Improved post-nonlinear independent component analysis method based on Gaussian Mixture Model

For conventional post-nonlinear independent component analysis (ICA) methods, the mutual information (MI) of separated signals is estimated by using higher order statistics (HOS). These methods are sensitive to the initial parameters of separating matrix. An improved method based on Gaussian Mixture Model (GMM) is proposed in this paper to solve this problem. GMM is used as an auxiliary function to fit the probability density of separated signals and to convert the MI estimation of separated signals to the joint entropy estimation of auxiliary variables. Meanwhile, higher order odd polynomial (HOOP) is used to fit the inverse function of nonlinear mixing function. Then the coefficients of HOOP and the parameters of GMM are optimized by particle swarm optimization (PSO). Linear separating matrix is optimized by natural gradient algorithm. The two optimization processes iterate alternately until convergence. The simulation results demonstrate that the proposed approach is less dependent on the initial parameters of separating matrix and can obtain more accurate separated signals, in contrast to the conventional post-nonlinear ICA approaches.