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57
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 ..."
Abstract

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.
Independent component approach to the analysis of EEG and MEG recordings
 IEEE Transactions on Biomedical Engineering
, 2000
"... This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Helsinki University of Technology's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish t ..."
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Cited by 61 (8 self)
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This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Helsinki University of Technology's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to
BValidating the independent components of neuroimaging time series via clustering and visualization
 NeuroImage
, 2004
"... and visualization ..."
Independent Components of Magnetoencephalography: Localization
, 2002
"... We applied secondorder blind identification (SOBI), an independent component analysis (ICA) method, to MEG data collected during cognitive tasks. We explored SOBI's ability to help isolate underlying neuronal sources with relatively poor signaltonoise ratios, allowing their identification ..."
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Cited by 30 (11 self)
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We applied secondorder blind identification (SOBI), an independent component analysis (ICA) method, to MEG data collected during cognitive tasks. We explored SOBI's ability to help isolate underlying neuronal sources with relatively poor signaltonoise ratios, allowing their identification and localization. We compare localization of the SOBIseparated components to localization from unprocessed sensor signals, using an equivalent current dipole (ECD) modeling method. For visual and somatosensory modalities, SOBI preprocessing resulted in components that can be localized to physiologically and anatomically meaningful locations.
A Fast Algorithm for Joint Diagonalization with Nonorthogonal Transformations and its Application to Blind Source Separation
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2004
"... A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobeniusnorm formulation of the joint diagonalization problem, and addresses diagonalization with a general, nonorthogonal transformation. The iterative scheme of the algorithm i ..."
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Cited by 22 (3 self)
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A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobeniusnorm formulation of the joint diagonalization problem, and addresses diagonalization with a general, nonorthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm 's efficiency stems from the special approximation of the cost function resulting in a sparse, blockdiagonal Hessian to be used in the computation of the quasiNewton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing stateoftheart joint diagonalization algorithms.
Efficient independent component analysis (I
, 2003
"... Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on Mestimates have been proposed for estimating the mixing matrix. Recently, several nonpar ..."
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Cited by 12 (4 self)
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Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on Mestimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have been developed, but indepth analysis of asymptotic efficiency has not been available. We analyze ICA using semiparametric theories and propose a straightforward estimate based on the efficient score function by using Bspline approximations. The estimate is asymptotically efficient under moderate conditions and exhibits better performance than standard ICA methods in a variety of simulations.
Independent component analysis for noisy data MEG data analysis
 Neural Networks
, 2000
"... ICA (independent component analysis) is a new, simple and powerful idea for analyzing multivariant data. One of the successful applications is neurobiological data analysis such as EEG (electroencephalography), MRI (magnetic resonance imaging), and MEG (magnetoencephalography). But there remain ..."
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Cited by 11 (0 self)
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ICA (independent component analysis) is a new, simple and powerful idea for analyzing multivariant data. One of the successful applications is neurobiological data analysis such as EEG (electroencephalography), MRI (magnetic resonance imaging), and MEG (magnetoencephalography). But there remain a lot of problems. In most cases, neurobiological data contain a lot of sensory noise, and the number of independent components is unknown. In this article, we discuss an approach to separate noisecontaminated data without knowing the number of independent components. A wellknown two stage approach to ICA is to preprocess the data by PCA (principal component analysis), and then the necessary rotation matrix is estimated. Since PCA does not work well for noisy data, we implement a factor analysis model for preprocessing. In the new preprocessing, the number of the sources and the amount of the sensory noise are estimated. After the preprocessing, the rotation matrix is estimate...
Icasso: Software For Investigating the Reliability of ICA Estimates by Clustering and Visualization
 In Proc. 2003 IEEE workshop on neural networks for signal processing (NNSP’2003
, 2003
"... A major problem in application of independent component analysis (ICA) is that the reliability of the estimated independent components is not known. Firstly, the finite sample size induces statistical errors in the estimation. Secondly, as real data never exactly follows the ICA model, the contrast ..."
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Cited by 11 (1 self)
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A major problem in application of independent component analysis (ICA) is that the reliability of the estimated independent components is not known. Firstly, the finite sample size induces statistical errors in the estimation. Secondly, as real data never exactly follows the ICA model, the contrast function used in the estimation may have many local minima which are all equally good, or the practical algorithm may not always perform properly, for example getting stuck in local minima with strongly suboptimal values of the contrast function. We present an explorative visualization method for investigating the relations between estimates from FastICA. The algorithmic and statistical reliability is investigated by running the algorithm many times with di#erent initial values or with di#erently bootstrapped data sets, respectively. Resulting estimates are compared by visualizing their clustering according to a suitable similarity measure. Reliable estimates correspond to tight clusters, and unreliable ones to points which do not belong to any such cluster. We have developed a software package called Icasso to implement these operations. We also present results of this method when applying Icasso on biomedical data.