Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein

• URL: http://arxiv.org/abs/2310.03398v1
• Date: Thu, 5 Oct 2023 09:04:53 GMT
• Title: Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein
• Authors: Hugues Van Assel, C\'edric Vincent-Cuaz, Titouan Vayer, R\'emi Flamary, Nicolas Courty
• Abstract summary: Correspondances between input and embedding samples are computed through a semi-relaxed Gromov-Wasserstein optimal transport problem. When the embedding's dimensionality is unconstrained, we show that the OT plan delivers a competitive hard clustering.
• Score: 13.656958543737211
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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