Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent
Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent
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DOI：
10.1155/2013/259863
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发表时间：
2013-06
影响因子：
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通讯作者：
Zunyi Tang;Shuxue Ding;Zhenni Li;Linlin Jiang
中科院分区：
文献类型：
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作者：
Zunyi Tang;Shuxue Ding;Zhenni Li;Linlin Jiang
基于过完备字典的信号稀疏表示近年来受到了广泛关注，因为它在各种应用中产生了有希望的结果。由于信号和字典的非负性在一些应用中是必需的，例如，多谱数据分析，传统的字典学习方法仅仅强加于非负性可能变得不适用。在本文中，我们提出了一种新的方法来学习非负的、过完备的字典。这是通过将非负信号的稀疏表示作为具有稀疏性约束的非负矩阵分解（NMF）问题来实现的。采用坐标下降策略进行优化，并将其扩展到多变量并行处理中，提出了一种并行坐标下降字典学习（PCDDL）算法，该算法通过迭代求解两个最优问题，即字典的学习过程和构造信号的系数估计过程来构建。数值实验表明，该算法优于传统的非负K-SVD （NN-KSVD）算法和其他几种算法进行比较。其计算量明显低于所比较算法。
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.