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30
Multichannel Blind Deconvolution: Fir Matrix Algebra And Separation Of Multipath Mixtures
, 1996
"... A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and mat ..."
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Cited by 74 (0 self)
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A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feedforward memory connections, wideband array processing, and in problems with a multiinput, multioutput network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...
Negentropy and Kurtosis as Projection Pursuit Indices Provide Generalised ICA Algorithms
, 1997
"... We develop a generalised form of the independent component analysis (ICA) algorithm introduced by Bell and Sejnowski [1], Amari et al [2] and lately by Pearlmutter and Parra [3] and also MacKay [4]. Motivated by information theoretic indices for exploratory projection pursuit (EPP) we show that maxi ..."
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Cited by 20 (0 self)
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We develop a generalised form of the independent component analysis (ICA) algorithm introduced by Bell and Sejnowski [1], Amari et al [2] and lately by Pearlmutter and Parra [3] and also MacKay [4]. Motivated by information theoretic indices for exploratory projection pursuit (EPP) we show that maximisation by natural gradient ascent of the divergence of a multivariate distribution from normality, using the negentropy as a distance measure, yields a generalised ICA. We introduce a form of nonlinearity which has an inherently simple form and exhibits the Bussgang property [30] within the algorithm. We show that this is sufficient to perform ICA on data which has latent variables exhibiting either unimodal or bimodal probability density functions (PDF) or both. Kurtosis has been used as a moment based projection pursuit index and as a contrast for ICA [5, 6, 7]. We introduce a simple adaptive nonlinearity which is formed by online estimation of the latent variable kurtosis and demonstra...
A Tensor Approximation Approach to Dimensionality Reduction
"... Abstract Dimensionality reduction has recently been extensively studied for computer vision applications. We present a novel multilinear algebra based approach to reduced dimensionality representation of multidimensional data, such as image ensembles, video sequences and volume data. Before reducing ..."
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Cited by 10 (0 self)
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Abstract Dimensionality reduction has recently been extensively studied for computer vision applications. We present a novel multilinear algebra based approach to reduced dimensionality representation of multidimensional data, such as image ensembles, video sequences and volume data. Before reducing the dimensionality we do not convert it into a vector as is done by traditional dimensionality reduction techniques like PCA. Our approach works directly on the multidimensional form of the data (matrix in 2D and tensor in higher dimensions) to yield what we call a DatumasIs representation. This helps exploit spatiotemporal redundancies with less information loss than imageasvector methods. An efficient rankR tensor approximation algorithm is presented to approximate higherorder tensors. We show that rankR tensor approximation using DatumasIs representation generalizes many existing approaches that use imageasmatrix representation, such as generalized low rank approximation of matrices (GLRAM) (Ye, Y. in Mach. Learn. 61:167–191, 2005), rankone decomposition of matrices (RODM) (Shashua, A., Levin, A. in CVPR’01:
A Constrained EM Algorithm for Independent Component Analysis
 Neural Computation
, 2001
"... We introduce a novel way of performing independent component analysis using a constrained version of the expectation maximization algorithm. The source distributions are modeled as D onedimensional mixtures of Gaussians. The observed data are modeled as linear mixtures of the sources with additi ..."
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Cited by 8 (1 self)
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We introduce a novel way of performing independent component analysis using a constrained version of the expectation maximization algorithm. The source distributions are modeled as D onedimensional mixtures of Gaussians. The observed data are modeled as linear mixtures of the sources with additive, isotropic noise. This generative model is t to the data using constrained EM. The simpler \softswitching" approach is introduced, which uses only one parameter to decide on the sub or superGaussian nature of the sources. It is explained how our approach relates to independent factor analysis. 1
A stochastic algorithm for feature selection in pattern recognition
 Journal of Machine Learning Research
, 2007
"... We introduce a new model addressing feature selection from a large dictionary of variables that can be computed from a signal or an image. Features are extracted according to an efficiency criterion, on the basis of specified classification or recognition tasks. This is done by estimating a probabil ..."
