Independent Component Analysis of Signals using Local Exponential Nonlinearities
Muhammad Ahsan Tufail, Masahide Abe, Masayuki Kawamata · 電子情報通信学会技術研究報告. VLD, VLSI設計技術 · 2005
In this paper we propose exponential type nonlinearities in order to blindly separate instantaneous mixtures of signals with symmetric probability distributions using the online relative gradient algorithm. These nonlinear functions are applied only in a certain range around zero in order to ensure the stability of the separating algorithm. The proposed truncated nonlinearities neutralize the effect of outliers while the higher order terms inherently present in the exponential function result in fast convergence especially for signals with bounded support. By varying the truncation threshold, signals with both sub-Gaussian and super-Gaussian probability distributions can be separated. For certain class of probability distributions (generalized Gaussian model), the optimal size of the threshold is obtained by examining the local stability conditions of the relative gradient algorithm. In order to separate sources consisting of both sub-Gaussian and super-Gaussian signals, we chose an adequate value of the threshold parameter based on the sign of normalized kurtosis estimated from the observed data. Finally, some computer simulations are presented to demonstrate the superior performance of the proposed idea.