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Online Learning for Matrix Factorization and Sparse Coding

Julien Mairal 1, 2, * Francis Bach 1, 2 Jean Ponce 1, 2 Guillermo Sapiro 3 
* Corresponding author
1 WILLOW - Models of visual object recognition and scene understanding
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : 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.
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Submitted on : Wednesday, February 10, 2010 - 8:18:13 PM
Last modification on : Thursday, March 17, 2022 - 10:08:39 AM
Long-term archiving on: : Thursday, September 23, 2010 - 11:18:04 AM


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  • 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, Microtome Publishing, 2010, 11 (1), pp.19--60. ⟨inria-00408716v2⟩



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