Robust clustering tools based on optimal transportation

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.

References in corpus (2)

• A general trimming approach to robust Cluster Analysis
• Joint Modeling and Registration of Cell Populations in Cohorts of High-Dimensional Flow Cytometric Data

Cited by in corpus (4)

• On clustering uncertain and structured data with Wasserstein barycenters and a geodesic criterion for the number of clusters
• An Agglomerative Clustering of Simulation Output Distributions Using Regularized Wasserstein Distance
• Decentralized Distributed Optimization for Saddle Point Problems
• Improving Model Choice in Classification: An Approach Based on Clustering of Covariance Matrices