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主成分提取信息准则的加权规则

杜柏阳 孔祥玉 罗家宇

杜柏阳, 孔祥玉, 罗家宇. 主成分提取信息准则的加权规则. 自动化学报, 2021, 47(12): 2815−2822 doi: 10.16383/j.aas.c190226
引用本文: 杜柏阳, 孔祥玉, 罗家宇. 主成分提取信息准则的加权规则. 自动化学报, 2021, 47(12): 2815−2822 doi: 10.16383/j.aas.c190226
Du Bo-Yang, Kong Xiang-Yu, Luo Jia-Yu. Weighted rules for principal components extraction information criteria. Acta Automatica Sinica, 2021, 47(12): 2815−2822 doi: 10.16383/j.aas.c190226
Citation: Du Bo-Yang, Kong Xiang-Yu, Luo Jia-Yu. Weighted rules for principal components extraction information criteria. Acta Automatica Sinica, 2021, 47(12): 2815−2822 doi: 10.16383/j.aas.c190226

主成分提取信息准则的加权规则

doi: 10.16383/j.aas.c190226
基金项目: 国家自然科学基金(61374120, 61673387)资助
详细信息
    作者简介:

    杜柏阳:西安高科技研究所博士, 96901部队助理研究员. 主要研究方向为信号特征提取. E-mail: duboyangepgc@163.com

    孔祥玉:西安高科技研究所副教授. 2004年获得西安交通大学博士学位. 主要研究方向为多元信号分析, 信号处理. 本文通信作者. E-mail: xiangyukong01@163.com

    罗家宇:西安高科技研究所硕士研究生. 2017年获得湖南大学学士学位. 主要研究方向为偏最小二乘分析. E-mail: luojiayuepgc@163.com

Weighted Rules for Principal Components Extraction Information Criteria

Funds: Supported by National Natural Science Foundation of China (61374120, 61673387)
More Information
    Author Bio:

    DU Bo-Yang Ph.D. at the Xi' an Researching Institute of High Technology and assistant research fellow at the 96901 Unit of PLA. His main research interest is signal feature extraction

    KONG Xiang-Yu Associate professor at the Xi'an Researching Institute of High Technology. He received his Ph.D. degree from Xi'an Jiaotong University in 2004. His research interest covers multivariant signal analysis and signal processing. Corresponding author of this paper

    LUO Jia-Yu Master student at the Xi'an Researching Institute of High Technology. He received his bachelor degree from Hunan University in 2017. His main research interest is partial least square analysis

  • 摘要: 并行主成分提取算法在信号特征提取中具有十分重要的作用, 采用加权规则将主子空间(Principal subspace, PS)提取算法转变为并行主成分提取算法是很有效的方式, 但研究加权规则对状态矩阵影响的理论分析非常少. 对加权规则影响的分析不仅可以提供加权规则下的主成分提取算法动力学的详细认知, 而且对于其他子空间跟踪算法转变为并行主成分提取算法的可实现性给出判断条件. 本文通过比较Oja的主子空间跟踪算法和加权Oja并行主成分提取算法, 通过两种算法的差异分析了加权规则对算法提取矩阵方向的影响. 首先, 针对二维输入信号, 研究了提取两个主成分时加权规则的信息准则对状态矩阵方向的作用方式. 进而, 针对大于二维输入信号的情况, 给出加权规则影响多个主成分提取方式的讨论. 最后, MATLAB仿真验证了所提出理论的有效性.
  • 图  1  Oja信息准则和加权Oja信息准则在$\theta$变化情况下的数值变化

    Fig.  1  Curves of the information criterion Oja and weighted Oja algorithms on $\theta$

    图  2  Oja信息准则和加权Oja信息准则在$\theta = \dfrac{\pi}{2}$处的投影

    Fig.  2  Projection of the information criterion Oja and weighted Oja algorithms when $\theta = \dfrac{\pi}{2}$

    图  3  Oja信息准则在$\theta$变化情况下的数值变化

    Fig.  3  Curves of Oja information criterion on $\theta$

    图  4  加权Oja信息准则在$\theta$变化情况下的数值变化

    Fig.  4  Curves of weighted Oja information criterion on $\theta$

    图  5  Miao信息准则和Ouyang信息准则在$\theta$变化情况下的数值变化

    Fig.  5  Curves of the information criterion Miao and Ouyang algorithms on $\theta$

    图  6  Miao信息准则和Ouyang信息准则在$\theta = \dfrac{\pi}{2}$处的投影

    Fig.  6  Projection of the information criterion Miao and Ouyang algorithms when $\theta = \dfrac{\pi}{2}$

    图  7  Miao信息准则在$\theta$变化情况下的数值变化

    Fig.  7  Curves of Miao information criterion on $\theta$

    图  8  Ouyang信息准则在$\theta$变化情况下的数值变化

    Fig.  8  Curves of Ouyang information criterion on $\theta$

    图  9  原始和重建的Lena图像

    Fig.  9  Original and reconstructed Lena images

  • [1] Gersho A, Gray R M. Vector Quantization and Signal Compression. Boston, MA: KLuwer, 1992.
    [2] Oja E. Subspace Methods of Pattern Recognition. Letchworth, UK: Research Studies Press, 1992.
    [3] 潘宗序, 禹晶, 肖创柏, 等. 基于光谱相似性的高光谱图像超分辨率算法. 自动化学报, 2014, 40(12): 2797−2807.

