A new constrained fixed-point algorithm for ordering independent components

Abstract

Independent component analysis (ICA) aims to recover a set of unknown mutually independent components (ICs) from their observed mixtures without knowledge of the mixing coefficients. In the classical ICA model there exists ICs' indeterminacy on permutation and dilation. Constrained ICA is one of methods for solving this problem through introducing constraints into the classical ICA model. In this paper we first present a new constrained ICA model which composed of three parts: a maximum likelihood criterion as an objective function, statistical measures as inequality constraints and the normalization of demixing matrix as equality constraints. Next, we incorporate the new fixed-point (newFP) algorithm into this constrained ICA model to construct a new constrained fixed-point algorithm. Computation simulations on synthesized signals and speech signals demonstrate that this combination both can eliminate ICs' indeterminacy to a certain extent, and can provide better performance. Moreover, comparison results with the existing algorithm verify the efficiency of our new algorithm furthermore, and show that it is more simple to implement than the existing algorithm due to its advantage of not using the learning rate. Finally, this new algorithm is also applied for the real-world fetal ECG data, experiment results further indicate the efficiency of the new constrained fixed-point algorithm.

An Improved Independent Component Analysis Algorithm Based on Artificial Immune System

“…Moreover, the order of the independent components (ICs) is difficult to be determined. These two problems are the main drawbacks of FastICA algorithm [7]- [9]. To overcome these disadvantages, an improved ICA algorithm based on artificial immune system (AIS) (called AIS-ICA) is presented.…”

Blind source separation with nonlinear autocorrelation and non-Gaussianity

“…Several methods for BSS using the statistical properties of original sources have been proposed, such as non-Gaussianity (or equivalently, independent component analysis, ICA) [1,3,[5][6][7]9,[12][13][14]19,27], or time-structure information, such as linear predictability or smoothness [2,6], linear autocorrelation [4,16,26], coding complexity [10,20,21,23], temporal predictability [18], nonstationarity [11,15,17], energy predictability [22], nonlinear innovation [24], nonlinear autocorrelation [25], etc. One often solves the BSS problem by using only one statistical property of original sources, e.g., only non-Gaussianity or only time-structure information.…”

A fixed-point algorithm for blind source separation with nonlinear autocorrelation

“…Several methods for BSS using the statistical properties of original sources have been proposed, such as non-Gaussianity (or equivalently, independent component analysis, ICA) [1,3,[5][6][7][8][11][12][13]24,34], linear predictability or smoothness [2,6], linear autocorrelation [4,19,31], coding complexity [9,26,27,29], temporal predictability [23], nonstationarity [10,18,21], sparsity [14,15,25,35], energy predictability [28], nonlinear innovation [30] and nonnegativity [20,22], etc.…”