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69
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
Neural Approaches to Independent Component Analysis and Source Separation
, 1996
"... Independent Component Analysis (ICA) is a recently developed technique that in many cases characterizes the data in a natural way. The main application area of the linear ICA model is blind source separation. Here, unknown source signals are estimated from their unknown linear mixtures using the str ..."
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Cited by 56 (9 self)
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Independent Component Analysis (ICA) is a recently developed technique that in many cases characterizes the data in a natural way. The main application area of the linear ICA model is blind source separation. Here, unknown source signals are estimated from their unknown linear mixtures using the strong assumption that the sources are mutually independent. In practice, separation can be achieved by using suitable higherorder statistics or nonlinearities. Various neural approaches have recently been proposed for blind source separation and ICA. In this paper, these approaches and the respective learning algorithms are briefly reviewed, and some extensions of the basic ICA model are discussed. 1. Introduction A recent trend in neural network research is to study various forms of unsupervised learning beyond standard Principal Component Analysis (PCA). Such techniques are often called nonlinear PCA methods. They can be developed from various starting points, usually leading to different ...
Independent component analysis applied to feature extraction from colour and stereo images
 Network Computation in Neural Systems
, 2000
"... Previous work has shown that independent component analysis (ICA) applied to feature extraction from natural image data yields features resembling Gabor functions and simplecell receptive fields. This article considers the effects of including chromatic and stereo information. The inclusion of colo ..."
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Cited by 56 (6 self)
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Previous work has shown that independent component analysis (ICA) applied to feature extraction from natural image data yields features resembling Gabor functions and simplecell receptive fields. This article considers the effects of including chromatic and stereo information. The inclusion of colour leads to features divided into separate red/green, blue/yellow, and bright/dark channels. Stereo image data, on the other hand, leads to binocular receptive fields which are tuned to various disparities. The similarities between these results and observed properties of simple cells in primary visual cortex are further evidence for the hypothesis that visual cortical neurons perform some type of redundancy reduction, which was one of the original motivations for ICA in the first place. In addition, ICA provides a principled method for feature extraction from colour and stereo images; such features could be used in image processing operations such as denoising and compression, as well as in pattern recognition.
Flexible Independent Component Analysis
, 2000
"... This paper addresses an independent component analysis (ICA) learning algorithm with flexible nonlinearity, so named as flexible ICA, that is able to separate instantaneous mixtures of suband superGaussian source signals. In the framework of natural Riemannian gradient, we employ the parameterized ..."
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Cited by 43 (13 self)
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This paper addresses an independent component analysis (ICA) learning algorithm with flexible nonlinearity, so named as flexible ICA, that is able to separate instantaneous mixtures of suband superGaussian source signals. In the framework of natural Riemannian gradient, we employ the parameterized generalized Gaussian density model for hypothesized source distributions. The nonlinear function in the flexible ICA algorithm is controlled by the Gaussian exponent according to the estimated kurtosis of demixing filter output. Computer simulation results and performance comparison with existing methods are presented.
Adaptive blind signal processingneural network approaches
 Proc. of the IEEE
, 1998
"... Learning algorithms and underlying basic mathematical ideas are presented for the problem of adaptive blind signal processing, especially instantaneous blind separation and multichannel blind deconvolution/equalization of independent source signals. We discuss recent developments of adaptive learnin ..."
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Cited by 43 (3 self)
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Learning algorithms and underlying basic mathematical ideas are presented for the problem of adaptive blind signal processing, especially instantaneous blind separation and multichannel blind deconvolution/equalization of independent source signals. We discuss recent developments of adaptive learning algorithms based on the natural gradient approach and their properties concerning convergence, stability, and efficiency. Several promising schemas are proposed and reviewed in the paper. Emphasis is given to neural networks or adaptive filtering models and associated online adaptive nonlinear learning algorithms. Computer simulations illustrate the performances of the developed algorithms. Some results presented in this paper are new and are being published for the first time.
