Interpolating Between Clustering and Dimensionality Reduction with Gromov-Wasserstein
Abstract
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.
Cite
Text
Van Assel et al. "Interpolating Between Clustering and Dimensionality Reduction with Gromov-Wasserstein." NeurIPS 2023 Workshops: OTML, 2023.Markdown
[Van Assel et al. "Interpolating Between Clustering and Dimensionality Reduction with Gromov-Wasserstein." NeurIPS 2023 Workshops: OTML, 2023.](https://mlanthology.org/neuripsw/2023/assel2023neuripsw-interpolating/)BibTeX
@inproceedings{assel2023neuripsw-interpolating,
title = {{Interpolating Between Clustering and Dimensionality Reduction with Gromov-Wasserstein}},
author = {Van Assel, Hugues and Vincent-Cuaz, Cédric and Vayer, Titouan and Flamary, Rémi and Courty, Nicolas},
booktitle = {NeurIPS 2023 Workshops: OTML},
year = {2023},
url = {https://mlanthology.org/neuripsw/2023/assel2023neuripsw-interpolating/}
}