Statistics and Computing

, Volume 29, Issue 1, pp 139–160 | Cite as

Robust clustering tools based on optimal transportation

  • E. del Barrio
  • J. A. Cuesta-Albertos
  • C. MatránEmail author
  • A. Mayo-Íscar


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 to be feasible. 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 clustering setup in which each of m units processes a portion of the data, producing a clustering report, encoded as k probabilities. We prove that the trimmed k-barycenter of the \(m\times k\) reports produces a consistent aggregation which we consider the result of a ‘wide consensus’. We also prove that a weighted version of trimmed k-means algorithms based on k-barycenters in the space of Wasserstein keeps the descending character of the concentration step, guaranteeing convergence to local minima. We illustrate the methodology with simulated and real data examples. These include clustering populations by age distributions and analysis of cytometric data.


Cluster prototypes k-barycenter Trimmed barycenter Robust aggregation Wasserstein distance Monge–Kantorovich problem Transport maps Trimmed distributions Parallelized inference Bragging Subragging Trimmed k-means algorithm 

Mathematics Subject Classification

Primary 62H30 62G35 Secondary 62G20 62P99 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Estadística e Investigación Operativa and IMUVAUniversidad de ValladolidValladolidSpain
  2. 2.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

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