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Adaptive Step-Size Natural Gradient ICA Algorithm with Weighted Orthogonalization

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Abstract

To improve the stability of the traditional natural gradient independent component analysis (ICA) algorithm and the accuracy of its separated results, a adaptive step-size natural gradient ICA algorithm with weighted orthogonalization is proposed. First, to take advantage of the pre-whitening pre-processing and keep the equivariance property of the ICA algorithm, based on the weighted orthogonal constraint on the separating matrix without pre-whitening of observed signals, weighted orthogonalization is introduced after the traditional gradient update. Then, according to the error estimation from the smoothed distance between separated outputs and optimal outputs, we obtain two adaptive step sizes based, respectively, on an unconstrained natural gradient ICA process and a weighted orthogonalization process. Simulation experiment results show that the speed of convergence of the adaptive step-size natural gradient ICA algorithms with weighted orthogonalization are faster than the traditional one; also, the stability of the algorithms and the accuracy of the separated results are improved observably.

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References

  1. S.I. Amari, Natural gradient works efficiently in learning. Neural Comput. 10(2), 251–276 (1998)

    Article  MathSciNet  Google Scholar 

  2. J.F. Cardoso, B.H. Laheld, Equivariant adaptive source separation. IEEE Trans. Signal Process. 44(12), 3017–3030 (1996)

    Article  Google Scholar 

  3. M.T. Chu, N.T. Trendafilov, On a differential equation approach to the weighted orthogonal Procrustes problem. Stat. Comput. 8(2), 125–133 (1998)

    Article  Google Scholar 

  4. A. Hyvrinen, E. Oja, A fast fixed-point algorithm for independent component analysis. Neural Comput. 9(7), 1483–1492 (1997)

    Article  Google Scholar 

  5. A. Hyvrinen, J. Karhunen, E. Oja, Independent Component Analysis (Wiley, New York, 2001)

    Book  Google Scholar 

  6. W. Lu, J.C. Rajapakse, Approach and applications of constrained ICA. IEEE Trans. Neural Netw. 16(1), 203–212 (2005)

    Article  Google Scholar 

  7. J.H. Manton, Optimization algorithms exploiting unitary constraints. IEEE Trans. Signal Process. 50(3), 635–650 (2002)

    Article  MathSciNet  Google Scholar 

  8. W.B. Mikhael, R. Ranganathan, T. Yang, Complex adaptive ICA employing the conjugate gradient technique for signal separation in time-varying flat fading channels. Circuits Syst. Signal Process. 29(3), 469–480 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  9. T.P. von Hoff, A.G. Lindgren, Adaptive step-size control in blind source separation. Neurocomputing 49(1–4), 119–138 (2002)

    Article  MATH  Google Scholar 

  10. H.H. Yang, Serial updating rule for blind separation derived from the method of scoring. IEEE Trans. Signal Process. 47(8), 2279–2285 (1999)

    Article  Google Scholar 

  11. H.H. Yang, S.I. Amari, Adaptive on-line learning algorithms for blind separation: maximum entropy and minimum mutual information. Neural Comput. 9(7), 1457–1482 (1997)

    Article  Google Scholar 

  12. J.M. Ye, T. Huang, New fast-ICA algorithms for blind source separation without prewhitening. Appl. Inf. Commun. 225, 579–585 (2011)

    Article  Google Scholar 

  13. J.M. Ye, H.H. Jin, Q.R. Zhang, Adaptive weighted orthogonal constrained algorithm for blind source separation. Digit. Signal Process. 23, 514–521 (2013)

    Article  MathSciNet  Google Scholar 

  14. L.X. Yuan, W.W. Wang, J.A. Chambers, Variable step-size sign natural gradient algorithm for sequential blind source separation. IEEE Signal Process. Lett. 12(8), 589–592 (2005)

    Article  Google Scholar 

  15. X.D. Zhang, X.L. Zhu, Z. Bao, Grading learning for blind source separation. Sci. China, Ser. F 46(1), 31–44 (2003)

    Article  MATH  Google Scholar 

  16. Y.G. Zhang, N. Li, J.A. Chambers et al., New gradient-based variable step-size LMS algorithms. EURASIP J. Adv. Signal Process. 2008(105) (2008)

  17. W.T. Zhang, N. Liu, S.T. Lou, Joint approximate diagonalization using bilateral rank-reducing householder transform with application in blind source separation. Chin. J. Electron. 18(3), 471–476 (2009)

    Google Scholar 

  18. X.L. Zhu, X.D. Zhang, Blind source separation based on optimally selected estimating functions. J. Xidian Univ. 30(3), 335–339 (2003)

    Google Scholar 

  19. X.L. Zhu, X.D. Zhang, Z.Z. Ding et al., Adaptive nonlinear PCA algorithms for blind source separation without prewhitening. IEEE Trans. Circuits Syst. 53(3), 745–753 (2006)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under grants 61075117, 11101322.

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Authors and Affiliations

  1. School of Science, Xidian University, Xi’an, 710071, China

    Xingjia Tang, Xiufang Zhang & Jimin Ye

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  1. Xingjia Tang
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  2. Xiufang Zhang
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  3. Jimin Ye
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Correspondence to Xingjia Tang.

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Tang, X., Zhang, X. & Ye, J. Adaptive Step-Size Natural Gradient ICA Algorithm with Weighted Orthogonalization. Circuits Syst Signal Process 33, 211–221 (2014). https://doi.org/10.1007/s00034-013-9624-1

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  • DOI: https://doi.org/10.1007/s00034-013-9624-1

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