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Cited by 8 (2 self)
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We introduce a new model addressing feature selection from a large dictionary of variables that can be computed from a signal or an image. Features are extracted according to an efficiency criterion, on the basis of specified classification or recognition tasks. This is done by estimating a probability distribution P on the complete dictionary, which distributes its mass over the more efficient, or informative, components. We implement a stochastic gradient descent algorithm, using the probability as a state variable and optimizing a multitask goodness of fit criterion for classifiers based on variable randomly chosen according to P. We then generate classifiers from the optimal distribution of weights learned on the training set. The method is first tested on several pattern recognition problems including face detection, handwritten digit recognition, spam classification and microarray analysis. We then compare our approach with other stepwise algorithms like random forests or recursive feature elimination. Keywords: stochastic learning algorithms, RobbinsMonro application, pattern recognition, classification algorithm, feature selection
Algorithm for blind signal separation and recovery in static and dynamics environments
 Proc. IEEE Symposium on Circuits and Systems
, 1997
"... We propose update laws for the problem of blind separation in static and dynamic environments. The energy function is based on an approximation of the mutual information as a measure of independence. Both feedforward and feedback structures of the neural network are considered. A general framework t ..."
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Cited by 6 (1 self)
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We propose update laws for the problem of blind separation in static and dynamic environments. The energy function is based on an approximation of the mutual information as a measure of independence. Both feedforward and feedback structures of the neural network are considered. A general framework to develop the update law for the dynamic model is proposed. Computer simulations to support the analytical work are provided. 1.
Unmixing mix traffic
 In Proc. of Privacy Enhancing Technologies workshop (PET 2005
, 2005
"... Abstract. We apply blind source separation techniques from statistical signal processing to separate the traffic in a mix network into either individual flows or groups of flows. This separation requires no a priori information about the individual flows. As a result, unlinkability can be compromise ..."
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Cited by 4 (1 self)
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Abstract. We apply blind source separation techniques from statistical signal processing to separate the traffic in a mix network into either individual flows or groups of flows. This separation requires no a priori information about the individual flows. As a result, unlinkability can be compromised without ever observing individual flows. Our experiments show that this attack is effective and scalable. By correlating separated groups of flows across nodes, a passive attacker can get an accurate traffic map of the mix network. We use a nontrivial network to show that the combined attack works. The experiments also show that multicast traffic can be dangerous for anonymity networks. 1
Text extraction from graphical document images using sparse representation
 in Proceedings of the 9th International Workshop on Document Analysis Systems, 2010
"... A novel text extraction method from graphical document images is presented in this paper. Graphical document images containing text and graphics components are considered as twodimensional signals by which text and graphics have different morphological characteristics. The proposed algorithm relies ..."
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Cited by 4 (2 self)
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A novel text extraction method from graphical document images is presented in this paper. Graphical document images containing text and graphics components are considered as twodimensional signals by which text and graphics have different morphological characteristics. The proposed algorithm relies upon a sparse representation framework with two appropriately chosen discriminative overcomplete dictionaries, each one gives sparse representation over one type of signal and nonsparse representation over the other. Separation of text and graphics components is obtained by promoting sparse representation of input images in these two dictionaries. Some heuristic rules are used for grouping text components into text strings in postprocessing steps. The proposed method overcomes the problem of touching between text and graphics. Preliminary experiments show some promising results on different types of document.
ICA based on a Smooth Estimation of the Differential Entropy
"... In this paper we introduce the MeanNN approach for estimation of main information theoretic measures such as differential entropy, mutual information and divergence. As opposed to other nonparametric approaches the MeanNN results in smooth differentiable functions of the data samples with clear geom ..."
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Cited by 4 (2 self)
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In this paper we introduce the MeanNN approach for estimation of main information theoretic measures such as differential entropy, mutual information and divergence. As opposed to other nonparametric approaches the MeanNN results in smooth differentiable functions of the data samples with clear geometrical interpretation. Then we apply the proposed estimators to the ICA problem and obtain a smooth expression for the mutual information that can be analytically optimized by gradient descent methods. The improved performance of the proposed ICA algorithm is demonstrated on several test examples in comparison with stateoftheart techniques. 1
Feature Selection and Dimensionality Reduction in Genomics and Proteomics
, 2006
"... Finding reliable, meaningful patterns in data with high numbers of attributes can be extremely difficult. Feature selection helps us to decide what attributes or combination of attributes are most important for finding these patterns. In this chapter, we study feature selection methods for building ..."
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Cited by 2 (2 self)
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Finding reliable, meaningful patterns in data with high numbers of attributes can be extremely difficult. Feature selection helps us to decide what attributes or combination of attributes are most important for finding these patterns. In this chapter, we study feature selection methods for building classification models from highthroughput genomic (microarray) and proteomic (mass spectrometry) data sets. Thousands of feature candidates must be analyzed, compared and combined in such data sets. We describe the basics of four different approaches used for feature selection and illustrate their effects on an MS cancer proteomic data set. The closing discussion provides assistance in performing an analysis in highdimensional genomic and proteomic data