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.
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  • HAL Id : hal-02266419, version 1

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

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