Evolving Trends in Independent Component Analysis with Application

Abstract

The thesis is aimed to explore ICA to comprehend massive data fully. Financial time series’ data from KSE is used to compute ICs with JADE, SOBI, and FastICA algorithms and a deep insight of the series is targeted through study of the internal structure. Attempts from different directions are made to achieve the goal. Ordering of the ICs to define their priority in retention is addressed. A new regression based method is successfully introduced where regression coefficients obtained by regressing the original series on ICs are used. The magnitudes of the mixing coefficients are compared with regression coefficients for their compatibility to determine the order of the ICs. A novel approach, based upon comparing original and reconstructed series gauged through is proposed to decide how many ICs should be retained to reconstruct the series successfully. Identification of clusters is attempted to reduce the dimensionality in natural way. Two ICA based approaches namely adapted estimated mixing coefficients approach and ranked approach have been proposed and demonstrated. The first approach is based upon sum of squares of mixing coefficients whereas the second approach uses rank order of at predefined threshold levels. Internal and external structures of clusters are also explored through different metrics. Moreover, compatibility of the clusters is contrasted with the available grouping mechanisms. Keywords: Dimension Reduction; Financial Time Series; Ordering ICs; Reconstruction of Series; Regression; Clustering