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Ensemble learning for independent component analysis
 IN ADVANCES IN INDEPENDENT COMPONENT ANALYSIS
, 2000
"... This thesis is concerned with the problem of Blind Source Separation. Specifically we considerthe Independent Component Analysis (ICA) model in which a set of observations are modelled by xt = Ast: (1) where A is an unknown mixing matrix and st is a vector of hidden source components attime t. The ..."
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Cited by 59 (3 self)
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This thesis is concerned with the problem of Blind Source Separation. Specifically we considerthe Independent Component Analysis (ICA) model in which a set of observations are modelled by xt = Ast: (1) where A is an unknown mixing matrix and st is a vector of hidden source components attime t. The ICA problem is to find the sources given only a set of observations. In chapter 1, the blind source separation problem is introduced. In chapter 2 the methodof Ensemble Learning is explained. Chapter 3 applies Ensemble Learning to the ICA model and chapter 4 assesses the use of Ensemble Learning for model selection.Chapters 57 apply the Ensemble Learning ICA algorithm to data sets from physics (a medical imaging data set consisting of images of a tooth), biology (data sets from cDNAmicroarrays) and astrophysics (Planck image separation and galaxy spectra separation).
Efficient Variant of Algorithm for FastICA for Independent Component Analysis Attaining the CramérRao Lower Bound
 IEEE Trans. Neural Net
, 2006
"... Abstract—FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA alg ..."
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Cited by 54 (5 self)
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Abstract—FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramér–Rao lower bound (CRB). The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian (GG) distributions with parameter, denoted GG () for 2. We name the algorithm efficient FastICA (EFICA). Computational complexity of a Matlab implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simulations corroborate these claims and show superior performance of the algorithm compared with algorithm JADE of Cardoso and Souloumiac and nonparametric ICA of Boscolo et al. on separating sources with distributionGG ( ) with arbitrary, as well as on sources with bimodal distribution, and a good performance in separating linearly mixed speech signals. Index Terms—Algorithm FastICA, blind deconvolution, blind source separation, Cramér–Rao lower bound (CRB), independent component analysis (ICA). I.
Source Separation: From Dusk Till Dawn
"... The first part of this paper is concerned by the history of source separation. It include our comments and those of a few other researchers on the development of this new research field. The second part is focused on recent developments of the separation in nonlinear mixtures. ..."
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Cited by 17 (5 self)
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The first part of this paper is concerned by the history of source separation. It include our comments and those of a few other researchers on the development of this new research field. The second part is focused on recent developments of the separation in nonlinear mixtures.
Blind Source Separation: the Sparsity Revolution
, 2008
"... Over the last few years, the development of multichannel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the socalled blind source separation (BSS) problem. In this conte ..."
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Cited by 7 (5 self)
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Over the last few years, the development of multichannel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the socalled blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. We give here some essential insights into the use of sparsity in source separation and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper overviews a sparsitybased BSS method coined Generalized Morphological Component Analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient blind source separation method. In remote sensing applications, the specificity of hyperspectral data should be accounted for. We extend the proposed GMCA framework to deal with hyperspectral data. In a general framework, GMCA provides a basis for multivariate data analysis in the scope of a wide range of classical multivariate data restorate. Numerical results are given in color image denoising and inpainting. Finally, GMCA is applied to the simulated ESA/Planck data. It is shown to give effective astrophysical component separation.
Semiparametric Approach to Blind Separation of Dynamic Systems
 In Proceedings of NOLTA’99
, 1999
"... In this paper we present a semiparametric approach to blind separation of nonlinear dynamical systems with linear output equations. First we formulate blind deconvolution in a framework of semiparametric model and derive a family of estimating functions for the blind separation problem by using a no ..."
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In this paper we present a semiparametric approach to blind separation of nonlinear dynamical systems with linear output equations. First we formulate blind deconvolution in a framework of semiparametric model and derive a family of estimating functions for the blind separation problem by using a nonholonomic reparametrization. The natural gradient learning algorithm is derived in the semiparametric models. We prove that under certain conditions the natural gradient learning algorithm converges to the true solution locally. I. Introduction Blind source separation has received great attention recently because of its theoretic significance and growing applications in signal processing as in speech recognition systems, medical signal processing and telecommunications. The goal of blind source separation is to recover independent sources given only sensor observations that are unknown linear/nonlinear mixtures of unobserved independent source signals. Several neural networks and statist...
Semiparametric Approach to Multichannel Blind Deconvolution of Nonminimum Phase Systems
 Advances in Neural Information Processing Systems 12
, 2000
"... In this paper we discuss the semiparametric statistical model for blind deconvolution. First we introduce a Lie Group to the manifold of noncausal FIR filters. Then blind deconvolution problem is formulated in the framework of a semiparametric model, and a family of estimating functions is deriv ..."
