@inproceedings{
assel2023interpolating,
title={Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein},
author={Hugues Van Assel and C{\'e}dric Vincent-Cuaz and Titouan Vayer and R{\'e}mi Flamary and Nicolas Courty},
booktitle={NeurIPS 2023 Workshop Optimal Transport and Machine Learning},
year={2023},
url={https://openreview.net/forum?id=CmgB5fGWbN}
}
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.
Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein
Hugues Van Assel Cédric Vincent-Cuaz Titouan Vayer Rémi Flamary Nicolas Courty