Interpolating between Clustering and Dimensionality Reduction with
  Gromov-Wasserstein
Hugues Van Assel Cédric Vincent-Cuaz Titouan Vayer Rémi Flamary Nicolas Courty
We present a versatile adaptation of existing dimensionality reduction (DR)
objectives, enabling the simultaneous reduction of both sample and feature
sizes. Correspondances between input and embedding samples are computed through
a semi-relaxed Gromov-Wasserstein optimal transport (OT) problem. When the
embedding sample size matches that of the input, our model recovers classical
popular DR models. When the embedding's dimensionality is unconstrained, we
show that the OT plan delivers a competitive hard clustering. We emphasize the
importance of intermediate stages that blend DR and clustering for summarizing
real data and apply our method to visualize datasets of images.