A Completed Adaptive De-mixing Algorithm on Stiefel Manifold for ICA

Authors: Jianwei Wu

Abstract:

Based on the one-bit-matching principle and by turning the de-mixing matrix into an orthogonal matrix via certain normalization, Ma et al proposed a one-bit-matching learning algorithm on the Stiefel manifold for independent component analysis [8]. But this algorithm is not adaptive. In this paper, an algorithm which can extract kurtosis and its sign of each independent source component directly from observation data is firstly introduced.With the algorithm , the one-bit-matching learning algorithm is revised, so that it can make the blind separation on the Stiefel manifold implemented completely in the adaptive mode in the framework of natural gradient.

Keywords: Independent component analysis, kurtosis, Stiefel manifold, super-gaussians or sub-gaussians.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082025

References:

[1] Cichocki, A.,Amari, S.I., 2002. Adaptive Blind Signal and Image Processing. John Wiley & Sons, Ltd.
[2] Hyv¨arinen, A., Karhunen, J., Oja, E., 2001. Independent component analysis. John Wiley and Sons. Inc.
[3] Amari, S.I., Cichocki, A., Yang, H. 1996. A new learning algorithm for blind separation of sources. Advances in neural information processing, 8 (pp.757-763).Combridge, MA:MIT Press..
[4] Cardoso, J. F.and Laheld, B. 1996. Equivalent adaptive source separation. IEEE Trans.Signal Processing, 44(12), 3017-3030.
[5] T. W. Lee, M.Girolami, T. J. Sejnouski. 1999. Independent component analysis using an extended infomax algorithm for mixed subgaussian and supergaussian sources. Neural Computation, 11(2),417-441.
[6] Xu, L., Cheung, C. C. and Amari, S. I. 1998. Learned parametric mixture based on ica algorithm. Neurocomputing, 22(1-3), 69-80.
[7] Choi, S., Cichocki, A. and Amari, S.I. 2000. Flexible Independent Component Analysis. Journal of VLSI Signal Processing, Vol.26, No.1,25-38.
[8] Jinwen Ma, Dengpan Gao, Fei Ge and Amari, S.I. 2006. A onebit- matching learning algorithm for independent component analysis. Independent Component Analysis and Blind Signal Separation: 6th Interenational Conference, ICA 2006, Charleston, sc, USA, March 5-8, 2006, 173-180.
[9] Cardoso, J. F. 1989. Source separation using higher order moments. Proc.IEEE ICASSP, vol. 4, 2109-2112.
[10] Jianwei Wu 2009. Estimating Source Kurtosis Directly from Observation Data for ICA. to be submmitted to Signal Processing.
[11] Jianwei Wu 2008. A de-mixing algorithm based on the second order sample moment for independent component analysis. International Conference on Signal Processing Proceedings. 56-59.