Results 1  10
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752
Independent Component Analysis
 Neural Computing Surveys
, 2001
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
Abstract

Cited by 1492 (93 self)
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A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1
Sparse coding with an overcomplete basis set: a strategy employed by V1
 Vision Research
, 1997
"... The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive f ..."
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Cited by 591 (7 self)
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The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive field properties may be accounted for in terms of a strategy for producing a sparse distribution of output activity in response to natural images. Here, in addition to describing this work in a more expansive fashion, we examine the neurobiological implications of sparse coding. Of particular interest is the case when the code is overcompletei.e., when the number of code elements is greater than the effective dimensionality of the input space. Because the basis functions are nonorthogonal and not linearly independent of each other, sparsifying the code will recruit only those basis functions necessary for representing a given input, and so the inputoutput function will deviate from being purely linear. These deviations from linearity provide a potential explanation for the weak forms of nonlinearity observed in the response properties of cortical simple cells, and they further make predictions about the expected interactions among units in
Fast and robust fixedpoint algorithms for independent component analysis
 IEEE TRANS. NEURAL NETW
, 1999
"... Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informat ..."
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Cited by 511 (34 self)
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Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informationtheoretic approach and the projection pursuit approach. Using maximum entropy approximations of differential entropy, we introduce a family of new contrast (objective) functions for ICA. These contrast functions enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model, and it is shown how to choose contrast functions that are robust and/or of minimum variance. Finally, we introduce simple fixedpoint algorithms for practical optimization of the contrast functions. These algorithms optimize the contrast functions very fast and reliably.
Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE Trans Image Processing
, 2003
"... Abstract—We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussi ..."
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Cited by 350 (18 self)
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Abstract—We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 298 (1 self)
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This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that has been contaminated with additive noise, the goal is to identify which elementary signals participated and to approximate their coefficients. Although many algorithms have been proposed, there is little theory which guarantees that these algorithms can accurately and efficiently solve the problem. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure that convex relaxation succeeds. As evidence of the broad impact of these results, the paper describes how convex relaxation can be used for several concrete signal recovery problems. It also describes applications to channel coding, linear regression, and numerical analysis.
Nonnegative matrix factorization with sparseness constraints
 Jour. of
, 2004
"... www.cs.helsinki.fi/patrik.hoyer ..."
Independent Component Filters Of Natural Images Compared With Simple Cells In Primary Visual Cortex
, 1998
"... this article we investigate to what extent the statistical properties of natural images can be used to understand the variation of receptive field properties of simple cells in the mammalian primary visual cortex. The receptive fields of simple cells have been studied extensively (e.g., Hubel & Wies ..."
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Cited by 273 (0 self)
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this article we investigate to what extent the statistical properties of natural images can be used to understand the variation of receptive field properties of simple cells in the mammalian primary visual cortex. The receptive fields of simple cells have been studied extensively (e.g., Hubel & Wiesel 1968, DeValois et al. 1982a, DeAngelis et al. 1993): they are localised in space and time, have bandpass characteristics in the spatial and temporal frequency domains, are oriented, and are often sensitive to the direction of motion of a stimulus. Here we will concentrate on the spatial properties of simple cells. Several hypotheses as to the function of these cells have been proposed. As the cells preferentially respond to oriented edges or lines, they can be viewed as edge or line detectors. Their joint localisation in both the spatial domain and the spatial frequency domain has led to the suggestion that they mimic Gabor filters, minimising uncertainty in both domains (Daugman 1980, Marcelja 1980). More recently, the match between the operations performed by simple cells and the wavelet transform has attracted attention (e.g., Field 1993). The approaches based on Gabor filters and wavelets basically consider processing by the visual cortex as a general image processing strategy, relatively independent of detailed assumptions about image statistics. On the other hand, the edge and line detector hypothesis is based on the intuitive notion that edges and lines are both abundant and important in images. This theme of relating simple cell properties with the statistics of natural images was explored extensively by Field (1987, 1994). He proposed that the cells are optimized specifically for coding natural images. He argued that one possibility for such a code, sparse coding...
Regularization networks and support vector machines
 Advances in Computational Mathematics
, 2000
"... Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples – in particular the regression problem of approximating a multivariate function from sparse data. Radial Basis Functions, for example, are a special case of both regularization a ..."
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Cited by 266 (33 self)
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Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples – in particular the regression problem of approximating a multivariate function from sparse data. Radial Basis Functions, for example, are a special case of both regularization and Support Vector Machines. We review both formulations in the context of Vapnik’s theory of statistical learning which provides a general foundation for the learning problem, combining functional analysis and statistics. The emphasis is on regression: classification is treated as a special case.
Face Recognition By Elastic Bunch Graph Matching
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1997
"... We present a system for recognizing human faces from single images out of a large database containing one image per person. Faces are represented by labeled graphs, based on a Gabor wavelet transform. Image graphs of new faces are extracted by an elastic graph matching process and can be compared b ..."
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Cited by 221 (7 self)
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We present a system for recognizing human faces from single images out of a large database containing one image per person. Faces are represented by labeled graphs, based on a Gabor wavelet transform. Image graphs of new faces are extracted by an elastic graph matching process and can be compared by a simple similarity function. The system differs from the preceding one [1] in three respects. Phase information is used for accurate node positioning. Objectadapted graphs are used to handle large rotations in depth. Image graph extraction is based on a novel data structure, the bunch graph, which is constructed from a small set of sample image graphs.