InformationTheoretic Approach to Blind Separation of Sources in Nonlinear Mixture
, 1998
"... The linear mixture model is assumed in most of the papers devoted to blind separation. A more realistic model for mixture should be nonlinear. In this paper, a twolayer perceptron is used as a demixing system to separate sources in nonlinear mixture. The learning algorithms for the demixing sys ..."
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Cited by 43 (4 self)
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The linear mixture model is assumed in most of the papers devoted to blind separation. A more realistic model for mixture should be nonlinear. In this paper, a twolayer perceptron is used as a demixing system to separate sources in nonlinear mixture. The learning algorithms for the demixing system are derived by two approaches: maximum entropy and minimum mutual information. The algorithms derived from the two approaches have a common structure. The new learning equations for the hidden layer are different from the learning equations for the output layer. The natural gradient descent method is applied in maximizing entropy and minimizing mutual information. The information (entropy or mutual information) backpropagation method is proposed to derive the learning equations for the hidden layer.
Neural Networks for Blind Decorrelation of Signals
, 1997
"... In this paper, we analyze and extend a class of adaptive networks for secondorder blind decorrelation of instantaneous signal mixtures. Firstly, we compare the performance of the decorrelation neural network employing global knowledge of the adaptive coefficients with a similar structure whose coeff ..."
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Cited by 36 (15 self)
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In this paper, we analyze and extend a class of adaptive networks for secondorder blind decorrelation of instantaneous signal mixtures. Firstly, we compare the performance of the decorrelation neural network employing global knowledge of the adaptive coefficients with a similar structure whose coefficients are adapted via local output connections. Through statistical analyses, the convergence behaviors and stability bounds for the algorithms' step sizes are studied and derived. Secondly, we analyze the behaviors of locallyadaptive multilayer decorrelation networks and quantify their performances for poorlyconditioned signal mixtures. Thirdly, we derive a robust locallyadaptive network structure based on a posteriori output signals that remains stable for any step size value. Finally, we present an extension of the locallyadaptive network for linearphase temporal and spatial whitening of multichannel signals. Simulations verify the analyses and indicate the usefulness of the locall...
Fast Joint Separation And Segmentation Of Mixed Images
, 2004
"... We consider the problem of the blind separation of noisy instantaneously mixed images. The images are modeled by hidden Markov fields with unknown parameters. Given the observed images, we give a Bayesian formulation and we propose a fast version of the MCMC algorithm based on the Bartlett decomposi ..."
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Cited by 31 (22 self)
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We consider the problem of the blind separation of noisy instantaneously mixed images. The images are modeled by hidden Markov fields with unknown parameters. Given the observed images, we give a Bayesian formulation and we propose a fast version of the MCMC algorithm based on the Bartlett decomposition for the resulting data augmentation problem. We separate the unknown variables into two categories: 1. The parameters of interest which are the mixing matrix, the noise covariance and the parameters of the sources distributions. 2. The hidden variables which are the unobserved sources and the unobserved pixel segmentation labels. The proposed algorithm provides, in the stationary regime, samples drawn from the posterior distributions of all the variables involved in the problem leading to great flexibility in the cost function choice. Finally, we show the results for both synthetic and real data to illustrate the feasibility of the proposed solution. 2004 SPIE and IS&T. [DOI: 10.1117/1.1666873] 1
Independent component analysis by complex nonlinearities
 in Proc. ICASSP
, 2004
"... A number of complex nonlinear functions are proposed for the independent component analysis (ICA) of complexvalued data. We discuss the properties of these nonlinearities and show their efficiency in generating the higher order statistics needed for ICA. 1. ..."
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Cited by 26 (14 self)
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A number of complex nonlinear functions are proposed for the independent component analysis (ICA) of complexvalued data. We discuss the properties of these nonlinearities and show their efficiency in generating the higher order statistics needed for ICA. 1.