clustering via Measure Quantization

Clustering is a fundamental task in data analysis, typically addressed through centroid-based methods such as K-means. In this work, we present a general framework for multi-domain clustering via measure quantization: given samples from multiple domains, we learn a shared set of cluster prototypes by minimizing a probability metric, such as the Sinkhorn divergence or the Maximum Mean Discrepancy, between each domain's probability measure and the measure of prototypes. Data points are then assigned to clusters either via nearest centroid, or via optimal transport, a collaborative strategy that couples all samples within a domain. A mini-batch optimization strategy makes both fitting and assignment scalable, reducing memory and computational cost while preserving clustering performance. Experimental results on 5 multi-domain benchmarks spanning image, audio and sensor data show that our Sinkhorn-based method consistently outperforms classical and multi-domain clustering baselines, and that this advantage persists when scaling to hundreds of thousands of samples.

cs.LG↗

arXiv2026

Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clustering

Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to learn a consensus embedding preserving shared relational structure. By leveraging intrinsic distances, the approach naturally handles nonlinear distortions across views. We also introduce Mean-GWMDS-C, a clustering-oriented formulation that averages distance matrices and learns reduced-support representations via a consensus Gromov-Wasserstein transport. Experiments on synthetic and real-world datasets show that the proposed framework yields stable and geometrically meaningful embeddings.

cs.LG↗

arXiv2026

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

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.

stat.ML↗