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189
An informationmaximization approach to blind separation and blind deconvolution
 NEURAL COMPUTATION
, 1995
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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
The "Independent Components" of Natural Scenes are Edge Filters
, 1997
"... It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm that attem ..."
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Cited by 477 (27 self)
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It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm that attempts to find a factorial code of independent visual features. We show here that a new unsupervised learning algorithm based on information maximization, a nonlinear "infomax" network, when applied to an ensemble of natural scenes produces sets of visual filters that are localized and oriented. Some of these filters are Gaborlike and resemble those produced by the sparsenessmaximization network. In addition, the outputs of these filters are as independent as possible, since this infomax network performs Independent Components Analysis or ICA, for sparse (supergaussian) component distributions. We compare the resulting ICA filters and their associated basis functions, with other decorrelating filters produced by Principal Components Analysis (PCA) and zerophase whitening filters (ZCA). The ICA filters have more sparsely distributed (kurtotic) outputs on natural scenes. They also resemble the receptive fields of simple cells in visual cortex, which suggests that these neurons form a natural, informationtheoretic
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...
Face recognition by independent component analysis
 IEEE Transactions on Neural Networks
, 2002
"... Abstract—A number of current face recognition algorithms use face representations found by unsupervised statistical methods. Typically these methods find a set of basis images and represent faces as a linear combination of those images. Principal component analysis (PCA) is a popular example of such ..."
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Cited by 189 (4 self)
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Abstract—A number of current face recognition algorithms use face representations found by unsupervised statistical methods. Typically these methods find a set of basis images and represent faces as a linear combination of those images. Principal component analysis (PCA) is a popular example of such methods. The basis images found by PCA depend only on pairwise relationships between pixels in the image database. In a task such as face recognition, in which important information may be contained in the highorder relationships among pixels, it seems reasonable to expect that better basis images may be found by methods sensitive to these highorder statistics. Independent component analysis (ICA), a generalization of PCA, is one such method. We used a version of ICA derived from the principle of optimal information transfer through sigmoidal neurons. ICA was performed on face images in the FERET database under two different architectures, one which treated the images as random variables and the pixels as outcomes, and a second which treated the pixels as random variables and the images as outcomes. The first architecture found spatially local basis images for the faces. The second architecture produced a factorial face code. Both ICA representations were superior to representations based on PCA for recognizing faces across days and changes in expression. A classifier that combined the two ICA representations gave the best performance. Index Terms—Eigenfaces, face recognition, independent component analysis (ICA), principal component analysis (PCA), unsupervised learning. I.
Non Linear Neurons in the Low Noise Limit: A Factorial Code Maximizes Information Transfer
, 1994
"... We investigate the consequences of maximizing information transfer in a simple neural network (one input layer, one output layer), focussing on the case of non linear transfer functions. We assume that both receptive fields (synaptic efficacies) and transfer functions can be adapted to the environm ..."
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Cited by 141 (18 self)
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We investigate the consequences of maximizing information transfer in a simple neural network (one input layer, one output layer), focussing on the case of non linear transfer functions. We assume that both receptive fields (synaptic efficacies) and transfer functions can be adapted to the environment. The main result is that, for bounded and invertible transfer functions, in the case of a vanishing additive output noise, and no input noise, maximization of information (Linsker'sinfomax principle) leads to a factorial code  hence to the same solution as required by the redundancy reduction principle of Barlow. We show also that this result is valid for linear, more generally unbounded, transfer functions, provided optimization is performed under an additive constraint, that is which can be written as a sum of terms, each one being specific to one output neuron. Finally we study the effect of a non zero input noise. We find that, at first order in the input noise, assumed to be small ...
Independent Component Representations for Face Recognition
"... In a task such as face recognition, much of the important information may be contained in the highorder relationships among the image pixels. A number of face recognition algorithms employ principal component analysis (PCA), which is based on the secondorder statistics of the image set, and does n ..."
