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92
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 1550 (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 ..."
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Cited by 535 (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.
A fast fixedpoint algorithm for independent component analysis
 Neural Computation
, 1997
"... Abstract. Independent Subspace Analysis (ISA; Hyvarinen & Hoyer, 2000) is an extension of ICA. In ISA, the components are divided into subspaces and components in different subspaces are assumed independent, whereas components in the same subspace have dependencies.In this paper we describe a fi ..."
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Cited by 447 (19 self)
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Abstract. Independent Subspace Analysis (ISA; Hyvarinen & Hoyer, 2000) is an extension of ICA. In ISA, the components are divided into subspaces and components in different subspaces are assumed independent, whereas components in the same subspace have dependencies.In this paper we describe a fixedpoint algorithm for ISA estimation, formulated in analogy to FastICA. In particular we give a proof of the quadratic convergence of the algorithm, and present simulations that confirm the fast convergence, but also show that the method is prone to convergence to local minima. 1
EEGLAB: an open source toolbox for analysis of singletrial EEG dynamics including independent component analysis
 J. Neurosci. Methods
"... Abstract: We have developed a toolbox and graphic user interface, EEGLAB, running under the crossplatform MATLAB environment (The Mathworks, Inc.) for processing collections of singletrial and/or averaged EEG data of any number of channels. Available functions include EEG data, channel and event i ..."
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Cited by 326 (33 self)
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Abstract: We have developed a toolbox and graphic user interface, EEGLAB, running under the crossplatform MATLAB environment (The Mathworks, Inc.) for processing collections of singletrial and/or averaged EEG data of any number of channels. Available functions include EEG data, channel and event information importing, data visualization (scrolling, scalp map and dipole model plotting, plus multitrial ERPimage plots), preprocessing (including artifact rejection, filtering, epoch selection, and averaging), Independent Component Analysis (ICA) and time/frequency decompositions including channel and component crosscoherence supported by bootstrap statistical methods based on data resampling. EEGLAB functions are organized into three layers. Toplayer functions allow users to interact with the data through the graphic interface without needing to use MATLAB syntax. Menu options allow users to tune the behavior of EEGLAB to available memory. Middlelayer functions allow users to customize data processing using command history and interactive ‘pop ’ functions. Experienced MATLAB users can use EEGLAB data structures and standalone signal processing functions to write custom and/or batch analysis scripts. Extensive function help and tutorial information are included. A ‘plugin ’ facility allows easy incorporation of new EEG modules into the main menu. EEGLAB is freely available
Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood Estimation
, 1999
"... Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. ..."
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Cited by 92 (14 self)
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Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. In this paper, we show how sparse coding can be used for denoising. Using maximum likelihood estimation of nongaussian variables corrupted by gaussian noise, we show how to apply a softthresholding (shrinkage) operator on the components of sparse coding so as to reduce noise. Our method is closely related to the method of wavelet shrinkage, but it has the important benefit over wavelet methods that the representation is determined solely by the statistical properties of the data. The wavelet representation, on the other hand, relies heavily on certain mathematical properties (like selfsimilarity) that may be only weakly related to the properties of natural data.
New Approximations of Differential Entropy for Independent Component Analysis and Projection Pursuit
, 1998
"... We derive a firstorder approximation of the density of maximum entropy for a continuous 1D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by GramCharlier and Edgeworth. Using this ..."
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Cited by 79 (6 self)
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We derive a firstorder approximation of the density of maximum entropy for a continuous 1D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by GramCharlier and Edgeworth. Using this approximation of density, an approximation of 1D differential entropy is derived. The approximation of entropy is both more exact and more robust against outliers than the classical approximation based on the polynomial density expansions, without being computationally more expensive. The approximation has applications, for example, in independent component analysis and projection pursuit.
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 61 (5 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.
Independent Component Analysis by General Nonlinear Hebbianlike Learning Rules
 Signal Processing
, 1998
"... A number of neural learning rules have been recently proposed... In this paper, we show that in fact, ICA can be performed by very simple Hebbian or antiHebbian learning rules, which may have only weak relations to such informationtheoretical quantities. Rather suprisingly, practically any nonlin ..."
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Cited by 57 (11 self)
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A number of neural learning rules have been recently proposed... In this paper, we show that in fact, ICA can be performed by very simple Hebbian or antiHebbian learning rules, which may have only weak relations to such informationtheoretical quantities. Rather suprisingly, practically any nonlinear function can be used in the learning rule, provided only that the sign of the Hebbian/antiHebbian term is chosen correctly. In addition to the Hebbianlike mechanism, the weight vector is here constrained to have unit norm, and the data is preprocessed by prewhitening, or sphering. These results imply that one can choose the nonlinearity so as to optimize desired statistical or numerical criteria.
BValidating the independent components of neuroimaging time series via clustering and visualization
 NeuroImage
, 2004
"... and visualization ..."