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Robust Bregman Clustering

Abstract : Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman divergences is that the standard Lloyd algorithm adapts to these distortion measures, and they are well-suited for clustering data sampled according to mixture models from exponential families. We prove that there exists an optimal codebook, and that an empirically optimal codebook converges a.s. to an optimal codebook in the distortion sense. Moreover, we obtain the sub-Gaussian rate of convergence for k-means 1 √ n under mild tail assumptions. Also, we derive a Lloyd-type algorithm with a trimming parameter that can be selected from data according to some heuristic, and present some experimental results.
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https://hal.archives-ouvertes.fr/hal-01948051
Contributor : Clément Levrard <>
Submitted on : Wednesday, September 9, 2020 - 3:57:21 PM
Last modification on : Tuesday, October 20, 2020 - 10:54:26 AM

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  • HAL Id : hal-01948051, version 3
  • ARXIV : 1812.04356

Citation

Aurélie Fischer, Clément Levrard, Claire Brécheteau. Robust Bregman Clustering. Annals of Statistics, Institute of Mathematical Statistics, In press. ⟨hal-01948051v3⟩

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