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Cited by 101 (8 self)
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In a task such as face recognition, much of the important information may be contained in the highorder relationships among the image pixels. A number of face recognition algorithms employ principal component analysis (PCA), which is based on the secondorder statistics of the image set, and does not address highorder statistical dependencies such as the relationships among three or more pixels. Independent component analysis (ICA) is a generalization of PCA which separates the highorder moments of the input in addition to the secondorder moments. ICA was performed on a set of face images by an unsupervised learning algorithm derived from the principle of optimal information transfer through sigmoidal neurons. 1 The algorithm maximizes the mutual information between the input and the output, which produces statistically independent outputs under certain conditions. ICA was performed on the face images under two different architectures. The first architecture provided a statistica...
HiddenArticulator Markov Models For Speech Recognition
 In Proc. IEEE Intl. Conf. on Acoustics, Speech, and Signal Processing
, 2000
"... In traditional speech recognition using Hidden Markov Models (HMMs), each state represents an acoustic portion of a phoneme. We explore the concept of an articulator based HMM, where each state represents a particular articulatory configuration [Erler 1996]. In this paper, we present a novel articul ..."
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Cited by 85 (20 self)
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In traditional speech recognition using Hidden Markov Models (HMMs), each state represents an acoustic portion of a phoneme. We explore the concept of an articulator based HMM, where each state represents a particular articulatory configuration [Erler 1996]. In this paper, we present a novel articulatory feature mapping and a new technique for model initialization. In addition, we use diphone modeling which allows context dependent training of transition probabilities. Our goal is to confirm that articulatory knowledge can assist speech recognition. We demonstrate this by showing that our mapping of articulatory configurations to phonemes performs better than random mappings. Furthermore, we demonstrate the practicality of the model by showing that, in combination with a standard model, a 1221% relative word error rate decrease occurs relative to the standard model alone. 1. INTRODUCTION Hidden Markov Models (HMMs) are a popular approach for speech recognition. Commonly, a lefttor...
A Unifying Informationtheoretic Framework for Independent Component Analysis
, 1999
"... We show that different theories recently proposed for Independent Component Analysis (ICA) lead to the same iterative learning algorithm for blind separation of mixed independent sources. We review those theories and suggest that information theory can be used to unify several lines of research. Pea ..."
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Cited by 82 (8 self)
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We show that different theories recently proposed for Independent Component Analysis (ICA) lead to the same iterative learning algorithm for blind separation of mixed independent sources. We review those theories and suggest that information theory can be used to unify several lines of research. Pearlmutter and Parra (1996) and Cardoso (1997) showed that the infomax approach of Bell and Sejnowski (1995) and the maximum likelihood estimation approach are equivalent. We show that negentropy maximization also has equivalent properties and therefore all three approaches yield the same learning rule for a fixed nonlinearity. Girolami and Fyfe (1997a) have shown that the nonlinear Principal Component Analysis (PCA) algorithm of Karhunen and Joutsensalo (1994) and Oja (1997) can also be viewed from informationtheoretic principles since it minimizes the sum of squares of the fourthorder marginal cumulants and therefore approximately minimizes the mutual information (Comon, 1994). Lambert (19...
Origins of Scaling in Natural Images
, 1997
"... One of the most robust qualities of our visual world is the scaleinvariance of natural images. Not only has scaling been found in different visual environments, but the phenomenon also appears to be calibration independent. This paper proposes a simple property of natural images which explains this ..."
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Cited by 81 (2 self)
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One of the most robust qualities of our visual world is the scaleinvariance of natural images. Not only has scaling been found in different visual environments, but the phenomenon also appears to be calibration independent. This paper proposes a simple property of natural images which explains this robustness: They are collages of regions corresponding to statistically independent "objects". Evidence is provided for these objects having a powerlaw distribution of sizes within images, from which follows scaling in natural images. It is commonly suggested that scaling instead results from edges, each with power spectrum 1/k². This hypothesis is refuted by example.