| 自稳定的双目的特征对提取算法及其收敛性分析 |
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| 引用本文： | 冯晓伟,孔祥玉,马红光,安秋生.自稳定的双目的特征对提取算法及其收敛性分析[J].控制与决策,2017,32(4):600-606. |
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| 作者姓名： | 冯晓伟 孔祥玉 马红光 安秋生 |
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| 作者单位： | 火箭军工程大学三系,西安710025,火箭军工程大学三系,西安710025,北京理工大学珠海学院,广东珠海519088\hspace{3pt},山西师范大学数学与计算机科学学院,山西临汾041004 |
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| 基金项目： | 国家自然科学基金项目(61673387, 61374120, 11405267)；陕西省自然科学基金项目(2016JM6015). |
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| 摘 要： | 提出一种自稳定的双目的算法用以提取信号自相关矩阵的特征对.该算法可以通过仅仅改变一个符号实现主/次特征向量估计的转化,并且可以通过估计的特征向量的模值信息估计对应的特征值,从而实现特征对的提取.基于确定性离散时间方法对所提出的算法进行收敛性分析,并确定算法收敛的边界条件.与已有算法对比的仿真实验验证了所提出算法的收敛性能.
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| 关 键 词： | 主成分分析 次成分分析 自稳定性 确定性离散时间 神经网络 特征对 |
Unified self-stabilizing eigen-pairs extraction algorithm and its convergence analysis |
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| FENG Xiao-wei,KONG Xiang-yu,MA Hong-guang and AN Qiu-sheng.Unified self-stabilizing eigen-pairs extraction algorithm and its convergence analysis[J].Control and Decision,2017,32(4):600-606. |
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| Authors: | FENG Xiao-wei KONG Xiang-yu MA Hong-guang and AN Qiu-sheng |
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| Affiliation: | Department 3,Xián Research Institute of High Technology,Xián 710025,China,Department 3,Xián Research Institute of High Technology,Xián 710025,China,Zhuhai College,Beijing Institute of Technology,Zhuhai519088,China and School of Mathematics and Computer Science,Shanxi Normal University,Linfen041004,China |
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| Abstract: | A self-stabilizing and unified algorithm is introduced to extract the eigen-pairs of a covariance matrix.The proposed algorithm is available for both principal component analysis(PCA) and minor component analysis(MCA) by simply altering the sign, and can estimate the corresponding eigenvalue from the norm of the estimated eigenvector, which can realize the eigen-pair extraction.The convergence analysis of the proposed algorithm based on the deterministic discrete time(DDT) approach is evaluated and the condition for convergence is also given.Finally, compared with existing algorithms, the convergence of the proposed algorithm is verified by the simulations. |
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