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23
Beyond independent components: trees and clusters
 Journal of Machine Learning Research
, 2003
"... We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a treestructured graphical model. This treedependent component analysi ..."
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Cited by 56 (0 self)
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We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a treestructured graphical model. This treedependent component analysis (TCA) provides a tractable and flexible approach to weakening the assumption of independence in ICA. In particular, TCA allows the underlying graph to have multiple connected components, and thus the method is able to find “clusters ” of components such that components are dependent within a cluster and independent between clusters. Finally, we make use of a notion of graphical models for time series due to Brillinger (1996) to extend these ideas to the temporal setting. In particular, we are able to fit models that incorporate treestructured dependencies among multiple time series.
A minimizationprojection (MP) approach for blind separating convolutive mixtures
 in ICASSP, 2004, Accepted
"... In this paper, a new approach for blind source separation is presented. This approach is based on minimization of the mutual information of the outputs using a nonparametric “gradient ” of mutual information, followed by a projection on the parametric model of the separation structure. It is applica ..."
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Cited by 7 (2 self)
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In this paper, a new approach for blind source separation is presented. This approach is based on minimization of the mutual information of the outputs using a nonparametric “gradient ” of mutual information, followed by a projection on the parametric model of the separation structure. It is applicable to different mixing system, linear as well as nonlinear, and the algorithms derived from this approach are very fast and efficient. 1.
A dataset for the design of smart ionselective electrode arrays for quantitative analysis
 IEEE Sensors Journal
, 2010
"... Progrès en traitement des signaux et analyse des images pour les analyses physicochimiques et la détection chimique ..."
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Cited by 7 (5 self)
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Progrès en traitement des signaux et analyse des images pour les analyses physicochimiques et la détection chimique
Blind separation of convolutive image mixtures
, 2008
"... Convolutive mixtures of images are common in photography of semireflections. They also occur in microscopy and tomography. Their formation process involves focusing on an object layer, over which defocused layers are superimposed. We seek blind source separation (BSS) of such mixtures. However, ach ..."
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Cited by 2 (1 self)
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Convolutive mixtures of images are common in photography of semireflections. They also occur in microscopy and tomography. Their formation process involves focusing on an object layer, over which defocused layers are superimposed. We seek blind source separation (BSS) of such mixtures. However, achieving this by direct optimization of mutual information is very complex and suffers from local minima. Thus, we devise an efficient approach to solve these problems. While achieving high quality image separation, we take steps that make the problem significantly simpler than a direct formulation of convolutive image mixtures. These steps make the problem practically convex, yielding a unique global solution to which convergence can be fast. The convolutive BSS problem is converted into a set of instantaneous (pointwise) problems, using a short time Fourier transform (STFT). Standard BSS solutions for instantaneous problems suffer, however, from scale and permutation ambiguities. We overcome these ambiguities by exploiting a parametric model of the defocus point spread function. Moreover, we enhance the efficiency of the approach by exploiting the sparsity of the STFT representation as a prior. We apply our algorithm to semireflections, and demonstrate it in experiments.
ICA Using Kernel Entropy Estimation with NlogN Complexity ⋆
"... Abstract. Mutual information (MI) is a common criterion in independent component analysis (ICA) optimization. MI is derived from probability density functions (PDF). There are scenarios in which assuming a parametric form for the PDF leads to poor performance. Therefore, the need arises for nonpara ..."
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Abstract. Mutual information (MI) is a common criterion in independent component analysis (ICA) optimization. MI is derived from probability density functions (PDF). There are scenarios in which assuming a parametric form for the PDF leads to poor performance. Therefore, the need arises for nonparametric PDF and MI estimation. Existing nonparametric algorithms suffer from high complexity, particularly in high dimensions. To counter this obstacle, we present an ICA algorithm based on accelerated kernel entropy estimation. It achieves both high separation performance and low computational complexity. For K sources with N samples, our ICA algorithm has an iteration complexity of at most O(KN log N + K 2 N). 1
Blind maximum likelihood separation of a linearquadratic mixture
"... Abstract. We proposed recently a new method for separating linearquadratic mixtures of independent real sources, based on parametric identification of a recurrent separating structure using an ad hoc algorithm. In this paper, we develop a maximum likelihood approach providing an asymptotically ef ..."