    Pan Zong-Xu, Yu Jing, Xiao Chuang-Bai, et al. Spectral similarity-based super resolution for hyperspectral images. Acta Automatica Sinica, 2014, 40(12): 2797−2807.
    [4] 肖进胜, 朱力, 赵博强, 等. 基于主成分分析的分块视频噪声估计. 自动化学报, 2018, 44(09): 1618−1625.

    Xiao Jin-sheng, Zhu li, Zhao Bo-qiang, et al. Block-based video noise estimation algorithm via principal component analysis Acta Automatica Sinica, 2018, 44(09): 1618−1625.
    [5] 周平, 张丽, 李温鹏, 等. 集成自编码与PCA 的高炉多元铁水质量随机权神经网络建模. 自动化学报, 2018, 44(10): 1700−1811.

    Zhou Ping, Zhang Li, Li Wen-Peng, et al. Autoencoder and PCA based RVFLNs modeling for multivariate molten iron quality in blast furnace ironmaking Acta Automatica Sinica, 2018, 44(10): 1700−1811.
    [6] Kong Xiangyu, Hu Changhua, Han Chongzhao. A dual purpose principal and minor subspace gradient flow. IEEE Transaction on Signal Processing, 2012, 60(1): 197−210. doi: 10.1109/TSP.2011.2169060
    [7] Oja Erkki. Neural networks, principal components, and subspaces. International Journal of Neural Systems, 1989, 01(01): 61−68. doi: 10.1142/S0129065789000475
    [8] Williams R J. Feature Discovery Through Error-Correction Learning. San Diego, California: Institute of Cognetive Science, University of California, 1985.
    [9] Lei Xu. Least mean square error reconstruction principle for self-organizing neural-nets. Neural Networks, 1993, 6(5): 627−648. doi: 10.1016/S0893-6080(05)80107-8
    [10] Yang bin. Projection approximation subspace tracking. IEEE Transaction on Signal Processing, 1995, 43(1): 95−107. doi: 10.1109/78.365290
    [11] Kong Xiangyu, Hu Changhua, Ma Hongguang, Han Chongzhao. A unified self-stabilizing neural network algorithm for principal and minor components extraction. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(2): 185−198. doi: 10.1109/TNNLS.2011.2178564
    [12] Kenji Kakimoto, Masao Yamagishi, Isao Yamada. Smoothing of adaptive eigenvector extraction in nested orthogonal complement structure with minimum disturbance principle. Multidimensional systems and signal processing, 2018, 29(1): 433−465. doi: 10.1007/s11045-017-0528-2
    [13] Ouyang Shan, Bao Zheng, Liao Guisheng. Robust recursive least squares learning algorithm for principal component analysis. IEEE Transaction on Neural Networks, 2000, 11(1): 215−221. doi: 10.1109/72.822524
    [14] Gao Yingbin, Kong Xiangyu, Zhang Huihui, Hou li’ an. A weighted information criterion for multiple minor components and its adaptive extraction algorithms. Neural Networks, 2017, 89: 1−10. doi: 10.1016/j.neunet.2017.02.006
    [15] Gao Yingbin, Kong Xiangyu, Hu Changhua, Li Hongzeng, Hou Lian. A generalized information criterion for generalized minor component extraction. IEEE transactions on signal processing, 2017, 65(4): 974−959.
    [16] Toshihisa Tanaka, Generalized weighted rules for principal components tracking. IEEE transactions on signal processing, 2005, 53(4): 1243−1253. doi: 10.1109/TSP.2005.843698
    [17] Kushner H J, Clark D S. Stochastic Approximation Methods for Constrained and Unconstrained Systems. New York, NY: Springer-Verlag, 1978.
    [18] Oja Erkki, Ogawa H, Wangviwattana J. Principal component analysis by homogeneous neural networks―Part I: Weighted subspace criterion. IEICE Transactions on Information Systems, 1992, 75(3): 366−375.
    [19] Zhang Yi, Ye Mao, Lv Jiancheng, Tan Kok Kiong. Convergence analysis of a deterministic discrete time system of Oja’s PCA learning algorithm. IEEE Transaction on Neural Networks, 2005, 16(6): 1318−1328. doi: 10.1109/TNN.2005.852236
    [20] Miao Yongfeng, Hua Yingbo. Fast subspace tracking and neural network learning by a novel information criterion. IEEE transactions on signal processing, 1998, 46(8): 1967−1979.
    [21] Ouyang Shan, Bao Zheng. Fast Principal Component Extraction by a Weighted Information Criterion. IEEE transactions on signal processing, 2002, 50(8): 1994−2002. doi: 10.1109/TSP.2002.800395
    [22] 方蔚涛, 马鹏, 成正斌, 等. 二维投影非负矩阵分解算法及其在人脸识别中的应用. 自动化学报, 2012, 38(9): 1503−1512.

    Fang Wei-Tao, Ma Peng, Cheng Zheng-Bin, et al. 2-dimensional projective non-negative matrix factorization and its application to face recognition. Acta Automatica Sinica, 2012, 38(9): 1503−1512.
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出版历程
  • 收稿日期:  2019-03-21
  • 录用日期:  2019-07-30
  • 网络出版日期:  2021-09-17
  • 刊出日期:  2021-12-23

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