| 基于加权最小二乘的字典学习算法 |
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| 引用本文： | 王粒宾,崔琛,李莹军. 基于加权最小二乘的字典学习算法[J]. 系统工程与电子技术, 2011, 33(8): 1896-1900. DOI: 10.3969/j.issn.1001-506X.2011.08.41 |
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| 作者姓名： | 王粒宾 崔琛 李莹军 |
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| 作者单位： | 1. 解放军电子工程学院信息工程系, 安徽 合肥 230037； 2. 中国人民解放军63893部队, 河南 洛阳 471003 |
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| 摘 要： | 冗余字典学习是信号稀疏表示理论中的一个重要研究方面。首先,针对各训练样本稀疏表示误差各不相同的现象,建立了误差加权的信号稀疏表示数学模型,根据该模型提出一种基于加权最小二乘的字典学习算法,推导了算法闭式解和讨论了最优加权矩阵的选取。其次,为避免闭式解中矩阵求逆运算,进一步推导了算法的在线计算形式,对训练样本依次学习,每学习一个样本,字典进行一次更新,直至样本结束。此外，对算法收敛性进行了理论分析。最后,分别从信号稀疏表示和已知字典恢复两个方面仿真验证了理论分析的正确性和算法的可行性和优越性。
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| 关 键 词： | 加权最小二乘 信号稀疏表示 冗余字典 字典学习 |
Dictionary learning algorithm based on weighted least square |
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| WANG Li-bin,CUI Chen,LI Ying-jun. Dictionary learning algorithm based on weighted least square[J]. System Engineering and Electronics, 2011, 33(8): 1896-1900. DOI: 10.3969/j.issn.1001-506X.2011.08.41 |
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| Authors: | WANG Li-bin CUI Chen LI Ying-jun |
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| Affiliation: | 1. Department of Information Engineering, Electronic Engineering Institute of PLA, Hefei 230037, China; ;2. Unit 63893 of the PLA, Luoyang 471003, China |
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| Abstract: | Redundant dictionary learning is an important part of signal sparse representation theory.The mathematical model of signal sparse representation against the differences among training vectors' representation errors is firstly established,and according to this model a novel dictionary learning algorithm based on weighted least square is presented.The closed solution of this novel algorithm is derived and the selection of the optimal weighting matrix is also discussed.Secondly,in order to avoid matrix inverse... |
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| Keywords: | weighted least square signal sparse representation redundant dictionary dictionary learning |
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