  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.
