Abstract
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.
Similar content being viewed by others
References
Belouchrani A., Cichocki A. (2000) Robust whitening procedure in blind source separation context. Electronics Letters 36(24): 2050–2053
Choi S., Cichocki A., Belouchrani A. (2002) Second order nonstationary source separation. Journal of VLSI Signal Processing 32(1–2): 93–104
Cichocki A., Amari S. (2002) Adaptive Blind Signal and Image Processing. Wiley, New York
Cardoso J.-F., Laheld B.H. (1996) Equivariant adaptive source separation. IEEE Trans. on Signal Processing 44(12): 3017–3030
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.
Hampel F.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.A. (1986) Robust Statistics: The Approach Based on Influence Functions. Wiley, New York
Hastie T., Tibshirani R., Friedman J. (2001) The Elements of Statistical Learning. Springer, New York
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,
Hyvärinen A. (1999) Fast and robust fixed-point algorithms for independent component , IEEE Trans. on Neural Network 10(3): 626–34
Hyvärinen A., Oja E. (1997) A fast fixed-point algorithm for independent component analysis. Neural Computation 9(7): 1483–1492
Hyvärinen A, Karhunen J., Oja E. (2001) Independent Component Analysis. Wiley, New York
Minami M., Eguchi S. (2002) Robust Blind Source Separation by beta-Divergence. Neural Computation 14: 1859–1886
Minami, M. and Eguchi, S.: Adaptive selection for minimum β-divergence method, Proceedings of ICA-2003 Conference, Nara, Japan
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): 166–190
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mollah, M.N.H., Eguchi, S. & Minami, M. Robust Prewhitening for ICA by Minimizing β-Divergence and Its Application to FastICA. Neural Process Lett 25, 91–110 (2007). https://doi.org/10.1007/s11063-006-9023-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-006-9023-8