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Learning Convex Concepts from Gaussian Distributions with PCA
"... Abstract—We present a new algorithm for learning a convex set in ndimensional space given labeled examples drawn from any Gaussian distribution. The complexity of the algorithm is bounded by a fixed polynomial in n times a function of k and ɛ where k is the dimension of the normal subspace (the spa ..."
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Cited by 6 (1 self)
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Abstract—We present a new algorithm for learning a convex set in ndimensional space given labeled examples drawn from any Gaussian distribution. The complexity of the algorithm is bounded by a fixed polynomial in n times a function of k and ɛ where k is the dimension of the normal subspace (the
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 611 (29 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
PCA Gaussianization for image processing
 in Proceedings of ICIP09
, 2009
"... The estimation of highdimensional probability density functions (PDFs) is not an easy task for many image processing applications. The linear models assumed by widely used transforms are often quite restrictive to describe the PDF of natural images. In fact, additional nonlinear processing is nee ..."
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Cited by 4 (3 self)
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in image synthesis and classification problems. Index Terms — Gaussianization, PCA, density estimation, image synthesis, oneclass image classification. 1.
Local PCA Learning with ResolutionDependent Mixtures of Gaussians
, 1999
"... A globally linear model, as implied by conventional Principal Component Analysis (PCA), may be insufficient to represent multivariate data in many situations. It has been known for some time that a combination of several "local " PCA's can provide a suitable approach in such cases [1, ..."
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Cited by 6 (0 self)
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A globally linear model, as implied by conventional Principal Component Analysis (PCA), may be insufficient to represent multivariate data in many situations. It has been known for some time that a combination of several "local " PCA's can provide a suitable approach in such cases [1
Nonconvex robust PCA
 In Advances in Neural Information Processing Systems
, 2014
"... We propose a new method for robust PCA – the task of recovering a lowrank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of lowrank matrices, and the set of sparse matrices; each projection ..."
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Cited by 3 (0 self)
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We propose a new method for robust PCA – the task of recovering a lowrank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of lowrank matrices, and the set of sparse matrices; each
Sparse PCA: Convex Relaxations, Algorithms and Applications
, 2010
"... Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse principal component analysis and has a wide array of applica ..."
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Cited by 17 (2 self)
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of applications in machine learning and engineering. Unfortunately, this problem is also combinatorially hard and we discuss convex relaxation techniques that efficiently produce good approximate solutions. We then describe several algorithms solving these relaxations as well as greedy algorithms that iteratively
Multivariate generalized gaussian distribution: Convexity and graphical models
 IEEE Transaction on Signal Processing
, 2013
"... Abstract—We consider covariance estimation in themultivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is nonconvex, yet it has been proved that its global solution can be often computed ..."
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Cited by 9 (3 self)
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Abstract—We consider covariance estimation in themultivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is nonconvex, yet it has been proved that its global solution can be often computed
Neurofuzzy modeling and control
 IEEE Proceedings
, 1995
"... Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framew ..."
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Cited by 231 (1 self)
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Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under
Provable Nonconvex Robust PCA
"... We propose a new method for robust PCA – the task of recovering a lowrank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of lowrank matrices, and the set of sparse matrices; each projectio ..."
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We propose a new method for robust PCA – the task of recovering a lowrank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of lowrank matrices, and the set of sparse matrices; each
Results 1  10
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140,778