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摘要
Independent component analysis (ICA) is one of the most powerful methods for solving blind source separation problem. In various ICA methods, the Fast-ICA is an excellent algorithm, and it finds the demixing matrix that optimizes the nonlinear contrast function. There are three original contrast functions in the Fast-ICA to separate super-Gaussian and sub-Gaussian sources, and their respective derivatives are similar to nonlinearities used in neural networks. For the separation of large-scale super-Gaussian sources, however, the contrast functions and the nonlinearities are not optimal owing to high computational cost. To solve this potential problem, this paper proposes four rational polynomial functions to replace the original nonlinearities. Because the rational polynomials can be quickly evaluated, when they are used in the Fast-ICA, the computational load of the algorithms can be effectively reduced. The proposed rational functions are derived by the Pade approximant from Taylor series expansion of the original nonlinearities. To reduce the error of approximation, we make the behaviors of rational functions approach that of the original ones within an effective range as well as possible. The simulation results show that the Fast-ICA algorithms with rational nonlinearities not only can speed up the convergence but also improve the separation performance of super-Gaussian blind source separation.
