June 2021 Robust Bregman clustering
Claire Brécheteau, Aurélie Fischer, Clément Levrard
Author Affiliations +
Ann. Statist. 49(3): 1679-1701 (June 2021). DOI: 10.1214/20-AOS2018

Abstract

Clustering with Bregman divergences encompasses a wide family of clustering procedures that are well suited to mixtures of distributions from exponential families (J. Mach. Learn. Res. 6 (2005) 1705–1749). However, these techniques are highly sensitive to noise. To address 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, where n denotes the sample size, 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 experiments assess the performance of our method on simulated and real datasets.

Citation

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Claire Brécheteau. Aurélie Fischer. Clément Levrard. "Robust Bregman clustering." Ann. Statist. 49 (3) 1679 - 1701, June 2021. https://doi.org/10.1214/20-AOS2018

Information

Received: 1 March 2019; Revised: 1 April 2020; Published: June 2021
First available in Project Euclid: 9 August 2021

MathSciNet: MR4298877
zbMATH: 1475.62177
Digital Object Identifier: 10.1214/20-AOS2018

Subjects:
Primary: 62H30
Secondary: 62G35

Keywords: Bregman divergence , clustering , robustness

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 3 • June 2021
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