International Journal of Computer Network and Information Security (IJCNIS)
IJCNIS Vol. 2, No. 1, 8 Nov. 2010
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Nonlinear Blind Source Separation Using Kernel Multi-set Canonical Correlation Analysis
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Author(s)
Hua-Gang Yu
1,*
Gao-Ming Huang
1
Jun Gao
1
Index Terms
Nonlinear blind source separation, kernel feature spaces, multi-set canonical correlation analysis, reduced feature space, joint diagonalization
Abstract
To solve the problem of nonlinear blind source separation (BSS), a novel algorithm based on kernel multi-set canonical correlation analysis (MCCA) is presented. Combining complementary research fields of kernel feature spaces and BSS using MCCA, the proposed approach yields a highly efficient and elegant algorithm for nonlinear BSS with invertible nonlinearity. The algorithm works as follows: First, the input data is mapped to a high-dimensional feature space and perform dimension reduction to extract the effective reduced feature space, translate the nonlinear problem in the input space to a linear problem in reduced feature space. In the second step, the MCCA algorithm was used to obtain the original signals.
Cite This Paper
Hua-Gang Yu, Gao-Ming Huang, Jun Gao, "Nonlinear Blind Source Separation Using Kernel Multi-set Canonical Correlation Analysis", International Journal of Computer Network and Information Security(IJCNIS), vol.2, no.1, pp.1-8, 2010. DOI:10.5815/ijcnis.2010.01.01
Reference
[1] S. Amari, A. Cichocki, H. -M. Park and S. -Y. Lee, “Blind source separation and independent component analysis: a review,” Neural Information Processing-Letters and Reviews, vol. 6, No. 1, pp. 1-57, Jan. 2005.
[2] C. Jutten, J. Karhunen, “Advances in Nonlinear Blind Source separation,” Proc. of 4th Int. Symposium on ICA and BSS (ICA2003), pp. 245-256, Nara, Japan, 2003.
[3] D. Martinez, A. Bray, “Nonlinear blind source separation using kernels,” IEEE Trans. Neural Networks, vol.14, No. 1, pp. 228–235, Jan. 2003.
[4] S. Harmeling, A. Ziehe, M. Kawanabe, K. -R. Muller, “Kernel-based nonlinear blind source separation,” Neural Computation, vol.15, No. 1, pp. 1089-1124, 2003.
[5] H.Hotelling, “Relations between two sets of variates,” Biometrika, vol. 28, pp. 312–377, 1936.
[6] D. R. Hardoon, S. Szedmak and J. Shawe-Taylor, “Canonical correlation analysis: an overview with application to learning methods,” Neural Computation, vol. 16, pp. 2639–2664, 2004.
[7] S. Y. Huang, M. H. Lee and C. K. Hsiao, “Nonlinear measures of association with kernel canonical correlation analysis and applications,” Journal of Statistical Planning and Inference, vol. 139, pp. 2162–2174, 2009.
[8] J. Via, I. Santamaria, and J. Perez, “Deterministic CCA-Based Algorithms for Blind Equalization of FIR-MIMO Channels,” IEEE Transactions on Signal Processing, vol. 55, pp. 3867-3878, 2007.
[9] W. Liu, D. P. Mandic, and A. Cichocki, “Analysis and Online Realization of the CCA Approach for Blind Source Separation,” IEEE Transactions on Neural Networks, vol. 18, pp. 1505-1510, 2007.
[10] Y. -O Li, T. Adali, W. Wang, and V. D. Calhoun, “Joint blind source separation by multiset canonical correlation analysis,” IEEE Transactions on Signal Processing, vol. 57, pp. 3918-3929, 2009.
[11] M. Borga and H. Knutsson, “A canonical correlation approach to blind source separation,” Dept. Biomed. Eng., Linkoping Univ., Linkoping, Sweden, Tech. Rep. LiU-IMT-EX-0062, Jun. 2001.
[12] J. Kettenring, “Canonical analysis of several sets of variables,” Biometrika, vol. 58, pp. 433-451, 1971.
[13] H. G. Yu, G. M. Huang, J. Gao, “Multiset Canonical Correlation Analysis Using for Blind Source Separation,” The 3rd International Conference on Networks Security, Wireless Communications and Trusted Computing, in press.
[14] A. Ziehe, P. Laskov, G. Nolte, and K.-R. Múller, “A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation,” J. Mach. Learn. Res., vol. 5, pp. 777–800, 2004.
[15] S. Degerine and E. Kane, “A Comparative Study of Approximate Joint Diagonalization Algorithms for Blind Source Separation in Presence of Additive Noise,” IEEE Transactions on Signal Processing, vol. 55 pp. 3022-3031, 2007.
[16] A. Talab, C. Jutten, “Source separation in post-nonlinear mixtures,” IEEE Transactions on Neural Networks, vol. 47, no. 10, pp. 2807-2820, Oct. 1999.
[17] A. Cichocki. and S. Amari, Adaptive blind signal and image processing. New York, USA: Wiley, 2002, pp. 161-162.
[18] G. M. Huang, L. X. Yang, Z. Y. He, “Blind Source Separation Based on Generalized Variance,” ISNN2006, LNCS, Vol.3971, pp. 496-501, 2006.