Clustering, factor discovery and optimal transport

DOI10.1093/IMAIAI/IAAA040zbMATH Open1490.62165arXiv1902.10288OpenAlexW3117257257MaRDI QIDQ5033277

Esteban G. Tabak, Hongkang Yang

Publication date: 22 February 2022

Published in: Information and Inference: A Journal of the IMA (Search for Journal in Brave)

Abstract: The clustering problem, and more generally, latent factor discovery --or latent space inference-- is formulated in terms of the Wasserstein barycenter problem from optimal transport. The objective proposed is the maximization of the variability attributable to class, further characterized as the minimization of the variance of the Wasserstein barycenter. Existing theory, which constrains the transport maps to rigid translations, is extended to affine transformations. The resulting non-parametric clustering algorithms include k-means as a special case and exhibit more robust performance. A continuous version of these algorithms discovers continuous latent variables and generalizes principal curves. The strength of these algorithms is demonstrated by tests on both artificial and real-world data sets.

Full work available at URL: https://arxiv.org/abs/1902.10288

zbMATH Keywords

clusteringoptimal transportWasserstein barycenterexplanation of variabilityprincipal curvefactor discovery

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30)

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