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In this paper we discuss the semiparametric statistical model for blind deconvolution. First we introduce a Lie Group to the manifold of noncausal FIR filters. Then blind deconvolution problem is formulated in the framework of a semiparametric model, and a family of estimating functions is derived for blind deconvolution. A natural gradient learning algorithm is developed for training noncausal filters. Stability of the natural gradient algorithm is also analyzed in this framework. 1 Introduction Recently blind separation/deconvolution has been recognized as an increasing important research area due to its rapidly growing applications in various fields, such as telecommunication systems, image enhancement and biomedical signal processing. Refer to review papers [7] and [13] for details. A semiparametric statistical model treats a family of probability distributions specified by a finitedimensional parameter of interest and an infinitedimensional nuisance parameter [12]. Amari...
LETTER Communicated by Jean François Cardoso Estimating Functions of Independent Component Analysis for Temporally Correlated Signals
"... This article studies a general theory of estimating functions of independent component analysis when the independent source signals are temporarily correlated. Estimating functions are used for deriving both batch and online learning algorithms, and they are applicable to blind cases where spatial ..."
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This article studies a general theory of estimating functions of independent component analysis when the independent source signals are temporarily correlated. Estimating functions are used for deriving both batch and online learning algorithms, and they are applicable to blind cases where spatial and temporal probability structures of the sources are unknown. Most algorithms proposed so far can be analyzed in the framework of estimating functions. An admissible class of estimating functions is derived, and related efficient online learning algorithms are introduced. We analyze dynamical stability and statistical efficiency of these algorithms. Different from the independently and identically distributed case, the algorithms work even when only the secondorder moments are used. The method of simultaneous diagonalization of crosscovariance matrices is also studied from the point of view of estimating functions. 1
Hybrid Higher Order Statistics Learning in Multiuser Detection
"... In this work we explore the significance of second and higher order statistics learning in communications systems. The final goal in spread spectrum communication systems is to receive a signal of interest completely free from interference caused by other concurrent signals. To achieve this end we ..."
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In this work we explore the significance of second and higher order statistics learning in communications systems. The final goal in spread spectrum communication systems is to receive a signal of interest completely free from interference caused by other concurrent signals. To achieve this end we exploit the structure of the interference, designing Second Order Statistics (SOS) detectors, such as the Minimum Square Error (MMSE) (known to be optimum linear detectors in noisy environments) in conjuction with Higher Order Statistics (HOS) techniques, such as the Blind Source Separation (BSS) and the Independent Component Analysis (ICA) (known to exhibit such remarkable properties in learning such as scale invariance and superefficiency). Such Hybrid Higher Order Statistics (HyHOS) approach enables us to alleviate BSS/ICA algorithms of one of their main problems, that is, their sensitiviness to high levels of noise as we benefit from their speed of learning and independence of the initial settings of the problem. We successfully applied the results of this approach to the design of multiuser detectors in Code Division Multiple Access (CDMA) channels.
HuygensFresnel Principle Generates Nonlinear ICA Reducible To Solvable Incoherent Limit Linear ICA
, 2001
"... Reticle trackers have been used successfully with a beam splitter for tracking and discrimination of several moving incoherent (heat) optical sources in the mathematical framework called Independent Component Analyses (ICA). Here we further explore the theoretical basis of the coherent and partially ..."
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Reticle trackers have been used successfully with a beam splitter for tracking and discrimination of several moving incoherent (heat) optical sources in the mathematical framework called Independent Component Analyses (ICA). Here we further explore the theoretical basis of the coherent and partially coherent illumination by laser for the possibility of blind source demixing. An application of the partial coherence theory and the HuygensFresnel principle is utilized to formulate the problem. When incoherence is assumed a linear ICA model is obtained while in most general case of either partially or totally coherent optical radiation the resulting signal model is inherently nonlinear. It can be transformed into linear one under very special condition that assumes no relative motion between the radiating sources. In the most general case of partially coherent radiation, tracking of the several moving optical sources by using the beam splitter based reticle trackers is possible either by using ICA algorithms developed for undercomplete representation or by introduction of one additional sensor.
NATURAL GRADIENT USING SIMULTANEOUS PERTURBATION WITHOUT PROBABILITY DENSITIES FOR BLIND SOURCE SEPARATION
"... When independent plural signals are mixed and the mixed plural signals are measured, blind signal separation technique is very interesting approach to separate these signals only based on the measured signals. It is ahot subject in the ¯elds of engineering, for example, communication engineering, si ..."
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When independent plural signals are mixed and the mixed plural signals are measured, blind signal separation technique is very interesting approach to separate these signals only based on the measured signals. It is ahot subject in the ¯elds of engineering, for example, communication engineering, signal processing, image processing, analysis of organs inside abody and so on. In this paper, we propose recursive methods to obtain aseparating matrix based on mutual information, via the simultaneous perturbation optimization method. The simultaneous perturbation method updates the separating matrix by using only two values of the mutual information. Then, probability densities of source signals, which are used in ordinary gradient methods, are not required. Asimple example is shown to con¯rm afeasibility of the proposed methods. 1.