A class of complex ICA algorithms based on the kurtosis cost function

IEEE Transactions on Neural Networks

Volumn 19, Issue 3, 2008, Pages 408-420

  Li, Hualiang ^a   Adali, Tülay ^a  

^a University of Marylandw Baltimore County   (United States)

Author keywords

Complex independent component analysis; Complex Newton update; Fixed point update

Indexed keywords

ALGORITHMS; CONJUGATE GRADIENT METHOD; COST FUNCTIONS; DIFFERENTIAL EQUATIONS; NEWTON-RAPHSON METHOD;

COMPLEX NEWTON UPDATE; FIXED-POINT UPDATE;

INDEPENDENT COMPONENT ANALYSIS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; HUMAN; NONLINEAR SYSTEM; SIGNAL PROCESSING;

ALGORITHMS; HUMANS; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 41049111573     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2007.908636     Document Type: Article

References (42)

1. T. Adali, T. Kim, and V. Calhoun, "Independent component analysis by complex nonlinearities," in Proc. Int. Conf. Acoust. Speech Signal Process., Montreal, ON, Canada, May 2004, vol. 5, pp. 525-528.
2. T. Adali and H. Li, "A practical formulation for computation of complex gradients and its application to maximum likelihood," in Proc. IEEE Int. Conf. Acoust. Speech Signal Process., Honolulu, HI, Apr. 2007, vol. 2, pp. 633-636.
3. J. Anemüller, T. Sejnowski, and S. Makeig, "Complex independent component analysis of frequency-domain electroencephalographic data," Neural Netw., vol. 16, pp. 1311-1323, Nov. 2003.
4. T. J. Abatzoglou, J. M. Mendel, and G. A. Harada, "The constrained total least squares technique and its applications to harmonic superresolution," IEEE Trans. Signal Process., vol. 39, no. 5, pp. 1070-1087, May 1991.
5. S.-I. Amari, "Natural gradient works efficiently in learning," Neural Comput., vol. 10, pp. 251-276, 1998.
6. S.-I. Amari, A. Cichocki, and H. Yang, "A new learning algorithm for blind signal separation," in Proc. Neural Inf. Process. Syst., 1996, vol. 8, pp. 757-763.
7. E. Bingham and A. Hyvarinen, "A fast fixed-point algorithm for independent component analysis of complex valued signals," Int. J. Neural Syst., vol. 10, pp. 1-8, Feb. 2000.
8. A. Bell and T. Sejnowski, "An information maximization approach to blind separation and blind deconvolution," Neural Comput., vol. 7, pp. 1129-1159, Nov. 1995.
9. D. Brandwood, "A complex gradient operator and its application in adaptive array theory," Proc. Inst. Electr. Eng., vol. 130, pp. 11-16, Feb. 1983.
10. A. V. D. Bos, "Complex gradient and Hessian," Proc. Inst. Elec. Eng., Vision, Image, Signal Process., vol. 141, pp. 380-382, Dec. 1994.
11. A. V. D. Bos, "Estimation of complex parameters," in Proc. 10th Int. Federation Autom. Control (IFAC) Symp. Identif., 1994, vol. 3, pp. 495-499.
12. V. Calhoun and T. Adali, "Complex Infomax: Convergence and approximation of Infomax with complex nonlinearities," in Proc. Neural Netw. Signal Process., Martigny, Switzerland, Sep. 2002, pp. 307-316.
13. J.-F. Cardoso and A. Souloumiac, "Blind beamforming for non-Gaussian signals," Proc. Inst. Electr. Eng. Radar Signal Process., vol. 140, pp. 362-370, 1993.
14. J.-F. Cardoso and T. Adali, "The maximum likelihood approach to complex ICA," in Proc. Int. Conf. Acoust. Speech Signal Process., Toulouse, France, May 2006, pp. 673-676.
15. J.-F. Cardoso and B. Laheld, "Equivariant adaptive source separation," IEEE Trans. Signal Process., vol. 44, no. 12, pp. 3017-3030, Dec. 1996.
16. P. Comon, "Independent component analysis, A new concept?," Signal Process., vol. 36, pp. 287-314, 1994.
17. L. Castedo, C. J. Escudero, and A. Dapena, "A blind signal separation method for multiuser communications," IEEE Trans. Signal Process. vol. 45, no. 5, pp. 1343-1348, May 1997.
