Search results for "FastICA"

showing 7 items of 7 documents

The squared symmetric FastICA estimator

2017

In this paper we study the theoretical properties of the deflation-based FastICA method, the original symmetric FastICA method, and a modified symmetric FastICA method, here called the squared symmetric FastICA. This modification is obtained by replacing the absolute values in the FastICA objective function by their squares. In the deflation-based case this replacement has no effect on the estimate since the maximization problem stays the same. However, in the symmetric case we obtain a different estimate which has been mentioned in the literature, but its theoretical properties have not been studied at all. In the paper we review the classic deflation-based and symmetric FastICA approaches…

Mathematical optimizationaffine equivarianceminimum distance indexMathematics - Statistics TheoryIndependent component analysis02 engineering and technologyEstimating equationsStatistics Theory (math.ST)01 natural sciences010104 statistics & probabilityMatrix (mathematics)0202 electrical engineering electronic engineering information engineeringFOS: MathematicsApplied mathematics62H10 62H120101 mathematicsElectrical and Electronic EngineeringMathematicsta113ta112ta111EstimatorContrast (statistics)riippumattomien komponenttien analyysi020206 networking & telecommunicationsMaximizationIndependent component analysisNonlinear systemControl and Systems EngineeringSignal ProcessingFastICAComputer Vision and Pattern Recognitionlimiting normalitySoftware
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Deflation-Based FastICA With Adaptive Choices of Nonlinearities

2014

Deflation-based FastICA is a popular method for independent component analysis. In the standard deflation-base d approach the row vectors of the unmixing matrix are extracted one after another always using the same nonlinearities. In prac- tice the user has to choose the nonlinearities and the efficiency and robustness of the estimation procedure then strongly depends on this choice as well as on the order in which the components are extracted. In this paper we propose a novel adaptive two- stage deflation-based FastICA algorithm that (i) allows one to use different nonlinearities for different components and (ii) optimizes the order in which the components are extracted. Based on a consist…

Mathematical optimizationta112Asymptotic distribution020206 networking & telecommunications02 engineering and technology01 natural sciencesIndependent component analysis010104 statistics & probabilityNonlinear systemRobustness (computer science)Signal Processing0202 electrical engineering electronic engineering information engineeringFastICAEquivariant mapAffine transformation0101 mathematicsElectrical and Electronic EngineeringAlgorithmFinite setMathematicsIEEE Transactions on Signal Processing
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Independent component analysis based on symmetrised scatter matrices

2007

A new method for separating the mixtures of independent sources has been proposed recently in [Oja et al. (2006). Scatter matrices and independent component analysis. Austrian J. Statist., to appear]. This method is based on two scatter matrices with the so-called independence property. The corresponding method is now further examined. Simple simulation studies are used to compare the performance of so-called symmetrised scatter matrices in solving the independence component analysis problem. The results are also compared with the classical FastICA method. Finally, the theory is illustrated by some examples. peerReviewed

Statistics and ProbabilityApplied MathematicsIndependence propertyStatistical computationhajontamatriisitIndependent component analysisComputational MathematicsComputational Theory and MathematicsComponent analysisSimple (abstract algebra)CalculusSource separationFastICAApplied mathematicsICAIndependence (probability theory)MathematicsComputational Statistics & Data Analysis
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On Independent Component Analysis with Stochastic Volatility Models

2017

Consider a multivariate time series where each component series is assumed to be a linear mixture of latent mutually independent stationary time series. Classical independent component analysis (ICA) tools, such as fastICA, are often used to extract latent series, but they don't utilize any information on temporal dependence. Also financial time series often have periods of low and high volatility. In such settings second order source separation methods, such as SOBI, fail. We review here some classical methods used for time series with stochastic volatility, and suggest modifications of them by proposing a family of vSOBI estimators. These estimators use different nonlinearity functions to…

Statistics and ProbabilityAutoregressive conditional heteroskedasticity01 natural sciencesQA273-280GARCH model010104 statistics & probabilityblind source separation0502 economics and businessSource separationEconometricsApplied mathematics0101 mathematics050205 econometrics MathematicsStochastic volatilitymultivariate time seriesApplied MathematicsStatistics05 social sciencesAutocorrelationEstimatorIndependent component analysisHA1-4737nonlinear autocorrelationFastICAStatistics Probability and UncertaintyVolatility (finance)Probabilities. Mathematical statistics
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fICA : FastICA Algorithms and Their Improved Variants

2019

Abstract In independent component analysis (ICA) one searches for mutually independent non gaussian latent variables when the components of the multivariate data are assumed to be linear combinations of them. Arguably, the most popular method to perform ICA is FastICA. There are two classical versions, the deflation-based FastICA where the components are found one by one, and the symmetric FastICA where the components are found simultaneously. These methods have been implemented previously in two R packages, fastICA and ica. We present the R package fICA and compare it to the other packages. Additional features in fICA include optimization of the extraction order in the deflation-based vers…

Statistics and ProbabilityR-kieliNumerical AnalysisalgorimitComputer sciencealgoritmitFastICAsignaalianalyysiStatistics Probability and UncertaintyAlgorithm
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Fourth Moments and Independent Component Analysis

2015

In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting wi…

Statistics and ProbabilityjadeMultivariate random variableGeneral MathematicsMathematics - Statistics TheoryStatistics Theory (math.ST)02 engineering and technologyEstimating equations01 natural sciences010104 statistics & probabilityTransformation matrixFastICAFOS: Mathematics0202 electrical engineering electronic engineering information engineeringAffine equivarianceApplied mathematics0101 mathematicsLinear combinationMathematicsComponent (thermodynamics)kurtosis020206 networking & telecommunicationsFOBIIndependent component analysisJADEFastICAStatistics Probability and UncertaintyRandom variable
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Non-negative matrix factorization Vs. FastICA on mismatch negativity of children

2009

In this presentation two event-related potentials, mismatch negativity (MMN) and P3a, are extracted from EEG by non-negative matrix factorization (NMF) simultaneously. Typically MMN recordings show a mixture of MMN, P3a, and responses to repeated standard stimuli. NMF may release the source independence assumption and data length limitations required by Fast independent component analysis (FastICA). Thus, in theory NMF could reach better separation of the responses. In the current experiment MMN was elicited by auditory duration deviations in 102 children. NMF was performed on the time-frequency representation of the raw data to estimate sources. Support to Absence Ratio (SAR) of the MMN co…

business.industrySpeech recognitionMismatch negativityPattern recognitionbehavioral disciplines and activitiesIndependent component analysisElectronic mailMatrix decompositionNon-negative matrix factorizationP3aTime–frequency representationFastICAArtificial intelligencebusinesspsychological phenomena and processesMathematics2009 International Joint Conference on Neural Networks
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