Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein

TL;DR

This paper introduces a flexible dimensionality reduction method that uses semi-relaxed Gromov-Wasserstein optimal transport to simultaneously reduce sample and feature sizes, bridging clustering and DR for data visualization.

Contribution

It presents a novel adaptation of DR objectives with Gromov-Wasserstein OT, enabling simultaneous sample and feature reduction and bridging clustering with DR.

Findings

Recovers classical DR models when embedding sample size matches input.

Provides competitive clustering when embedding's dimensionality is unconstrained.

Effective for visualizing image datasets.

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.