Robust clustering tools based on optimal transportation

Date(s) : 04/12/2017   iCal
14 h 00 min - 15 h 00 min

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.

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