Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein

Published: 27 Oct 2023, Last Modified: 28 Dec 2023OTML 2023 PosterEveryoneRevisionsBibTeX
Keywords: Optimal Transport, Clustering, Dimensionality Reduction
TL;DR: A versatile framework for performing joint clustering and dimensionality reduction based on 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.
Submission Number: 54