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We present a versatile adaptation of existing dimensionality reduction (DR)objectives, enabling the simultaneous reduction of both sample and featuresizes. Correspondances between input and embedding samples are computed througha semi-relaxed Gromov-Wasserstein optimal transport (OT) problem. When theembedding sample size matches that of the input, our model recovers classicalpopular DR models. When the embedding's dimensionality is unconstrained, weshow that the OT plan delivers a competitive hard clustering. We emphasize theimportance of intermediate stages that blend DR and clustering for summarizingreal data and apply our method to visualize datasets of images.

Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein