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Structured Support Exploration For Multilayer Sparse Matrix Factorization

Quoc-Tung Le 1 Rémi Gribonval 1
1 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
Abstract : Matrix factorization with sparsity constraints plays an important role in many machine learning and signal processing problems such as dictionary learning, data visualization, dimension reduction. Among the most popular tools for sparse matrix factorization are proximal algorithms, a family of algorithms based on proximal operators. In this paper, we address two problems with the application of proximal algorithms to sparse matrix factorization. On the one hand, we analyze a weakness of proximal algorithms in sparse matrix factorization: the premature convergence of the support. A remedy is also proposed to address this problem. On the other hand, we describe a new tractable proximal operator called Generalized Hungarian Method, associated to so-called k-regular matrices, which are useful for the factorization of a class of matrices associated to fast linear transforms. We further illustrate the effectiveness of our proposals by numerical experiments on the Hadamard Transform and magnetoencephalography matrix factorization.
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https://hal.inria.fr/hal-03132013
Contributor : Quoc-Tung Le <>
Submitted on : Thursday, February 4, 2021 - 5:38:36 PM
Last modification on : Thursday, March 25, 2021 - 1:50:29 PM

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Quoc-Tung Le, Rémi Gribonval. Structured Support Exploration For Multilayer Sparse Matrix Factorization. ICASSP 2021 - IEEE International Conference on Acoustics, Speech and Signal Processing, Jun 2021, Toronto, Ontario, Canada. pp.1-5. ⟨hal-03132013⟩

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