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Independent Component Analysis
 Neural Computing Surveys
, 2001
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
Abstract

Cited by 1492 (93 self)
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A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1
Fast and robust fixedpoint algorithms for independent component analysis
 IEEE TRANS. NEURAL NETW
, 1999
"... Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informat ..."
Abstract

Cited by 511 (34 self)
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Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informationtheoretic approach and the projection pursuit approach. Using maximum entropy approximations of differential entropy, we introduce a family of new contrast (objective) functions for ICA. These contrast functions enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model, and it is shown how to choose contrast functions that are robust and/or of minimum variance. Finally, we introduce simple fixedpoint algorithms for practical optimization of the contrast functions. These algorithms optimize the contrast functions very fast and reliably.
An Experimental Comparison of Neural Algorithms for Independent Component Analysis and Blind Separation
, 1999
"... In this paper, we compare the performance of five prominent neural or adaptive algorithms designed for Independent Component Analysis (ICA) and blind source separation (BSS). In the first part of the study, we use artificial data for comparing the accuracy, convergence speed, computational load, and ..."
Abstract

Cited by 13 (4 self)
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In this paper, we compare the performance of five prominent neural or adaptive algorithms designed for Independent Component Analysis (ICA) and blind source separation (BSS). In the first part of the study, we use artificial data for comparing the accuracy, convergence speed, computational load, and other relevant properties of the algorithms. In the second part, the algorithms are applied to three dioeerent realworld data sets. The task is either blind source separation or finding interesting directions in the data for visualisation purposes. We develop criteria for selecting the most meaningful basis vectors of ICA and measuring the quality of the results. The comparison reveals characteristic differences between the studied ICA algorithms. The most important conclusions of our comparison are robustness of the ICA algorithms with respect to modest modeling imperfections, and the superiority of fixedpoint algorithms with respect to the computational load.
Extensions of Linear Independent Component Analysis: Neural and InformationTheoretic Methods
"... Obtaining information from measured data is a general problem which is encountered in numerous applications and fields of science. A goal of many data analysis methods is to transform the observed data into a representation which reveals the information contained in the data. Methods for obtaining s ..."
Abstract
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Obtaining information from measured data is a general problem which is encountered in numerous applications and fields of science. A goal of many data analysis methods is to transform the observed data into a representation which reveals the information contained in the data. Methods for obtaining such representations include principal component analysis, projection pursuit, cluster analysis, and neural unsupervised learning methods.