Robust Bregman Clustering - Ecole Centrale de Nantes Accéder directement au contenu
Article Dans Une Revue Annals of Statistics Année : 2020

Robust Bregman Clustering

Résumé

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.
Fichier principal
Vignette du fichier
RobustBregmanClustering_VHAL.pdf (2.15 Mo) Télécharger le fichier
biblio.bib (18.44 Ko) Télécharger le fichier
imsart-number.bst (40.51 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01948051 , version 1 (11-12-2018)
hal-01948051 , version 2 (10-04-2020)
hal-01948051 , version 3 (09-09-2020)

Identifiants

Citer

Claire Brécheteau, Aurélie Fischer, Clément Levrard. Robust Bregman Clustering. Annals of Statistics, In press. ⟨hal-01948051v3⟩
462 Consultations
456 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More