Robust Bregman Clustering

Abstract : Clustering with Bregman divergences encompasses a wide family of clustering procedures that are well-suited to mixtures of distributions from exponential families. However these techniques are highly sensitive to noise. To adress the issue of clustering data with possibly adversarial noise, we introduce a robustified version of Bregman clustering based on a trimming approach. We investigate its theoretical properties, showing for instance that our estimator converges at a sub-Gaussian rate 1/ √ n in terms of the sample size n, under mild tail assumptions. We also show that it is robust to a certain amount of noise, stated in terms of Breakdown Point. We also derive a Lloyd-type algorithm with a trimming parameter, along with a heuristic to select this parameter and the number of clusters from sample. Some numerical experimentation assesses the performance of our method on simulated and real datasets.
Complete list of metadatas

Cited literature [37 references]  Display  Hide  Download
Contributor : Claire Brécheteau <>
Submitted on : Wednesday, August 14, 2019 - 12:37:48 PM
Last modification on : Friday, August 16, 2019 - 1:15:39 AM


Files produced by the author(s)


  • HAL Id : hal-02266419, version 1


Claire Brécheteau, Aurélie Fisher, Clément Levrard. Robust Bregman Clustering. 2019. ⟨hal-02266419⟩



Record views


Files downloads