Dictionary Learning for Massive Matrix Factorization

Arthur Mensch 1 Julien Mairal 2 Bertrand Thirion 1 Gaël Varoquaux 1
1 PARIETAL - Modelling brain structure, function and variability based on high-field MRI data
NEUROSPIN - Service NEUROSPIN, Inria Saclay - Ile de France
2 Thoth - Apprentissage de modèles à partir de données massives
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann
Abstract : Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized methods, that reduce the complexity in one of the matrix dimension, but not in both of them. In this paper, we tackle very large matrices in both dimensions. We propose a new factorization method that scales gracefully to terabyte-scale datasets, that could not be processed by previous algorithms in a reasonable amount of time. We demonstrate the efficiency of our approach on massive functional Magnetic Resonance Imaging (fMRI) data, and on matrix completion problems for recommender systems, where we obtain significant speed-ups compared to state-of-the art coordinate descent methods.
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  • HAL Id : hal-01308934, version 2
  • ARXIV : 1605.00937

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Arthur Mensch, Julien Mairal, Bertrand Thirion, Gaël Varoquaux. Dictionary Learning for Massive Matrix Factorization. International Conference on Machine Learning, Jun 2016, New York, United States. pp.1737-1746. ⟨hal-01308934v2⟩

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