A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 3 Issue 2
Apr.  2016

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Xiaowei Feng, Xiangyu Kong and Hongguang Ma, "Coupled Cross-correlation Neural Network Algorithm for Principal Singular Triplet Extraction of a Cross-covariance Matrix," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 2, pp. 147-156, 2016.
Citation: Xiaowei Feng, Xiangyu Kong and Hongguang Ma, "Coupled Cross-correlation Neural Network Algorithm for Principal Singular Triplet Extraction of a Cross-covariance Matrix," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 2, pp. 147-156, 2016.

Coupled Cross-correlation Neural Network Algorithm for Principal Singular Triplet Extraction of a Cross-covariance Matrix

Funds:

This work was supported by National Natural Science Foundation of China (61174207,61374120,61074072,11405267).

  • This paper proposes a novel coupled neural network learning algorithm to extract the principal singular triplet (PST) of a cross-correlation matrix between two high-dimensional data streams. We firstly introduce a novel information criterion (NIC), in which the stationary points are singular triplet of the crosscorrelation matrix. Then, based on Newton's method, we obtain a coupled system of ordinary differential equations (ODEs) from the NIC. The ODEs have the same equilibria as the gradient of NIC, however, only the first PST of the system is stable (which is also the desired solution), and all others are (unstable) saddle points. Based on the system, we finally obtain a fast and stable algorithm for PST extraction. The proposed algorithm can solve the speed-stability problem that plagues most noncoupled learning rules. Moreover, the proposed algorithm can also be used to extract multiple PSTs effectively by using sequential method.

     

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  • [1]
    Kaiser A, Schenck W, Möoller R. Coupled singular value decomposition of a cross-covariance matrix. International Journal of Neural Systems, 2010, 20(4): 293-318
    [2]
    Cochocki A, Unbehauen R. Neural Networks for Optimization and Signal Processing. New York: John Wiley, 1993.
    [3]
    Yuille A L, Kammen D M, Cohen D S. Quadrature and the development of orientation selective cortical cells by Hebb rules. Biological Cybernetics, 1989, 61(3): 183-194
    [4]
    Feng D Z, Bao Z, Zhang X D. A cross-associative neural network for SVD of non-squared data matrix in signal processing. IEEE Transactions on Neural Networks, 2001, 12(5): 1215-1221
    [5]
    Diamantaras K I, Kung S Y. Cross-correlation neural network models. IEEE Transactions on Signal Processing, 1994, 42(11): 3218-3223
    [6]
    Bunch J R, Nielsen C P. Updating the singular value decomposition. Numerische Mathematik, 1978, 31(2): 111-129
    [7]
    Comon P, Golub G H. Tracking a few extreme singular values and vectors in signal processing. Proceedings of the IEEE, 1990, 78(8): 1327-1343
    [8]
    Ferzali W, Proakis J G. Adaptive SVD algorithm for covariance matrix eigenstructure computation. In: Proceedings of the 1990 International Conference on Acoustics, Speech, and Signal Processing. Albuquerque, NM: IEEE, 1990. 2615-2618
    [9]
    Moonen M, Van Dooren P, Vandewalle J. A singular value decomposition updating algorithm for subspace tracking. SIAM Journal on Matrix Analysis and Applications, 1992, 13(4): 1015-1038
    [10]
    Helmke U, Moore J B. Singular-value decomposition via gradient and self-equivalent flows. Linear Algebra and Its Applications, 1992, 169: 223-248
    [11]
    Moore J B, Mahony R E, Helmke U. Numerical gradient algorithms for eigenvalue and singular value calculations. SIAM Journal on Matrix Analysis and Applications, 1994, 15(3): 881-902
    [12]
    Hori G. A general framework for SVD flows and joint SVD flows. In: Proceedings of the 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing. Hong Kong: IEEE, 2003. II-693-6
    [13]
    Feng D Z, Bao Z, Shi W X. Cross-correlation neural network models for the smallest singular component of general matrix. Signal Processing, 1998, 64(3): 333-346
    [14]
    Feng D Z, Zhang X D, Bao Z. A neural network learning for adaptively extracting cross-correlation features between two high-dimensional data streams. IEEE Transactions on Neural Networks, 2004, 15(6): 1541-1554
    [15]
    Hasan M A. A logarithmic cost function for principal singular component analysis. In: Proceedings of the 2008 IEEE International Conference on Acoustics, Speech, and Signal Processing. Las Vegas, NV: IEEE, 2008. 1933-1936
    [16]
    Kong X Y, Ma H G, An Q S, Zhang Q. An effective neural learning algorithm for extracting cross-correlation feature between two highdimensional data streams. Neural Processing Letters, 2015, 42(2): 459-477
    [17]
    Cheng L, Hou Z G, Tan M. A simplified neural network for linear matrix inequality problems. Neural Processing Letters, 2009, 29(3): 213-230
    [18]
    Cheng L, Hou Z G, Lin Y, Tan M, Zhang W C, Wu F X. Recurrent neural network for non-smooth convex optimization problems with application to the identification of genetic regulatory networks. IEEE Transactions on Neural Networks, 2011, 22(5): 714-726
    [19]
    Liu Q S, Huang T W, Wang J. One-layer continuous-and discretetime projection neural networks for solving variational inequalities and related optimization problems. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(7): 1308-1318
    [20]
    Möoller R, Köonies A. Coupled principal component analysis. IEEE Transactions on Neural Networks, 2004, 15(1): 214-222
    [21]
    Noble B, Daniel J W. Applied Linear Algebra (Third edition). Englewood Cliffs, NJ: Prentice Hall, 1988.
    [22]
    Hotelling H. Some new methods in matrix calculation. The Annals of Mathematical Statistics, 1943, 14(1): 1-34
    [23]
    Hotelling H. Further points on matrix calculation and simultaneous equations. The Annals of Mathematical Statistics, 1943, 14(4): 440-441

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