# Robust clustering tools based on optimal transportation

arXiv: https://arxiv.org/abs/1607.01179 · HTML: https://mlsanity.com/paper/1607.01179/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2016.

## Built on by (most cited first, 10 of 10)

- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Transport and Merge: Cross-Architecture Merging for Large Language Models](https://mlsanity.com/paper/2602.05495/) (2026)
- [Asymptotic Theory of Geometric and Adaptive k-Means Clustering](https://mlsanity.com/paper/2202.13423/) (2022)
- [An Agglomerative Clustering of Simulation Output Distributions Using Regularized Wasserstein Distance](https://mlsanity.com/paper/2407.12100/) (2024)
- [Byzantine-tolerant distributed learning of finite mixture models](https://mlsanity.com/paper/2407.13980/) (2024)
- [Kernel K-means clustering of distributional data](https://mlsanity.com/paper/2509.18037/) (2025)
- [Collision-based Dynamics for Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2412.16385/) (2024)
- [Wasserstein-based Kernel Principal Component Analysis for Clustering Applications](https://mlsanity.com/paper/2503.14357/) (2025)
- [Consistency and inconsistency in k-means clustering](https://mlsanity.com/paper/2507.06226/) (2025)
- [Beyond Looking Up, Try Looking Around: Harmonizing Global Structure and Local Consistency in Optimal Transport for Short Text Clustering](https://mlsanity.com/paper/2607.10548/) (2026)

## Abstract (arXiv)

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× 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.