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Volume 7 Issue 6
Oct.  2020

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2020  >  7(6): 1585-1592
Haidi Dong, Yingbin Gao and Gang Liu, "Convergence Analysis of a Self-Stabilizing Algorithm for Minor Component Analysis," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1585-1592, Nov. 2020. doi: 10.1109/JAS.2019.1911636
Citation: Haidi Dong, Yingbin Gao and Gang Liu, "Convergence Analysis of a Self-Stabilizing Algorithm for Minor Component Analysis," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1585-1592, Nov. 2020. doi: 10.1109/JAS.2019.1911636
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Convergence Analysis of a Self-Stabilizing Algorithm for Minor Component Analysis

doi: 10.1109/JAS.2019.1911636
Funds:  This work was supported by the National Natural Science Foundation of China (61903375, 61673387, 61374120) and Shaanxi Province Natural Science Foundation (2016JM6015)
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    Abstract
  • The Möller algorithm is a self-stabilizing minor component analysis algorithm. This research document involves the study of the convergence and dynamic characteristics of the Möller algorithm using the deterministic discrete time (DDT) methodology. Unlike other analysis methodologies, the DDT methodology is capable of serving the distinct time characteristic and having no constraint conditions. Through analyzing the dynamic characteristics of the weight vector, several convergence conditions are drawn, which are beneficial for its application. The performing computer simulations and real applications demonstrate the correctness of the analysis’s conclusions.

     

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    • References(17)
  • [1]
    B. Y. Ye, M. Cirrincione, M. Pucci, and G. Cirrincione, “Speed sensorless control of induction motors based on MCA EXIN Pisarenko method,” in Proc. IEEE Conf. Energy Conversion Congress and Exposition, Sep. 2015, pp. 2176–2183.
    [2]
    Y. B. Gao, X. Y. Kong, H. H. Zhang, and L. A. Hou, “A weighted information criterion for multiple minor components and its adaptive extraction algorithms,” Neural Networks, vol. 89, no. 5, pp. 1–10, 2017.
    [3]
    Y. D. Jou, C. M. Sun, and F. K. Chen, “Eigenfilter design of FIR digital filters using minor component analysis,” in Proc. 9th Int. Conf. Communications and Signal Processing, Dec. 2013, pp. 1–5.
    [4]
    R. Wang, M. L. Yao, D. M. Zhang, and H. X. Zou, “A novel orthonormalization matrix based fast and stable DPM algorithm for principal and minor subspace tracking,” IEEE Trans. Signal Processing, vol. 60, no. 1, pp. 466–472, 2011.
    [5]
    R. Möller, “A self-stabilizing learning rule for minor component analysis,” Int. J. Neural Systems, vol. 14, no. 1, pp. 1–8, 2004. doi: 10.1142/S0129065704001863
    [6]
    Y. H. Shao, N. Y. Deng, W. J. Chen, and Z. Wang, “Improved generalized eigenvalue proximal support vector machine,” IEEE Signal Processing Letters, vol. 20, no. 3, pp. 213–216, 2013. doi: 10.1109/LSP.2012.2216874
    [7]
    M. Thameri, K. Abed-Meraim, and A. Belouchrani, “Low complexity adaptive algorithms for principal and minor component analysis,” Digital Signal Processing, vol. 23, pp. 19–29, 2013. doi: 10.1016/j.dsp.2012.09.007
    [8]
    T. D. Nguyen and I. Yamada, “A unified convergence analysis of normalized PAST algorithms for estimating principal and minor components,” Signal Processing, vol. 93, pp. 176–184, 2013. doi: 10.1016/j.sigpro.2012.07.020
    [9]
    P. J. Zufiria, “On the discrete-time dynamics of the basic Hebbian neural-network node,” IEEE Trans. Neural Networks, vol. 13, no. 6, pp. 1342–1352, 2002. doi: 10.1109/TNN.2002.805752
    [10]
    D. Z. Peng, Y. Zhang, Y. Xiang, and H. X. Zhang, “A globally convergent MC algorithm with an adaptive learning rate,” IEEE Trans. Neural Networks and Learning Systems, vol. 23, no. 2, pp. 359–365, 2012. doi: 10.1109/TNNLS.2011.2179310
    [11]
    T. D. Nguyen and I. Yamada, “Necessary and sufficient conditions for convergence of the DDT systems of the normalized PAST algorithms,” Signal Processing, vol. 94, pp. 288–299, 2014. doi: 10.1016/j.sigpro.2013.06.017
    [12]
    Y. B. Gao, X. Y. Kong, C. H. Hu, and L. A. Hou, “Modified Möller algorithm for multiple minor components extraction,” Control and Decision, vol. 32, no. 3, pp. 493–497, 2017.
    [13]
    R. Möller, Derivation of Coupled PCA and SVD Learning Rules from a Newton Zero-finding Framewor. Computer Engineering, Faculty of Technology, Bielefeld University, 2017.
    [14]
    G. ORegan, Matrix Theory. Switzerland: Springer International Publishing, 2016.
    [15]
    K. L. Du, and M. N. S. Swamy, Principal Component Analysis. Springer London, 2014.
    [16]
    Y. Zhang, Y. Mao, L. J. C. Lv., and K. K. Tan, “Convergence analysis of a deterministic discrete time system of Oja’s PCA learning algorithm,” IEEE Trans. Neural Networks, vol. 16, no. 6, pp. 1318–1328, 2005. doi: 10.1109/TNN.2005.852236
    [17]
    X. Y. Kong, C. H. Hu, and Z. S. Duan, Principal Component Analysis Networks and Algorithms. Springer Singapore, 2017.
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    Highlights

    • When the smallest eigenvalues are equal, the dynamic characteristic analysis of M?ller algorithm is finished.
    • Some conditions are drawn to guarantee the convergence of the Möller algorithm.
    • The range of the learning rate is expanded.

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