Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein
<|reference_start|>Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein: 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.<|reference_end|>
@article{van assel2024distributional,
    title={Distributional Reduction: Unifying Dimensionality Reduction and
  Clustering with Gromov-Wasserstein},
    author={Hugues Van Assel, C'edric Vincent-Cuaz, Nicolas Courty, R'emi
  Flamary, Pascal Frossard, Titouan Vayer},
    journal={arXiv preprint arXiv:2402.02239},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.02239},
    primaryClass={cs.LG stat.ML}
}