An ICA Algorithm Based On Exponential Power Family Of Densities And Gaussian Mixture Densities Models

Independent Component Analysis is a kind of powerful method for Blind Signal Processing.It plays an important role in many research fields.It becomes one of the most exciting topics both in signal processing and artificial neural networks and has been concerned by more and more researchers now.In the past few years,ICA has been rapidly developed in theory and application.This paper introduces the development process of ICA briefly and discusses the objective functions,algorithms and performance of ICA in detail. Then an algorithm for ICA without any knowledge of their probability distributions was provided.It was achieved under a maximum likelihood framework by considering Gaussian mixture densities and exponential power family of densities models.The main work of this paper can be summarized as follows:1.Basic ICA models are introduced.The conditions for identifiability,separability and uniqueness are given in theorem.Estimation principles and algorithms are arranged in the aspects of information theory and statistical theory,including:maximum likelihood estimation,minimization of mutual information and maximally nongaussian components. At last,we discuss the stability of the natural gradient algorithm and fixed-point algorithm.2.An ICA algorithm with adaptive score functions to various marginal densities is proposed. It enables to separate mixtures of sub-Gaussian and super-Gaussian sources,symmetric and asymmetric sources.Alternative score functions in the algorithm are derived by using Gaussian mixture densities and exponential power family of densities models.The functions are adaptive based on estimating the high-order moments of extracted signals. Moreover,a stability condition of the proposed algorithm for separating the true solution is given.Simulation experiment results are presented to illustrate the performance and effectiveness of the proposed algorithm.