Abstract
Extracting independent source signals from their nonlinear mixtures is a very important issue in many realistic models. This paper proposes a new method for solving nonlinear blind source separation (NBSS) problems by exploiting particle swarm optimization (PSO) algorithm and natural gradient descent. First, we address the problem of separation of mutually independent sources in post-nonlinear mixtures. The natural gradient descent is used to estimate the separation matrix. Then we define the mutual information between output signals as the fitness function of PSO. The mutual information is used to measure the statistical dependence of the outputs of the demixing system. PSO can rapidly obtain the globally optimal coefficients of the higher order polynomial functions. Compared to conventional NBSS approaches, the main characteristics of this method are its simplicity, the rapid convergence and high accuracy. In particular, it is robust against local minima in search for inverse functions. Experiments are discussed to demonstrate these results.
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References
Cichocki, A., Amari, S.I.: Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. John Wiley and Sons, New York (2002)
Li, Y., Cichocki, A., Amari, S.: Blind Estimation of Channel Parameters and Source Components for EEG Signals: A Sparse Factorization Approach. IEEE Transactions on Neural Networks 17(2), 419–431 (2006)
Hyvärinen, A., Oja, E.: Independent Component Analysis: Algorithms and Applications. Neural Networks 13(4-5), 411–430 (2000)
Zhang, L., Amari, S., Cichocki, A.: Equi-convergence Algorithm for Blind Separation of Sources with Arbitrary Distributions. In: Mira, J., Prieto, A.G. (eds.) IWANN 2001. LNCS, vol. 2085, pp. 826–833. Springer, Heidelberg (2001)
Bell, A., Sejnowski, T.J.: An Information-maximization Approach to Blind Separation and Blind Beconvolution. Neural Computation, 1129–1159 (1995)
Taleb, A., Jutten, C.: Source Separation in Post-nonlinear Mixtures. IEEE Transactions on Signal Processing 47(10), 2807–2820 (1999)
Yang, H.H., Amari, S., Cichocki, A.: Information-theoretic Approach to Blind Separation of Sources in Nonlinear Mixture. Signal Processing 64, 291–300 (1998)
Tan, Y., Wang, J., Zurada, J.M.: Nonlinear Blind Source Separation using a Radial Basis Function Network. IEEE Transactions on Neural Networks 12, 124–134 (2001)
Jutten, C., Karhunen, J.: Advances in Blind Source Separation (BSS) and Independent Component Analysis (ICA) for Nonlinear Mixtures. Int. J. of Neural Systems 14(5), 267–292 (2004)
Tan, Y., Wang, J.: Nonlinear Blind Source Separation using Higher Order Statistics and A Genetic Algorithm. IEEE Trans. Evol. Comput. 5, 600–612 (2001)
Rojas, F.: Blind Source Separation in Post-Nonlinear Mixtures Using Competitive Learning, Simulated Annealing, and a Genetic Algorithm. IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews 34(4), 407–416 (2004)
Amari, S.I.: Natural Gradient Works Efficiently in Learning. Neural Computation 10, 251–276 (1998)
Clerc, M., Kennedy, J.: The Particle Swarm: Explosion, Stability, and Convergence in A Multi-dimensional Complex Space. IEEE Trans. Evol. Comput. 6, 58–73 (2002)
Abraham, A., Grosan, C., Ramos, V.: Swarm Intelligence and Data Mining. Studies in Computational Intelligence, vol. 34. Springer, Heidelberg (2006)
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Song, K., Ding, M., Wang, Q., Liu, W. (2007). Blind Source Separation in Post-nonlinear Mixtures Using Natural Gradient Descent and Particle Swarm Optimization Algorithm. In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72395-0_89
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DOI: https://doi.org/10.1007/978-3-540-72395-0_89
Publisher Name: Springer, Berlin, Heidelberg
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