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Abstract. We proposed recently a new method for separating linearquadratic mixtures of independent real sources, based on parametric identification of a recurrent separating structure using an ad hoc algorithm. In this paper, we develop a maximum likelihood approach providing an asymptotically efficient estimation of the model parameters. A major advantage of this method is that the explicit form of the inverse of the mixing model is not required to be known. Thus, the method can be easily generalized to more complicated polynomial mixtures. 1
Maximum likelihood blind image separation using nonsymmetrical halfplane markov random fields
 IEEE Trans. on Image Processing
, 2009
"... Abstract—This paper presents a maximum likelihood approach for blindly separating linear instantaneous mixtures of images. The spatial autocorrelation within each image is described using nonsymmetrical halfplane (NSHP) Markov random fields in order to simplify the joint probability density functi ..."
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Abstract—This paper presents a maximum likelihood approach for blindly separating linear instantaneous mixtures of images. The spatial autocorrelation within each image is described using nonsymmetrical halfplane (NSHP) Markov random fields in order to simplify the joint probability density functions of the source images. A first implementation assuming stationary sources is presented. It is then extended to a more realistic nonstationary image model: two approaches, respectively based on blocking and kernel smoothing, are proposed to cope with the nonstationarity of the images. The estimation of the mixing matrix is performed using an iterative equivariant version of the NewtonRaphson algorithm. Moreover, score functions, required for the computation of the updating rule, are approximated at each iteration by parametric polynomial estimators. Results achieved with artificial mixtures of both artificial and realworld images, including an astrophysical application, clearly prove the high performance of our methods, as compared to classical algorithms. Index Terms—Blind source separation (BSS), maximum likelihood approach, nonstationary sources, nonsymmetrical halfplane (NSHP) Markov random fields. I.
Research Letter Generalized Cumulative Residual Entropy for Distributions with Unrestricted Supports
, 2008
"... We consider the cumulative residual entropy (CRE) a recently introduced measure of entropy. While in previous works distributions with positive support are considered, we generalize the definition of CRE to the case of distributions with general support. We show that several interesting properties ..."
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We consider the cumulative residual entropy (CRE) a recently introduced measure of entropy. While in previous works distributions with positive support are considered, we generalize the definition of CRE to the case of distributions with general support. We show that several interesting properties of the earlier CRE remain valid and supply further properties and insight to problems such as maximum CRE power moment problems. In addition, we show that this generalized CRE can be used as an alternative to differential entropy to derive informationbased optimization criteria for system identification purpose.
An analysis of entropy estimators for blind source separation
, 2005
"... An extensive analysis of a nonparametric, informationtheoretic method for instantaneous blind source separation (BSS) is presented. As a result a modified stochastic information gradient estimator is proposed to reduce the computational complexity and to allow the separation of subGaussian source ..."
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An extensive analysis of a nonparametric, informationtheoretic method for instantaneous blind source separation (BSS) is presented. As a result a modified stochastic information gradient estimator is proposed to reduce the computational complexity and to allow the separation of subGaussian sources. Interestingly, the modification enables the method to simultaneously exploit spatial and spectral diversity of the sources. Consequently, the new algorithm is able to separate i.i.d. sources, which requires higherorder spatial statistics, and it is also able to separate temporally correlated Gaussian sources, which requires temporal statistics. Three reasons are given why Renyi’s entropy estimators for InformationTheoretic Learning (ITL), on which the proposed method is based, is to be preferred over Shannon’s entropy estimators for ITL. Also contained herein is an extensive comparison of the proposed method with JADE, Infomax, Comon’s MI, FastICA, and a nonparametric, informationtheoretic method that is based on Shannon’s entropy. Performance comparisons are shown as a function of the data length, source kurtosis, number of sources, and
Blind Source Separation 1
, 2009
"... In this paper, the problem of Blind Source Separation (BSS) through mutual information minimization is addressed. For mutual information minimization, multivariate score functions are first introduced, which can be served to construct a nonparametric “gradient ” for mutual information. Then, two g ..."
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In this paper, the problem of Blind Source Separation (BSS) through mutual information minimization is addressed. For mutual information minimization, multivariate score functions are first introduced, which can be served to construct a nonparametric “gradient ” for mutual information. Then, two general gradient based approaches for minimizing mutual information in a parametric model are presented. Although, in this paper, these approaches are only used in BSS, they are quiet general, and can be applied in other mutual information optimization problems.