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arXiv · 1607.01179

Robust clustering tools based on optimal transportation

E. del Barrio·J. A. Cuesta-Albertos·C. Matrán·A. Mayo-Íscar
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Abstract

A robust clustering method for probabilities in Wasserstein space is introduced. This new "trimmed $k$-barycenters" approach relies on recent results on barycenters in Wasserstein space that allow intensive computation, as required by clustering algorithms. The possibility of trimming the most discrepant distributions results in a gain in stability and robustness, highly convenient in this setting. As a remarkable application we consider a parallelized estimation setup in which each of $m$ units processes a portion of the data, producing an estimate of $k$-features, encoded as $k$ probabilities. We prove that the trimmed $k$-barycenter of the $m\times k$ estimates produces a consistent aggregation. We illustrate the methodology with simulated and real data examples. These include clustering populations by age distributions and analysis of cytometric data.

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E. del Barrio, J. A. Cuesta-Albertos, C. Matrán, A. Mayo-Íscar. 2016-07-05. Robust clustering tools based on optimal transportation. https://doi.org/10.1007/s11222-018-9800-z

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