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37
Multichannel Blind Deconvolution and Equalization Using the Natural Gradient
 In The First Signal Processing Workshop on Signal Processing Advances in Wireless Communications
, 1997
"... Multichannel deconvolution and equalization is an important task for numerous applications in communications, signal processing, and control. In this paper, we extend the efficient natural gradient search method in [1] to derive a set of online algorithms for combined multichannel blind source separ ..."
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Cited by 119 (24 self)
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Multichannel deconvolution and equalization is an important task for numerous applications in communications, signal processing, and control. In this paper, we extend the efficient natural gradient search method in [1] to derive a set of online algorithms for combined multichannel blind source separation and timedomain deconvolution/equalization of additive, convolved signal mixtures. Through formal analysis, we prove that the doublyinfinite multichannel equalizer based on the maximum entropy cost function with natural gradient possesses the socalled "equivariance property" such that its asymptotic performance depends on the normalized stochastic distribution of the source signals and not on the mixing characteristics of the unknown channel. We also provide the necessary approximations to enable a computationallysimple finiteimpulseresponse implementation of the naturalgradientbased multichannel deconvolution scheme. Simulations indicate the ability of the algorithm to perform e...
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).
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 54 (16 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.
Combining timedelayed decorrelation and ICA: Towards solving the cocktail party problem
 In Proc. ICASSP98
, 1998
"... We present methods to separate blindly mixed signals recorded in a room. The learning algorithm is based on the information maximization in a single layer neural network. We focus on the implementation of the learning algorithm and on issues that arise when separating speakers in room recordings. We ..."
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Cited by 26 (5 self)
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We present methods to separate blindly mixed signals recorded in a room. The learning algorithm is based on the information maximization in a single layer neural network. We focus on the implementation of the learning algorithm and on issues that arise when separating speakers in room recordings. We used an infomax approach in a feedforward neural network implemented in the frequency domain using the polynomial filter matrix algebra technique. Fast convergence speed was achieved by using a timedelayed decorrelation method as a preprocessing step. Under minimumphasemixing conditions this preprocessing step was sufficient for the separation of signals. These methods successfully separated a recorded voice with music in the background(cocktail party problem). Finally, we discuss problems that arise in real world recordings and their potential solutions. 1.
Selfadaptive blind source separation based on activation functions adaptation
 Neural Networks, IEEE Transactions on
"... Abstract—Independent component analysis is to extract independent signals from their linear mixtures without assuming prior knowledge of their mixing coefficients. As we know, a number of factors are likely to affect separation results in practical applications, such as the number of active source ..."
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Cited by 23 (5 self)
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Abstract—Independent component analysis is to extract independent signals from their linear mixtures without assuming prior knowledge of their mixing coefficients. As we know, a number of factors are likely to affect separation results in practical applications, such as the number of active sources, the distribution of source signals, and noise.The purpose of this paper to develop a general framework of blind separation from a practical point of view with special emphasis on the activation function adaptation. First, we propose the exponential generative model for probability density functions. A method of constructing an exponential generative model from the activation functions is discussed. Then, a learning algorithm is derived to update the parameters in the exponential generative model. The learning algorithm for the activation function adaptation is consistent with the one for training the demixing model. Stability analysis of the learning algorithm for the activation function is also discussed. Both theoretical analysis and simulations show that the proposed approach is universally convergent regardless of the distributions of sources. Finally, computer simulations are given to demonstrate the effectiveness and validity of the approach. Index Terms—Activation function, blind source separation, exponential family, independent component analysis. I.
SelfStabilized Gradient Algorithms for Blind Source Separation With Orthogonality Constraints
, 1999
"... { Recently, developments in selfstabilized algorithms for gradient adaptation of orthonormal matrices have resulted in simple but powerful principal and minor subspace analysis methods. In this paper, we extend these ideas to develop algorithms for instantaneous prewhitened blind separation of homo ..."
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Cited by 20 (7 self)
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{ Recently, developments in selfstabilized algorithms for gradient adaptation of orthonormal matrices have resulted in simple but powerful principal and minor subspace analysis methods. In this paper, we extend these ideas to develop algorithms for instantaneous prewhitened blind separation of homogeneous signal mixtures. Our algorithms are proven to be selfstabilizing to the Stiefel manifold of orthonormal matrices, such that the rows of the adaptive demixing matrix do not need to be periodically reorthonormalized. Several algorithm forms are developed, including those that are equivariant with respect to the prewhitened mixing matrix. Simulations verify the excellent numerical properties of the proposed methods for the blind source separation task. submitted to IEEE TRANSACTIONS ON NEURAL NETWORKS TNN Paper No. A544  Revised September 12, 1999. This work was supported in part by the Oce of Research and Development under Contract No. 98F135700000. y Please address corresp...
