Fourth-order cumulant based estimator for independent component analysis

2001 ◽  
Vol 37 (7) ◽  
pp. 469
Author(s):  
A.K. Nandi ◽  
F. Herrmann
Keyword(s):  
Independent Component Analysis ◽  
Fourth Order ◽  
Component Analysis ◽  
Independent Component ◽  
Fourth Order Cumulant

scholarly journals Mode Separation for Multimodal Ultrasonic Lamb Waves Using Dispersion Compensation and Independent Component Analysis of Forth-Order Cumulant

2019 ◽  
Vol 9 (3) ◽  
pp. 555 ◽  
Author(s):  
Xiao Chen ◽  
Dandan Ma
Keyword(s):  
Independent Component Analysis ◽  
Fourth Order ◽  
Lamb Wave ◽  
Lamb Waves ◽  
Dispersion Compensation ◽  
Single Mode ◽  
Component Analysis ◽  
Independent Component ◽  
Mode Separation ◽  
Fourth Order Cumulant

Ultrasonic Lamb wave testing has been successfully applied in nondestructive testing. However, because of Lamb wave multimodal and dispersion characteristics, the received signals are often multimodal and overlapping, which makes them very complicated. This paper proposes a mode separation method by combining dispersion compensation with the independent component analysis of fourth-order cumulant. Taking two-mode overlapped signals as an example, the single-mode dispersion compensation is performed according to the measured distance difference between the two sets of signals. The two sets of signals are returned to the same distance. The fourth-order cumulant independent component analysis method is further used to process the Lamb wave signals of different superposition situations at the same distance. The corresponding mode signal contained in the two sets of signals is separated through the joint diagonalization of the whitened fourth-order cumulant matrix. The different modes are compensated and separated successively, achieving the multimodal signal separation. Experimental results in steel plates show that the presented method can accurately achieve mode separation for the multimodal overlapping Lamb waves. This is helpful for the signal processing of multimodal Lamb waves.

Robust Independent Component Analysis for Cognitive Informatics

2011 ◽  
pp. 368-380
Author(s):  
N. Gadhok ◽  
W. Kinsner
Keyword(s):  
Independent Component Analysis ◽  
Fourth Order ◽  
Performance Index ◽  
Component Analysis ◽  
Independent Component ◽  
Separation Performance ◽  
Contrast Function ◽  
Rotation Error ◽  
Function Difference ◽  
Angle Of Rotation

This article evaluates the outlier sensitivity of five independent component analysis (ICA) algorithms (FastICA, Extended Infomax, JADE, Radical, and ß-divergence) using (a) the Amari separation performance index, (b) the optimum angle of rotation error, and (c) the contrast function difference in an outlier-contaminated mixture simulation. The Amari separation performance index has revealed a strong sensitivity of JADE and FastICA (using third- and fourth-order nonlinearities) to outliers. However, the two contrast measures demonstrated conclusively that ß-divergence is the least outlier-sensitive algorithm, followed by Radical, FastICA (exponential and hyperbolic-tangent nonlinearities), Extended Infomax, JADE, and FastICA (third- and fourth-order nonlinearities) in an outlier-contaminated mixture of two uniformly distributed signals. The novelty of this article is the development of an unbiased optimization-landscape environment for assessing outlier sensitivity, as well as the optimum angle of rotation error and the contrast function difference as promising new measures for assessing the outlier sensitivity of ICA algorithms.

Optimal Pairwise Fourth-Order Independent Component Analysis

2006 ◽  
Vol 54 (8) ◽  
pp. 3049-3063 ◽  
Author(s):  
V. Zarzoso ◽  
J.J. Murillo-Fuentes ◽  
R. Boloix-Tortosa ◽  
A.K. Nandi
Keyword(s):  
Independent Component Analysis ◽  
Fourth Order ◽  
Component Analysis ◽  
Independent Component

Independent component analysis: Jacobi-like diagonalization of optimized composite-order cumulants

2009 ◽  
Vol 465 (2105) ◽  
pp. 1393-1411 ◽  
Author(s):  
Shafayat Abrar ◽  
Asoke Kumar Nandi
Keyword(s):  
Independent Component Analysis ◽  
Fourth Order ◽  
A Priori ◽  
Component Analysis ◽  
Independent Component ◽  
Simultaneous Diagonalization ◽  
Statistical Knowledge ◽  
Common Framework ◽  
Ica Algorithm ◽  
Number Of Authors

In the field of blind source separation, Jacobi-like diagonalization-based approaches constitute an important tool for independent component analysis (ICA). Recently, simultaneous diagonalization of cumulant matrices of third- and fourth-order has been studied by a number of authors. In this work, we present an optimal parametrized composition of these cumulants that puts two classical contrasts, namely, the cumulant-based ICA and the weighted fourth-order contrast in a common framework. It is shown that the optimal weight parameter depends on the a priori statistical knowledge of the original mixing sources. Following the same spirit of the ICA algorithm, we derive the analytical solution for the case of two sources. Finally, a number of computer simulations have been performed to illustrate the behaviour of the Jacobi-like iterations for the maximization of the proposed parametrized contrast.

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