采用Pade逼近的有理非线性Fast-ICA

Fast-ICA with rational nonlinearity based on Pade approximation

针对快速独立分量分析(fast independent component analysis, Fast-ICA)算法中非线性(nonlinearity)本身的计算负担会造成算法收敛速度下降的问题,提出一种有理多项式函数替代经典非线性的方法。通过将传统的非线性进行泰勒级数展开,利用Pade逼近技术推导出相应的有理多项式函数。有理函数的分子采用一次多项式,而分母采用二次多项式,在保证有理函数为真分式的同时还简化了其计算。仿真结果表明,采用有理非线性的Fast-ICA算法不仅能够提高算法的收敛速度,而且还能提高算法的盲源分离(blind source separation, BSS)性能。

Aiming at the problem that the computational burden of nonlinearity in the fast independent component analysis(Fast-ICA) algorithm will reduce the convergence speed of the algorithm, a rational polynomial function is proposed to replace the classical nonlinearity. Through the Taylor series expansion of the traditional nonlinear, the corresponding rational polynomial function is derived by using the Pade approximation technique. The numerator of a rational function adopts a first-order polynomial, and the denominator adopts a second-order polynomial, which simplifies its calculation while ensuring that the rational function is a true fraction. The simulation results show that the rational nonlinear Fast-ICA algorithm can not only improve the convergence speed of the algorithm, but also improve the blind source separation(BSS) performance of the algorithm.