Online Learning for Matrix Factorization and Sparse Coding - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Machine Learning Research Year : 2010

Online Learning for Matrix Factorization and Sparse Coding


Sparse coding---that is, modelling data vectors as sparse linear combinations of basis elements---is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set, adapting it to specific data. Variations of this problem include dictionary learning in signal processing, non-negative matrix factorization and sparse principal component analysis. In this paper, we propose to address these tasks with a new online optimization algorithm, based on stochastic approximations, which scales up gracefully to large datasets with millions of training samples, and extends naturally to various matrix factorization formulations, making it suitable for a wide range of learning problems. A proof of convergence is presented, along with experiments with natural images and genomic data demonstrating that it leads to state-of-the-art performance in terms of speed and optimization for both small and large datasets.
Fichier principal
Vignette du fichier
arxiv_mairal10a.pdf (2.24 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00408716 , version 1 (01-08-2009)
inria-00408716 , version 2 (10-02-2010)


  • HAL Id : inria-00408716 , version 2
  • ARXIV : 0908.0050


Julien Mairal, Francis Bach, Jean Ponce, Guillermo Sapiro. Online Learning for Matrix Factorization and Sparse Coding. Journal of Machine Learning Research, 2010, 11 (1), pp.19--60. ⟨inria-00408716v2⟩
15283 View
1920 Download



Gmail Facebook Twitter LinkedIn More