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.

A source contribution quantitative calculation method for mechanical systems based on the simplified independent component analysis with reference

2016 ◽  
Vol 230 (18) ◽  
pp. 3222-3240
Author(s):  
Jie Zhang ◽  
Zhousuo Zhang ◽  
Wei Cheng ◽  
Guanwen Zhu ◽  
Zhengjia He
Keyword(s):  
Independent Component Analysis ◽  
Prior Knowledge ◽  
Complex Structure ◽  
Component Analysis ◽  
Independent Component ◽  
Vibration Measurement ◽  
Contrast Function ◽  
Source Contribution ◽  
Quantitative Calculation ◽  
Reference Signals

The quantitative calculation of the source contribution is very important and critical for the identification of the main vibration sources and the reduction of vibration and noise in submarine. It is difficult to calculate the source contribution because of the submarine’s complex structure and the large amount of vibration sources. As a typical blind source separation method, independent component analysis (ICA) has recently been proved to be an effective method to solve the source identification problem in which the source signals and mixing models are unknown. However, the outcomes of the ICA algorithm are affected by random sampling and random initialization of variables. In our study, the prior knowledge of the vibration sources can be obtained through the vibration measurement of submarine. Obviously, information in addition to mixed signals from sensors can lead to a more accurate separation. Therefore the contrast function of ICA can be enhanced by the reference signals obtained by the prior knowledge. In this paper, a closeness measurement between the independent components and the reference signals obtained by the prior knowledge is introduced, and the closeness measurement is constructed to have the same optimization direction with the traditional contrast function: negentropy. The closeness measurement is used to enhance the contrast function and then the enhanced contrast function is optimized by means of the Newton iteration and the deflation approach. Thus the simplified independent component analysis with reference (ICA-R) algorithm is obtained. After that a method to quantitatively calculate the source contribution is proposed based on the outcomes of the simplified ICA-R. Finally, the effectiveness of the proposed method is verified by the numerical simulation studies. The performance offered by the proposed method is also investigated by the experiment: it appear as a very appealing tool for the quantitative calculation of the source contribution.

scholarly journals Spherical Mesh Adaptive Direct Search for Separating Quasi-Uncorrelated Sources by Range-Based Independent Component Analysis

2013 ◽  
Vol 25 (9) ◽  
pp. 2486-2522 ◽  
Author(s):  
S. Easter Selvan ◽  
Pierre B. Borckmans ◽  
A. Chattopadhyay ◽  
P.-A. Absil
Keyword(s):  
Independent Component Analysis ◽  
Nonsmooth Optimization ◽  
Optimization Algorithm ◽  
Component Analysis ◽  
Direct Search ◽  
Independent Component ◽  
Mesh Adaptive Direct Search ◽  
Local Optima ◽  
Contrast Function ◽  
Unit Norm

It is seemingly paradoxical to the classical definition of the independent component analysis (ICA), that in reality, the true sources are often not strictly uncorrelated. With this in mind, this letter concerns a framework to extract quasi-uncorrelated sources with finite supports by optimizing a range-based contrast function under unit-norm constraints (to handle the inherent scaling indeterminacy of ICA) but without orthogonality constraints. Albeit the appealing contrast properties of the range-based function (e.g., the absence of mixing local optima), the function is not differentiable everywhere. Unfortunately, there is a dearth of literature on derivative-free optimizers that effectively handle such a nonsmooth yet promising contrast function. This is the compelling reason for the design of a nonsmooth optimization algorithm on a manifold of matrices having unit-norm columns with the following objectives: to ascertain convergence to a Clarke stationary point of the contrast function and adhere to the necessary unit-norm constraints more naturally. The proposed nonsmooth optimization algorithm crucially relies on the design and analysis of an extension of the mesh adaptive direct search (MADS) method to handle locally Lipschitz objective functions defined on the sphere. The applicability of the algorithm in the ICA domain is demonstrated with simulations involving natural, face, aerial, and texture images.

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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