Titre :

Revisiting clustering as matrix factorisation on the Stiefel manifold

Auteur(s) :

Chretien, Stephane [Auteur]
National Physical Laboratory [Teddington] [NPL]
Guedj, Benjamin [Auteur]
The Inria London Programme [Inria-London]
Department of Computer science [University College of London] [UCL-CS]
MOdel for Data Analysis and Learning [MODAL]

Titre de la manifestation scientifique :

LOD 2020 - the Sixth International Conference on Machine Learning, Optimisation and Data Science

Ville :

Siena

Pays :

Italie

Date de début de la manifestation scientifique :

2020-07-19

Mot(s)-clé(s) en anglais :

Clustering
concentration inequalities
non-negative matrix factorisation
Gaussian mixtures
PAC-Bayes
optimisation on manifolds

Discipline(s) HAL :

Informatique [cs]/Apprentissage [cs.LG]
Statistiques [stat]/Machine Learning [stat.ML]

Résumé en anglais : [en]

This paper studies clustering for possibly high dimensional data (e.g. images, time series, gene expression data, and many other settings), and rephrase it as low rank matrix estimation in the PAC-Bayesian framework. Our ...
Lire la suite >This paper studies clustering for possibly high dimensional data (e.g. images, time series, gene expression data, and many other settings), and rephrase it as low rank matrix estimation in the PAC-Bayesian framework. Our approach leverages the well known Burer-Monteiro factorisation strategy from large scale optimisation, in the context of low rank estimation. Moreover, our Burer-Monteiro factors are shown to lie on a Stiefel manifold. We propose a new generalized Bayesian estimator for this problem and prove novel prediction bounds for clustering. We also devise a componentwise Langevin sampler on the Stiefel manifold to compute this estimator.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL