Robust clustering tools based on optimal transportation

Understand

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.