Natural Gradient Algorithm for Blind Separation of Overdetermined Mixture with Additive Noise
, 1999
"... In this letter we study the natural gradient approach to blind separation of overdetermined mixtures. First we introduce a Lie group on the manifold of overdetermined mixtures, and endow a Riemannian metric on the manifold based on the property of the Lie group. Then we derive the natural gradient o ..."
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Cited by 17 (6 self)
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In this letter we study the natural gradient approach to blind separation of overdetermined mixtures. First we introduce a Lie group on the manifold of overdetermined mixtures, and endow a Riemannian metric on the manifold based on the property of the Lie group. Then we derive the natural gradient on the manifold using the isometry of the Riemannian metric. Using the natural gradient, we present a new learning algorithm based on the minimization of mutual information.
Selfadaptive independent component analysis for subGaussian and superGaussian mixtures with an unknown number of sources and additive noise
 IN INTERNATIONAL SYMPOSIUM ON NONLINEAR THEORY AND APPLICATIONS
, 1997
"... In this paper we derive and analyze unsupervised adaptive on line algorithms for instantaneous blind separation of sources (BSS) in the case when sensors signals are noisy and they are mixture of unknown number of independent source signals with unknown statistics. Nonlinear activation functions a ..."
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Cited by 12 (6 self)
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In this paper we derive and analyze unsupervised adaptive on line algorithms for instantaneous blind separation of sources (BSS) in the case when sensors signals are noisy and they are mixture of unknown number of independent source signals with unknown statistics. Nonlinear activation functions are rigorously derived assuming that source have generalized Gaussian, Cauchy orRayleigh distributions. Extensive computer simulations con rmed that the proposed family of learning algorithms are able to separate sources from mixture of sub and superGaussian sources.
A Common Neural Network Model for Unsupervised Exploratory Data Analysis and Independent Component Analysis
, 1998
"... This paper presents the derivation of an unsupervised learning algorithm, which enables the identification and visualisation of latent structure within ensembles of high dimensional data. This provides a linear projection of the data onto a lower dimensional subspace to identify the characteristic s ..."
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Cited by 10 (0 self)
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This paper presents the derivation of an unsupervised learning algorithm, which enables the identification and visualisation of latent structure within ensembles of high dimensional data. This provides a linear projection of the data onto a lower dimensional subspace to identify the characteristic structure of the observations independent latent causes. The algorithm is shown to be a very promising tool for unsupervised exploratory data analysis and data visualisation. Experimental results confirm the attractiveness of this technique for exploratory data analysis and an empirical comparison is made with the recently proposed Generative Topographic Mapping (GTM) and standard principal component analysis (PCA). Based on standard probability density models a generic nonlinearity is developed which allows both; 1) identification and visualisation of dichotomised clusters inherent in the observed data and, 2) separation of sources with arbitrary distributions from mixtures, whose dimensiona...
Transpose Properties in the Stability and Performance of the Classic Adaptive Algorithms for Blind Source Separation and Deconvolution
, 2000
"... This paper presents a tutorial review of the problem of Blind Source Separation (BSS) and the properties of the classic adaptive algorithms when either the score function or a general (nonscore) nonlinearity is employed in the algorithm. In new findings it is shown that the separating solution for ..."
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Cited by 8 (4 self)
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This paper presents a tutorial review of the problem of Blind Source Separation (BSS) and the properties of the classic adaptive algorithms when either the score function or a general (nonscore) nonlinearity is employed in the algorithm. In new findings it is shown that the separating solution for both sub and superGaussian signals can be stabilized by an algorithm employing any given nonlinearity. For these separating solutions the steadystate error levels are also given in terms of the nonlinearity and the pdf.s of the source signals. These results show that a transpose symmetry exists between the nonlinear algorithms for suband superGaussian signals. The behavior of the algorithm is then detailed when the ideal scorefunction nonlinearity is replaced by a general (hard saturation or u³) nonlinearity. The phases of convergence to decorrelated output signals and then to recovery of the source signals are explained. The results are then extended to single and multichannel...