Dictionary Learning with Incoherence and Sparsity Constraints for Sparse Representation of Nonnegative Signals

Zunyi TANG; Shuxue DING

doi:10.1587/transinf.E96.D.1192

Dictionary Learning with Incoherence and Sparsity Constraints for Sparse Representation of Nonnegative Signals

Zunyi TANG, Shuxue DING

Full Text Views

0

Share
Cite this

Summary :

This paper presents a method for learning an overcomplete, nonnegative dictionary and for obtaining the corresponding coefficients so that a group of nonnegative signals can be sparsely represented by them. This is accomplished by posing the learning as a problem of nonnegative matrix factorization (NMF) with maximization of the incoherence of the dictionary and of the sparsity of coefficients. By incorporating a dictionary-incoherence penalty and a sparsity penalty in the NMF formulation and then adopting a hierarchically alternating optimization strategy, we show that the problem can be cast as two sequential optimal problems of quadratic functions. Each optimal problem can be solved explicitly so that the whole problem can be efficiently solved, which leads to the proposed algorithm, i.e., sparse hierarchical alternating least squares (SHALS). The SHALS algorithm is structured by iteratively solving the two optimal problems, corresponding to the learning process of the dictionary and to the estimating process of the coefficients for reconstructing the signals. Numerical experiments demonstrate that the new algorithm performs better than the nonnegative K-SVD (NN-KSVD) algorithm and several other famous algorithms, and its computational cost is remarkably lower than the compared algorithms.

Publication: IEICE TRANSACTIONS on Information Vol.E96-D No.5 pp.1192-1203

Publication Date: 2013/05/01

Publicized

Online ISSN: 1745-1361

DOI: 10.1587/transinf.E96.D.1192

Type of Manuscript: PAPER

Category: Biocybernetics, Neurocomputing

Cite this

Copy

Zunyi TANG, Shuxue DING, "Dictionary Learning with Incoherence and Sparsity Constraints for Sparse Representation of Nonnegative Signals" in IEICE TRANSACTIONS on Information, vol. E96-D, no. 5, pp. 1192-1203, May 2013, doi: 10.1587/transinf.E96.D.1192.
Abstract: This paper presents a method for learning an overcomplete, nonnegative dictionary and for obtaining the corresponding coefficients so that a group of nonnegative signals can be sparsely represented by them. This is accomplished by posing the learning as a problem of nonnegative matrix factorization (NMF) with maximization of the incoherence of the dictionary and of the sparsity of coefficients. By incorporating a dictionary-incoherence penalty and a sparsity penalty in the NMF formulation and then adopting a hierarchically alternating optimization strategy, we show that the problem can be cast as two sequential optimal problems of quadratic functions. Each optimal problem can be solved explicitly so that the whole problem can be efficiently solved, which leads to the proposed algorithm, i.e., sparse hierarchical alternating least squares (SHALS). The SHALS algorithm is structured by iteratively solving the two optimal problems, corresponding to the learning process of the dictionary and to the estimating process of the coefficients for reconstructing the signals. Numerical experiments demonstrate that the new algorithm performs better than the nonnegative K-SVD (NN-KSVD) algorithm and several other famous algorithms, and its computational cost is remarkably lower than the compared algorithms.
URL: https://globals.ieice.org/en_transactions/information/10.1587/transinf.E96.D.1192/_p

Copy

@ARTICLE{e96-d_5_1192,
author={Zunyi TANG, Shuxue DING, },
journal={IEICE TRANSACTIONS on Information},
title={Dictionary Learning with Incoherence and Sparsity Constraints for Sparse Representation of Nonnegative Signals},
year={2013},
volume={E96-D},
number={5},
pages={1192-1203},
abstract={This paper presents a method for learning an overcomplete, nonnegative dictionary and for obtaining the corresponding coefficients so that a group of nonnegative signals can be sparsely represented by them. This is accomplished by posing the learning as a problem of nonnegative matrix factorization (NMF) with maximization of the incoherence of the dictionary and of the sparsity of coefficients. By incorporating a dictionary-incoherence penalty and a sparsity penalty in the NMF formulation and then adopting a hierarchically alternating optimization strategy, we show that the problem can be cast as two sequential optimal problems of quadratic functions. Each optimal problem can be solved explicitly so that the whole problem can be efficiently solved, which leads to the proposed algorithm, i.e., sparse hierarchical alternating least squares (SHALS). The SHALS algorithm is structured by iteratively solving the two optimal problems, corresponding to the learning process of the dictionary and to the estimating process of the coefficients for reconstructing the signals. Numerical experiments demonstrate that the new algorithm performs better than the nonnegative K-SVD (NN-KSVD) algorithm and several other famous algorithms, and its computational cost is remarkably lower than the compared algorithms.},
keywords={},
doi={10.1587/transinf.E96.D.1192},
ISSN={1745-1361},
month={May},}

Copy

TY - JOUR
TI - Dictionary Learning with Incoherence and Sparsity Constraints for Sparse Representation of Nonnegative Signals
T2 - IEICE TRANSACTIONS on Information
SP - 1192
EP - 1203
AU - Zunyi TANG
AU - Shuxue DING
PY - 2013
DO - 10.1587/transinf.E96.D.1192
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E96-D
IS - 5
JA - IEICE TRANSACTIONS on Information
Y1 - May 2013
AB - This paper presents a method for learning an overcomplete, nonnegative dictionary and for obtaining the corresponding coefficients so that a group of nonnegative signals can be sparsely represented by them. This is accomplished by posing the learning as a problem of nonnegative matrix factorization (NMF) with maximization of the incoherence of the dictionary and of the sparsity of coefficients. By incorporating a dictionary-incoherence penalty and a sparsity penalty in the NMF formulation and then adopting a hierarchically alternating optimization strategy, we show that the problem can be cast as two sequential optimal problems of quadratic functions. Each optimal problem can be solved explicitly so that the whole problem can be efficiently solved, which leads to the proposed algorithm, i.e., sparse hierarchical alternating least squares (SHALS). The SHALS algorithm is structured by iteratively solving the two optimal problems, corresponding to the learning process of the dictionary and to the estimating process of the coefficients for reconstructing the signals. Numerical experiments demonstrate that the new algorithm performs better than the nonnegative K-SVD (NN-KSVD) algorithm and several other famous algorithms, and its computational cost is remarkably lower than the compared algorithms.
ER -