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Generalization of the K-SVD algorithm for minimization of β-divergence

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Generalization of the K-SVD algorithm for minimization of β-divergence. / Garcia-Molla, Victor M.; San Juan, Pablo; Virtanen, Tuomas; Vidal, Antonio M.; Alonso, Pedro.

In: Digital Signal Processing: A Review Journal, Vol. 92, 01.09.2019, p. 47-53.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Garcia-Molla, VM, San Juan, P, Virtanen, T, Vidal, AM & Alonso, P 2019, 'Generalization of the K-SVD algorithm for minimization of β-divergence', Digital Signal Processing: A Review Journal, vol. 92, pp. 47-53. https://doi.org/10.1016/j.dsp.2019.05.001

APA

Garcia-Molla, V. M., San Juan, P., Virtanen, T., Vidal, A. M., & Alonso, P. (2019). Generalization of the K-SVD algorithm for minimization of β-divergence. Digital Signal Processing: A Review Journal, 92, 47-53. https://doi.org/10.1016/j.dsp.2019.05.001

Vancouver

Garcia-Molla VM, San Juan P, Virtanen T, Vidal AM, Alonso P. Generalization of the K-SVD algorithm for minimization of β-divergence. Digital Signal Processing: A Review Journal. 2019 Sep 1;92:47-53. https://doi.org/10.1016/j.dsp.2019.05.001

Author

Garcia-Molla, Victor M. ; San Juan, Pablo ; Virtanen, Tuomas ; Vidal, Antonio M. ; Alonso, Pedro. / Generalization of the K-SVD algorithm for minimization of β-divergence. In: Digital Signal Processing: A Review Journal. 2019 ; Vol. 92. pp. 47-53.

Bibtex - Download

@article{7c3aaf9c79224d79ac57ef49e931e480,
title = "Generalization of the K-SVD algorithm for minimization of β-divergence",
abstract = "In this paper, we propose, describe, and test a modification of the K-SVD algorithm. Given a set of training data, the proposed algorithm computes an overcomplete dictionary by minimizing the β-divergence (β>=1) between the data and its representation as linear combinations of atoms of the dictionary, under strict sparsity restrictions. For the special case β=2, the proposed algorithm minimizes the Frobenius norm and, therefore, for β=2 the proposed algorithm is equivalent to the original K-SVD algorithm. We describe the modifications needed and discuss the possible shortcomings of the new algorithm. The algorithm is tested with random matrices and with an example based on speech separation.",
keywords = "Beta-divergence, K-SVD, Matching pursuit algorithms, NMF, Nonnegative K-SVD",
author = "Garcia-Molla, {Victor M.} and {San Juan}, Pablo and Tuomas Virtanen and Vidal, {Antonio M.} and Pedro Alonso",
year = "2019",
month = "9",
day = "1",
doi = "10.1016/j.dsp.2019.05.001",
language = "English",
volume = "92",
pages = "47--53",
journal = "Digital Signal Processing",
issn = "1051-2004",
publisher = "Elsevier",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Generalization of the K-SVD algorithm for minimization of β-divergence

AU - Garcia-Molla, Victor M.

AU - San Juan, Pablo

AU - Virtanen, Tuomas

AU - Vidal, Antonio M.

AU - Alonso, Pedro

PY - 2019/9/1

Y1 - 2019/9/1

N2 - In this paper, we propose, describe, and test a modification of the K-SVD algorithm. Given a set of training data, the proposed algorithm computes an overcomplete dictionary by minimizing the β-divergence (β>=1) between the data and its representation as linear combinations of atoms of the dictionary, under strict sparsity restrictions. For the special case β=2, the proposed algorithm minimizes the Frobenius norm and, therefore, for β=2 the proposed algorithm is equivalent to the original K-SVD algorithm. We describe the modifications needed and discuss the possible shortcomings of the new algorithm. The algorithm is tested with random matrices and with an example based on speech separation.

AB - In this paper, we propose, describe, and test a modification of the K-SVD algorithm. Given a set of training data, the proposed algorithm computes an overcomplete dictionary by minimizing the β-divergence (β>=1) between the data and its representation as linear combinations of atoms of the dictionary, under strict sparsity restrictions. For the special case β=2, the proposed algorithm minimizes the Frobenius norm and, therefore, for β=2 the proposed algorithm is equivalent to the original K-SVD algorithm. We describe the modifications needed and discuss the possible shortcomings of the new algorithm. The algorithm is tested with random matrices and with an example based on speech separation.

KW - Beta-divergence

KW - K-SVD

KW - Matching pursuit algorithms

KW - NMF

KW - Nonnegative K-SVD

U2 - 10.1016/j.dsp.2019.05.001

DO - 10.1016/j.dsp.2019.05.001

M3 - Article

VL - 92

SP - 47

EP - 53

JO - Digital Signal Processing

JF - Digital Signal Processing

SN - 1051-2004

ER -