Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein

• URL: http://arxiv.org/abs/2402.02239v2
• Date: Wed, 22 May 2024 15:34:07 GMT
• Title: Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein
• Authors: Hugues Van Assel, Cédric Vincent-Cuaz, Nicolas Courty, Rémi Flamary, Pascal Frossard, Titouan Vayer,
• Abstract summary: Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem. This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem.
• Score: 56.62376364594194
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or organizing points into meaningful clusters (clustering). In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem. This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem. We empirically demonstrate its relevance to the identification of low-dimensional prototypes representing data at different scales, across multiple image and genomic datasets.

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