An Efficient Algorithm by Kurtosis Maximization in Reference-Based Framework

Abstract

Abstract. This paper deals with the optimization of kurtosis for complex-valued signals in the independent component analysis (ICA) framework, where source signals are linearly and instantaneously mixed. Inspired by the recently proposed reference-based contrast schemes, a similar contrast function is put forward, based on which a new fast fixed-point (FastICA) algorithm is proposed. The new optimization method is similar in spirit to the former classical kurtosis-based FastICA algorithm but differs in the fact that it is much more efficient than the latter in terms of computational speed, which is significantly striking with large number of samples. The performance of this new algorithm is confirmed through computer simulations.

Blind Audio Source Separation Based On High Exploration Particle Swarm Optimization

“…A new crossover method that consists of three parent chromosomes [ 1,2,3] is suggested in this study, but it is not similar to the classical multi-crossover genetic algorithm proposed by Chang [35] which is based on only two chromosomes. We suppose that chromosomes are chosen from the population randomly.…”

“…Blind Source Separation (BSS) is a powerful tool that has been used to restore source signals from several observations without any prior knowledge about the source of the signals as well as their mixing process [1] [2]. Many algorithms have been proposed to solve the BSS problem depending on the mixture model: linear mixture [3], nonlinear mixture [4] and post-nonlinear mixture [5].…”

Adaptive Complex-Valued Independent Component Analysis Based on Second-Order Statistics

“…The first category includes methods based on a nonlinear function, such as complex-valued fastICA (C-fastICA) [7], noncircular complex fastICA (NC-fastICA) [8], complex maximization of non-Gaussiantiy (CMN) [9], complex-valued ICA by entropy bound minimization (CEBM) [10], complex-valued ICA by entropy rate bound minimization (CERBM) [11], and others [3,12]. The second category includes methods that are based on kurtosis or higher-order cumulants, such as joint approximative diagonalization of eigenmatrix (JADE) [4], kurtosis maximization (KM) [13], pseudo-Euclidean gradient iteration ICA (GEGI-ICA) [14], and others [15][16][17]. The third category includes methods based on second-order statistics, such as stronguncorrelating transform (SUT) [18,19] and its adaptive algorithms [2,[20][21][22] and pseudo-uncorrelating transform (PUT) [23].…”