Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913914439073792 |
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| author | Van Assel, Hugues Vincent-Cuaz, Cédric Courty, Nicolas Flamary, Rémi Frossard, Pascal Vayer, Titouan |
| author_facet | Van Assel, Hugues Vincent-Cuaz, Cédric Courty, Nicolas Flamary, Rémi Frossard, Pascal Vayer, Titouan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02239 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein Van Assel, Hugues Vincent-Cuaz, Cédric Courty, Nicolas Flamary, Rémi Frossard, Pascal Vayer, Titouan Machine Learning 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. |
| title | Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.02239 |