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90
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 588 (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
A Unifying Review of Linear Gaussian Models
, 1999
"... Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observa ..."
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Cited by 259 (17 self)
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Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model. We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models.
Separating style and content with bilinear models
 NEURAL COMPUTATION
, 2000
"... PERCEPTUAL systems routinely separate content from style, classifying familiar words spoken in an unfamiliar accent, identifying a font or handwriting style across letters, or recognizing a familiar face or object seen under unfamiliar viewing conditions. Yet a general and tractable computational mo ..."
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Cited by 171 (3 self)
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PERCEPTUAL systems routinely separate content from style, classifying familiar words spoken in an unfamiliar accent, identifying a font or handwriting style across letters, or recognizing a familiar face or object seen under unfamiliar viewing conditions. Yet a general and tractable computational model of this ability to untangle the underlying factors of perceptual observations remains elusive. Existing factor models are either insufficiently rich to capture the complex interactions of perceptually meaningful factors such as phoneme and speaker accent or letter and font, or do not allow efficient learning algorithms. Here we show how perceptual systems may learn to solve these crucial tasks using surprisingly simple bilinear models. We report promising results in three realistic perceptual domains: spoken vowel classification with a benchmark multispeaker database, extrapolation of fonts to unseen letters, and translation of faces to novel illuminants.
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...
Bayesian computation in recurrent neural circuits
 Neural Computation
, 2004
"... A large number of human psychophysical results have been successfully explained in recent years using Bayesian models. However, the neural implementation of such models remains largely unclear. In this paper, we show that a network architecture commonly used to model the cerebral cortex can implem ..."
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Cited by 59 (4 self)
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A large number of human psychophysical results have been successfully explained in recent years using Bayesian models. However, the neural implementation of such models remains largely unclear. In this paper, we show that a network architecture commonly used to model the cerebral cortex can implement Bayesian inference for an arbitrary hidden Markov model. We illustrate the approach using an orientation discrimination task and a visual motion detection task. In the case of orientation discrimination, we show that the model network can infer the posterior distribution over orientations and correctly estimate stimulus orientation in the presence of significant noise. In the case of motion detection, we show that the resulting model network exhibits direction selectivity and correctly computes the posterior probabilities over motion direction and position. When used to solve the wellknown random dots motion discrimination task, the model generates responses that mimic the activities of evidenceaccumulating neurons in cortical areas LIP and FEF. The framework introduced in the paper posits a new interpretation of cortical activities in terms of log posterior probabilities of stimuli occurring in the natural world. 1 1
Six Principles for BiologicallyBased Computational Models of Cortical Cognition
 TRENDS IN COGNITIVE SCIENCES
, 1998
"... This paper describes and motivates six principles for computational cognitive neuroscience models: biological realism, distributed representations, inhibitory competition, bidirectional activation propagation, errordriven task learning, and Hebbian model learning. Although these principles are suppo ..."
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Cited by 52 (15 self)
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This paper describes and motivates six principles for computational cognitive neuroscience models: biological realism, distributed representations, inhibitory competition, bidirectional activation propagation, errordriven task learning, and Hebbian model learning. Although these principles are supported by a number of cognitive, computational, and biological motivations, the prototypical neural network model (a feedforward backpropagation network) incorporates only two of them, and no widely used model incorporates all of them. This paper argues that these principles should be integrated into a coherent overall framework, and discusses some potential synergies and conflicts in doing so.
A MultiLayer Sparse Coding Network Learns Contour Coding From Natural Images
, 2002
"... An important approach in visual neuroscience considers how the function of the early visual system relates to the statistics of its natural input. Previous studies have shown how many basic properties of the primary visual cortex, such as the receptive fields of simple and complex cells and the sp ..."
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Cited by 49 (10 self)
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An important approach in visual neuroscience considers how the function of the early visual system relates to the statistics of its natural input. Previous studies have shown how many basic properties of the primary visual cortex, such as the receptive fields of simple and complex cells and the spatial organization (topography) of the cells, can be understood as efficient coding of natural images. Here we extend the framework by considering how the responses of complex cells could be sparsely represented by a higherorder neural layer. This leads to contour coding and endstopped receptive fields. In addition, contour integration could be interpreted as topdown inference in the presented model.
Facial Expression Space Learning
 In Proceedings of Pacific Graphics
, 2002
"... experienced increased attention recently. Most current research focuses on techniques for capturing, synthesizing, and retargeting facial expressions. Little attention has been paid to the problem of controlling and modifiing the expression itself. We present techniques that separate video data into ..."
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Cited by 47 (0 self)
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experienced increased attention recently. Most current research focuses on techniques for capturing, synthesizing, and retargeting facial expressions. Little attention has been paid to the problem of controlling and modifiing the expression itself. We present techniques that separate video data into expressive features and underlying content. This allows, for example, a sequence originally recorded with a happy expression to be modified so that the speaker appears to be speaking with an angry or neutral expression. Although the expression has been modified, the new sequences maintain the same visual speech content as the original sequence. The facial expression space that allows these transformations is learned with the aid of a factorization model 1
Generalization in Interactive Networks: The Benefits of Inhibitory Competition and Hebbian Learning
 Neural Computation
, 2001
"... Computational models in cognitive neuroscience should ideally use biological properties and powerful computational principles to produce behavior consistent with psychological findings. Errordriven backpropagation is computationally powerful, and has proven useful for modeling a range of psycholo ..."
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Cited by 45 (6 self)
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Computational models in cognitive neuroscience should ideally use biological properties and powerful computational principles to produce behavior consistent with psychological findings. Errordriven backpropagation is computationally powerful, and has proven useful for modeling a range of psychological data, but is not biologically plausible. Several approaches to implementing backpropagation in a biologically plausible fashion converge on the idea of using bidirectional activation propagation in interactive networks to convey error signals. This paper demonstrates two main points about these errordriven interactive networks: (a) they generalize poorly due to attractor dynamics that interfere with the network's ability to systematically produce novel combinatorial representations in response to novel inputs; and (b) this generalization problem can be remedied by adding two widely used mechanistic principles, inhibitory competition and Hebbian learning, that can be independent...
Positive Tensor Factorization
, 2001
"... : A novel fixed point algorithm for positive tensor factorization (PTF) is introduced. The update rules efficiently minimize the reconstruction error of a positive tensor over positive factors. Tensors of arbitrary order can be factorized, which extends earlier results in the literature. Experiments ..."
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Cited by 39 (0 self)
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: A novel fixed point algorithm for positive tensor factorization (PTF) is introduced. The update rules efficiently minimize the reconstruction error of a positive tensor over positive factors. Tensors of arbitrary order can be factorized, which extends earlier results in the literature. Experiments show that the factors of PTF are easier to interpret than those produced by methods based on the singular value decomposition, which might contain negative values. We also illustrate the tendency of PTF to generate sparsely distributed codes. Keywords: PCA, SVD, postive matrix factorization, feature extraction 1.