Convergence and stability of ICA with reference and its applications to EEG
Veluvolu, Swathi Sri
Date of Issue2016
School of Computer Engineering
Multi-channel signal observations in biomedical, radar and other communication applications are multivariate and contain contributions from multiple sources. Independent Component Analysis (ICA) has been widely used for separation of underlying sources from the observed mixtures for the subsequent analysis of such data. To e ciently extract a subset of desired sources, the Constrained ICA (cICA) that provides a framework to incorporate the prior information about these sources as constraints into the contrast function of ICA was introduced. ICA with Reference (ICA-R) proposed under the cICA framework incorporates priori information as reference signals (rough template) that guide source separation to automatically extract desired sources closer in some sense to the reference signal. However, the convergence of cICA and ICA-R to the desired subset of sources as well as the consistency of the separations estimated, greatly determines its applicability to the real world problems of source extraction. The factors that greatly a ect the convergence are: 1. the non-smooth penalized contrast function of ICA-R 2. the closeness function and lack of knowledge to choose the upper bound for the closeness measure 3. the sensitivity of the Newton-like learning (optimization) algorithm to the initialization of parameters and its inherent limitation to achieve global optimum Although di fferent closeness measures and initialization strategies have been investigated to improve the performance of ICA-R, not much research on the improvement of the optimization process of ICA-R has been attempted. This thesis mainly focuses on improving the convergence and stability of ICA-R and proposes ways to overcome the drawbacks of Newton-like learning algorithm by taking the advantage of the population-based evolutionary approaches that asymptotically converge to the desired global optima. First, we investigate the pros and cons of ICA-R and then discuss about the recent works that address the convergence and stability of ICA-R. The major contributions of the thesis are as follows: (i) a detailed analysis on convergence and stability of ICA-R and new ways of obtaining reliable reference signals, (ii) to avoid the formulation of a penalized objective function, a constrained di fferential evolutionary algorithm, termed cDE-ICAR, with a specifi c initialization strategy that incorporates the violation of closeness constraint to the selection process of evolution is proposed, (iii) to completely remove the upper-bound of closeness measure from the optimization problem of ICA-R, we propose a multi-objective optimization algorithm, termed MO-ICAR, that simultaneously optimizes the contrast function and the closeness measure and (iv) the utility and efficacy of the proposed methods in practical applications was demonstrated by extracting desired rhythms and removal of artifacts from EEG signals.