Neural Processing Letters

, Volume 25, Issue 2, pp 91–110 | Cite as

Robust Prewhitening for ICA by Minimizing β-Divergence and Its Application to FastICA

  • Md Nurul Haque Mollah
  • Shinto Eguchi
  • Mihoko Minami


Many estimation methods for independent component analysis (ICA) requires prewhitening of observed signals. This paper proposes a new method of prewhitening named β-prewhitening by minimizing the empirical β-divergence over the space of all the Gaussian distributions. The value of the tuning parameter β plays the key role in the performance of our current proposal. An attempt is made to propose an adaptive selection procedure for the tuning parameter β for this algorithm. At last, a measure of performance index is proposed for assessing prewhitening procedures. Simulation results show that β-prewhitening efficiently improves the performance over the standard prewhitening when outliers exist; it keeps equal performance otherwise. Performance of the proposed method is compared with the standard prewhitening by both FastICA and our proposed performance index.


independent component analysis β-prewhitening robustness adaptive selection one standard error 


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  1. 1.
    Belouchrani A., Cichocki A. (2000) Robust whitening procedure in blind source separation context. Electronics Letters 36(24): 2050–2053CrossRefGoogle Scholar
  2. 2.
    Choi S., Cichocki A., Belouchrani A. (2002) Second order nonstationary source separation. Journal of VLSI Signal Processing 32(1–2): 93–104MATHGoogle Scholar
  3. 3.
    Cichocki A., Amari S. (2002) Adaptive Blind Signal and Image Processing. Wiley, New YorkGoogle Scholar
  4. 4.
    Cardoso J.-F., Laheld B.H. (1996) Equivariant adaptive source separation. IEEE Trans. on Signal Processing 44(12): 3017–3030CrossRefGoogle Scholar
  5. 5.
    Cardoso, J.-F.: Source separation using high order moments, In: Proceedings of IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP’89), pp. 2109–2112, Glasgow, UK, 1989. Neural Computation 11 (1999), 157–192.Google Scholar
  6. 6.
    Hampel F.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.A. (1986) Robust Statistics: The Approach Based on Influence Functions. Wiley, New YorkMATHGoogle Scholar
  7. 7.
    Hastie T., Tibshirani R., Friedman J. (2001) The Elements of Statistical Learning. Springer, New YorkMATHGoogle Scholar
  8. 8.
    Hyvärinen, A.: One-unit contrast functions for independent component analysis: A statistical analysis, In: Neural Networks for Signal Processing VII (Proceedings of IEEE Workshop on Neural Networks for Signal Processing). pp. 388–397, Amelia Island,Google Scholar
  9. 9.
    Hyvärinen A. (1999) Fast and robust fixed-point algorithms for independent component , IEEE Trans. on Neural Network 10(3): 626–34CrossRefGoogle Scholar
  10. 10.
    Hyvärinen A., Oja E. (1997) A fast fixed-point algorithm for independent component analysis. Neural Computation 9(7): 1483–1492CrossRefGoogle Scholar
  11. 11.
    Hyvärinen A, Karhunen J., Oja E. (2001) Independent Component Analysis. Wiley, New YorkGoogle Scholar
  12. 12.
    Minami M., Eguchi S. (2002) Robust Blind Source Separation by beta-Divergence. Neural Computation 14: 1859–1886MATHCrossRefGoogle Scholar
  13. 13.
    Minami, M. and Eguchi, S.: Adaptive selection for minimum β-divergence method, Proceedings of ICA-2003 Conference, Nara, JapanGoogle Scholar
  14. 14.
    Mollah M.N.H., Minami M., Eguchi S. (2006) Exploring Latent Structure of Mixture ICA Models by the Minimum β-Divergence Method. Neural Computation 18(1): 166–190MATHCrossRefGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Md Nurul Haque Mollah
    • 1
  • Shinto Eguchi
    • 2
  • Mihoko Minami
    • 2
  1. 1.Department of Statistical ScienceThe Graduate University for Advanced StudiesTokyoJapan
  2. 2.The Institute of Statistical MathematicsThe Graduate University for Advanced StudiesTokyoJapan

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