A Study Of Independent Component Analysis Algorithms And Their Applications

Independent component analysis (ICA) is a newly developed and powerful technique for recovering latent independent sources given only their mixtures. The basic ICA model assumes that sources are linearly mixed and mutually independent. The data analyzed by ICA could originate from many different kinds of application fields, including digital images and document databases, as well as economic indicators and psychometric measurements, etc.Considering its wide and attractive applications, many researchers have studied ICA in the past twenty years so that ICA technique has been very much developed. However, ICA is still staying at the developing stage, and the investigation of its theory and application should be enhanced and improved further.In this thesis, after a brief introduction to the development history and the current research status and applications of ICA, simple mathematical preliminaries in ICA technique were given, including the mathematical definition of ICA, the assumptions made about ICA problems and the mathematical theory and methods commonly used in ICA, etc. Then, some algorithms and applications of ICA were investigated deeply, and several novel efficient methods were elaborated. The main works in this thesis can be introduced as follows:1) Based on a separated structure with two groups of multilayer perceptrons, a novel nonlinear ICA algorithm was proposed for the postnonlinear (PNL) mixing model. The problem of source separation of post-nonlinear (PNL) mixtures is an important extension of ICA to the nonlinear mixing case. To improve the disadvantages such as computation-demanding and imprecise estimate of score function, of the existing methods for PNL mixture, we proposed a novel post-nonlinear blind source separation algorithm based on mutual information minimization. This algorithm applies the general principle of the MISEP method which is widely used for general nonlinear independent component analysis. To best fit the wide class of post-nonlinear mixtures, we improve the MISEP method by making use of the a priori information about the mixtures. A network paradigm composing of two groups of three-layered perceptrons and one linear network is used...