Abstract
It is well known that principal component analysis (PCA) only considers the second-order statistics and that independent component analysis (ICA) exploits higher-order statistics of the data. In this paper, for whitened data, we give an elegant way to incorporate higher-order statistics implicitly in the form of second-order moments, and show that ICA can be performed by PCA following a simple transformation. This method is termed P-ICA. Kurtosis-based P-ICA is equivalent to the fourth-order blind identification (FOBI) algorithm [2]. Analysis of the transformation form enables us to give the robust version of P-ICA, which exploits the trade-off of all even order statistics of sources. Experimental comparisons of P-ICA with the prevailing ICA methods are presented. The main advantage of P-ICA is that it enables any PCA system, especially the dedicated hardware, to perform ICA after slight modification.
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References
Amari, S., Cichocki, A., Yang, H.H.: A new learning algorithm for blind signal separation. In: Advances in Neural Information Processing Systems (1996)
Cardoso, J.F.: Source separation using higher order moments. In: ICASSP 1989, pp. 2109–2112 (1989)
Cardoso, J.F., Souloumiac, A.: Blind beamforming for non-Gaussian signals. IEE Proceeding-F 140(6), 362–370 (1993)
Comon, P.: Separatin of stochastic processes. In: Proceedings of the Workshop on Higher-Order Spectral Analysis, Vail, Colorado, USA, June 1989, pp. 174–179 (1989)
Cornish, E.A., Fisher, R.A.: Moments and cumulants in the specification of distributions. Review of the International Statistical Institute 5, 307–320 (1937)
Harroy, F., Lacoume, J.L.: Maximum likelihood estimators and Cramer-Rao bounds in source separation. Signal Processing 55(2), 167–177 (1996)
Herrmann, F., Nandi, A.K.: Blind separation of linear instantaneous mixtures using closed-form estimators. Signal Processing 81, 1537–1556 (2001)
Hyvärinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks 10(3), 626–634 (1999a)
Lagrange, S., Jaulin, L., Vigneron, V., Jutten, C.: Analytical solution of the blind source separation problem using derivatives
Zarzoso, V., Nandi, A.K.: Closed-form estimators for blind separation of sources—part I: Real mixtures. Wireless Personal Communications 21, 5–28 (2002)
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© 2006 Springer-Verlag Berlin Heidelberg
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Zhang, K., Chan, LW. (2006). ICA by PCA Approach: Relating Higher-Order Statistics to Second-Order Moments. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_39
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DOI: https://doi.org/10.1007/11679363_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32630-4
Online ISBN: 978-3-540-32631-1
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