Window-based lerning for overcomplete independent component analysis

Abstract

The blind source separation (BSS) or independent component analysis (ICA) is a statistical technique for the separation of hidden source signals from observed signals in an unknown mixing system. This dissertation concerns the separation problem, where the number of sources (n) is greater than the number of observed signals (m). This situation is called overcomplete. Many existing algorithms are designed to identify the column vectors of the mixing matrix, basis components, which point toward the directions of independent components. However, most approaches assume that the number of sources mixed in the observed signals is known. This dissertation presents a new method to identify the mixing matrix without prior assumption on the number of sources. The proposed algorithm uses a window search length algorithm to identify the information index for preliminary filtering all relevant points clustered along the basic independent components. Then, the perturbed mean shift algorithm with entropy measure is applied to enhance the actual basic independent components. Finally, source signals are recovered by the minimum l1-norm method. From the experimental results on the speech signals from TIMIT database, the proposed algorithm is able to estimate the mixing matrix and the estimated source number is also given. The difference between the actual mixing matrix and the estimated mixing matrix using AMDI value of the proposed algorithm is less than that of standard k-mean method, AICA method, Yuanqing Li et al. ‘s algorithm, and Qv Lv et al. ‘s algorithm. Moreover, the algorithm can perform in noisy environments.