The Study Of Independent Component Analysis With Reference And Its Applications

The study of multivariate stochastic signals is a hot topic in information science field. The mainstream researches on this topic are how to discover the inherent factors or components from the multivariate stochastic signals. Recently, the independent component analysis (ICA) becomes a hotspot problem in artificial neural networks, statistical learning, signal processing, and etc. The high applied value of ICA has been verified by many successful applications of ICA in various fields.ICA is a research branch of blind source separation (BSS), which theoretically assumes that the observed multivariate signals are the linear mixtures of independent components (ICs) with non-Gaussian distributions. In many fields, researchers have some prior information on the desired ICs. However, the classic ICA methods have to calculate all the ICs and then choose the desired ICs by post-selection which is not only time-consuming but also unstable. And when the dimentsion of input data is high, the classic ICA methods maybe unable toproduce any correct results. The aim of this paper is to study how to use prior information, in the form of reference signals, to extract the desired ICs directly.The main contributions of the paper can be summarized as follows:1. We rigidly derived algorithm for the ICA with reference signals (ICA-R) under constrained ICA (cICA) framework, and found flaws in the previous works, then proposed an improved algorithm whose validity was proved not only by theoretical analyses but also by simulation on both artificial and real-world data.2. We probed problem of the unstable convergence of those previous ICA-R algorithms (under the framework of cICA) and found the reason was that the ICA contrast function can be nonconvex in the feasible region defined by the inequality constraint, which means that the KT condition is not globally sufficient. As the result, using Newton-like optimization algorithm (and other greedy algorithm) cannot guarantee the correct convergence. The proposed new ICA-R algorithm which can predict the future incorrect convergence was presented so as to avoid the instability of the previous algorithms which was confirmed by our experiments from which no incorrect convergence of the new algorithm was observed.3. We studied how to facilitate the application of the ICA-R algorithm. Since the parameter (or threshold) measuring the distance between reference signal and output is critical, we proposed a method that facilitates the parameter selection including reference deflation method and etc. Then we suggested that it is convenient to use one of the observed data channel as reference signal in some applications instead of concocting reference signal by manpower.4. We proposed the Complete ICA-R method for recovering all the underlying components as other classic ICAs done but without compulsively decorrelating the outputs. Therefore, the Complete ICA-R is flexible so as to remain the inherent structures of the outputs. The experimental results indicated that the Complete ICA-R algorithm would produce the outputs with better quality result compared to the classic methods. Particularly, the proposed Complete ICA-R has a unique feature which could help the users to judge the number of ICs when the number of the observed channels are more than the number of underlying components.5. A new method for ICA-R was presented which was not under the framework of cICA. The prior information in the form of reference signal should be used not only as a constraint which was the basic ideal of cICA but also before the learning of the weight vector. In this paper, an approach was proposed which used the reference to build the initial weight vector. It was found that the one-unit ICA algorithm could find the right demixing vector with the predesigned weight vector under some conditions. Moreover, the validity of the approach was proved and the detailed algorithm was presented.6. The theoretical flaw of the framework of cICA was found and proved in our work. In addition, we also proposed the new framework of ICA-R which can remedy the previous general framework of ICA-R.