A generalized minor component extraction algorithm and its convergence analysis

DU Bo-yang1 KONG Xiang-yu1 FENG Xiao-wei1 GAO Ying-bin1 LUO Jia-yu1

(1.College of Missile Engineering, The Rocket Force University of Engineering, Xi’an, Shaanxi Province, China 710025)

【Abstract】Generalized minor component analysis (GMCA) has played a vital role in many areas of modern signal processing. Up to now, few algorithms can possess four properties together, which are the information criterion corresponding to the algorithm, convergence, self-stabilizing, and ability of extracting multiple generalized minor components (GMCs). To deal with this problem, a novel information criterion is proposed and based on the criterion, an algorithm for GMCs extraction is derived. Then, the global convergence of the algorithm is analyzed with the deterministic discrete time method. Besides, self-stability is illustrated through theoretical research on the relationship between the convergence ability and the initial state of the algorithm. Furthermore, the application of the algorithm in multiple GMCs extraction is employed. In contrast with the existing algorithms, the proposed algorithm is the best of its kind in convergence speed. The properties of the algorithm are verified through MATLAB simulation.

【Keywords】 generalized minor component analysis (GMCA); deterministic discrete time (DDT); convergence analysis; self-stabilizing property;

【DOI】

【Funds】 National Natural Science Foundation of China (61374120, 61673387)

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    References

    [1] Gao K, Ahmad M O, Swamy M. Learning algorithm for total least-squares adaptive signal processing [J]. Electronics Letters, 1992, 28 (4): 430–432.

    [2] Feng D Z, Zheng W X, Jia Y. Neural network learning algorithms for tracking minor subspace in high-dimensional data stream [J]. IEEE Transactions on Neural Networks, 2005, 16 (3): 513–521.

    [3] Mathew G, Reddy V U, Development and analysis of a neural network approach to pisarenko’s harmonic retrieval method [J]. IEEE Transactions on Signal Processing, 1994, 42 (3): 663–667.

    [4] Wang R, Yao M L, Cheng Z, et al. Interference cancellation in GPS receiver using noise subspace tracking algorithm [J]. Signal Processing, 1994, 91 (2): 338–343.

    [5] Ye M, Liu Y, Wu H, et al. A few online algorithms for extracting minor generalized eigenvectors [C]. IEEE international Joint Conference on Neural Networks. Hong Kong: IEEE, 2008: 1714–1720.

    [6] Nguyen T D, Takahashi N, Yamada I. An adaptive extraction of generalized eigen subspace by using exact nested orthogonal complement structure [J]. Multidimensional System on Signal Processing, 2013, 24: 457–483.

    [7] Yang B. Projection approximation subspace tracking [J]. IEEE Transactions on Signal Processing, 1995, 43 (1): 95–107.

    [8] Yang J, Xi H, Yang F, et al. RLS-based adaptive algorithms for generalized eigen decomposition [J]. IEEE Transactions on Signal Processing, 2006, 54 (4): 1177–1188.

    [9] Sakai H, Shimizu K. A new adaptive algorithm for minor component analysis [J]. Signal Processing, 1998, 71: 301–308.

    [10] Nguyen T D, Yamada I. A unified convergence analysis of normalized PAST algorithms for estimating principal and minor components [J]. Signal Processing, 2013, 93 (1): 176–184.

    [11] Cirrincione G, Cirrincione M, Hérault J, et al. The MCAEXIN neuron for the minor component analysis [J]. IEEE Transactions on Neural Networks, 2002, 13 (1): 160–187.

    [12] Möller R, Könies A. Coupled principal component analysis [J]. IEEE Transactions on Neural Networks, 2004, 15 (1): 214–222.

    [13] Peng D, Zhang Y. Convergence analysis of a deterministic discrete time system of Feng’s MCAlearning algorithm [J]. IEEE Transactions on Signal Processing, 2006, 54 (9): 3626–3632.

    [14] Li H Z, Du B Y, Kong X Y, et al. A generalized minor component extraction algorithm and its analysis [J]. IEEE Access, 2018, 99 (7): 1–8.

    [15] Ouyang S, Bao Z, Liao G, et al. Adaptive minor component extraction with modular structure [J]. IEEE Transactions on Signal Processing, 2001, 49 (9): 2127–2137.

    [16] Toshihisa T. Fast generalized eigenvector tracking based on the power method [J]. IEEE Signal Processing Letters, 2009, 16 (11): 969–972.

    [17] Golub G H, Van Loan C F. Matrix computations [M]. 4th ed. Baltimore: Johns Hopkins University Press, 2013: 71–76.

    [18] Shougen W, Shuqin Z. An algorithm for Ax = λBx with symmetric and positive-definite A and B [J]. SIAM Journal of Matrix Analysis and Applications, 1991, 12: 654–660.

    [19] Dong H D, Liu G, He B, et al. Multiple minor generalized eigenvectors extraction information and its adaptive algorithm [J]. Control and Decision, 2019, 34 (1): 105–112 (in Chinese).

This Article

ISSN:1001-0920

CN: 21-1124/TP

Vol 35, No. 06, Pages 1505-1511

June 2020

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Abstract

  • 0 Introduction
  • 1 The proposed algorithm
  • 2 Self-stability of the proposed algorithm
  • 3 Convergence analysis of the proposed algorithm
  • 4 Multiple GMCs extraction
  • 5 Simulation examples
  • 6 Conclusions
  • References