18. S. Douglas, "On the convergence behavior of the FastICA algorithm," in Proc. Int. Symp. Independent Component Anal. Blind Signal Separat. Apr. 2003, pp. 409-414.
19. J. Eriksson and V. Koivunen, "Complex-valued ICA using second order statistics," in Proc. Workshop Mach. Learn. Signal Process., Saõ Luis, Brazil, 2004, pp. 183-191.
20. J. Eriksson, A.-M. Seppola, and V. Koivunen, "Complex ICA for circular and non-circular sources," in Proc. 13th Eur. Signal Process. Conf. (EUSIPCO), Antalaya, Turkey, Sep. 2005.
21. A. Hyvarinen and E. Oja, "A fast fixed-point algorithm for independent component analysis," Neural Comput., vol. 9, pp. 1483-1492, 1997.
22. A. Hyvarinen, "Fast and robust fixed-point algorithms for independent component analysis," IEEE Trans. Neural Netw., vol. 10, no. 3, pp. 626-634, May 1999.
23. A. Hyvarinen, J. Karhunen, and E. Oja, Independent Component Analysis New York: Wiley, 2001.
24. I. N. Herstein, Topics in Algebra. Lexington, MA: Xerox College Publishing, 1964.
25. R. A. Horn and C. R. Johnson, Matrix Analysis. New York: Cambridge Univ. Press, 1988.
26. Z. Koldovsky, P. Tichavsky, and E. Oja, "Efficient variant of algorithm FastICA for independent component analysis attaining the Cramer-Rao lower bound," IEEE Trans. Neural Netw., vol. 17, no. 5, pp. 1265-1277, Sep. 2006.
27. M. Mboup and P. A. Regalia, "A gradient search interpretation of the super-exponential algorithm," IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2731-2734, Nov. 2000.
28. M. Novey and T. Adali, "ICA by maximization of non-Gaussianity using complex functions," in Proc. Workshop Mach. Learn. Signal Process. Sep. 2005, pp. 21-26.
29. J. Nocedal and S. J. Wright, Numerical Optimization. New York: Springer-Verlag, 2000.
30. F. Neeser and J. Massey, "Proper complex random processes with applications to information theory," IEEE Trans. Inf. Theory, vol. 39, no. 4, pp. 1293-1302, Jul. 1993.
31. E. Oja, "Convergence of the symmetrical FastICA algorithm," in Proc. 9th Int. Conf. Neural Inf. Process., 2002, pp. 1368-1372.
32. E. Oja and Z. Yuan, "The FastICA algorithm revisited: Convergence analysis," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1370-1381, Nov. 2006.
33. C. Papadias, "Globally convergent blind source separation based on a multiuser kurtosis optimization criterion," IEEE Trans. Signal Process., vol. 48, no. 12, pp. 3508-3519, Dec. 2000.
34. K. B. Petersen and M. S. Pedersen, "The Matrix Cookbook," IMM, DTU, 2005, [Online]. Available: http://matrixcookbook.com/
35. R. Prasad, H. Saruwatari, A. Lee, and K. Shikano, "A fixed-point ICA algorithm for convoluted speech signal separation," in Proc. Int. Symp. Independent Component Anal. Blind Signal Separat., Apr. 2003, pp. 579-584.
36. P. A. Regalia and E. Kofidis, "Monotonic convergence of fixed-point algorithms for ICA," IEEE Trans. Neural Netw., vol. 14, no. 4, pp. 943-949, Jul. 2003.
37. R. Remmert, Theory of Complex Functions. New York: Springer-Verlag, 1991.
38. O. Shalvi and E. Weinstein, "New criteria for blind deconvolution of nonminimum phase systems (channels)," IEEE Trans. Inf. Theory, vol. 36, no. 2, pp. 312-321, Mar. 1990.
39. C. Therrien, Discrete Random Signals and Statistical Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1992.
40. G. Yan and H. Fan, "A Newton-like algorithm for complex variables with application in blind equalization," IEEE Trans. Signal Process., vol. 48, no. 2, pp. 553-556, Feb. 2000.
41. H. Sawada, R. Mukai, S. Araki, and S. Makino, "A polar-coordinate based activation function for frequency domain blind source separation," in Proc. Int. Conf. Acoust. Speech Signal Process., Orlando, FL, May 2002, pp. I-1001-I-1004.
42. T. Kim and T. Adali, "Approximation by fully-complex multilayer perceptrons," Neural Comput., vol. 15, no. 7, pp. 1641-1666, Jul. 2003.