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2013 Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent
Zunyi Tang, Shuxue Ding, Zhenni Li, Linlin Jiang
Abstr. Appl. Anal. 2013(SI14): 1-11 (2013). DOI: 10.1155/2013/259863


Sparse representation of signals via an overcomplete dictionary has recently received much attention as it has produced promising results in various applications. Since the nonnegativities of the signals and the dictionary are required in some applications, for example, multispectral data analysis, the conventional dictionary learning methods imposed simply with nonnegativity may become inapplicable. In this paper, we propose a novel method for learning a nonnegative, overcomplete dictionary for such a case. This is accomplished by posing the sparse representation of nonnegative signals as a problem of nonnegative matrix factorization (NMF) with a sparsity constraint. By employing the coordinate descent strategy for optimization and extending it to multivariable case for processing in parallel, we develop a so-called parallel coordinate descent dictionary learning (PCDDL) algorithm, which is structured by iteratively solving the two optimal problems, the learning process of the dictionary and the estimating process of the coefficients for constructing the signals. Numerical experiments demonstrate that the proposed algorithm performs better than the conventional nonnegative K-SVD (NN-KSVD) algorithm and several other algorithms for comparison. What is more, its computational consumption is remarkably lower than that of the compared algorithms.


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Zunyi Tang. Shuxue Ding. Zhenni Li. Linlin Jiang. "Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent." Abstr. Appl. Anal. 2013 (SI14) 1 - 11, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1359.68257
MathSciNet: MR3064519
Digital Object Identifier: 10.1155/2013/259863

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI14 • 2013
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