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364,574
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A âˆˆ IR nÃ—m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 423 (37 self)
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is combinatorial in nature, are there efficient methods for finding the sparsest solution? These questions have been answered positively and constructively in recent years, exposing a wide variety of surprising phenomena; in particular, the existence of easilyverifiable conditions under which optimallysparse
The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
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Cited by 538 (19 self)
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and graphs, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, and power networks). The collection meets a vital need that artificiallygenerated matrices cannot meet, and is widely used by the sparse matrix algorithms community
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vec ..."
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Cited by 958 (5 self)
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This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance
Sparse modeling of intrinsic correspondences
 Computer Graphics Forum
"... We present a novel sparse modeling approach to nonrigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor we ..."
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Cited by 14 (1 self)
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We present a novel sparse modeling approach to nonrigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor we
Robust face recognition via sparse representation
 IEEE TRANS. PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2008
"... We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse signa ..."
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Cited by 916 (41 self)
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We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse
Model Selection and Sparse Modeling
, 2007
"... Parametric signal models are used in a multitude of signal processing applications. This thesis deals with signals for which there are many candidate models, and it is not a priori known which model is the most appropriate one. The first part of the thesis treats cases for which the set of models is ..."
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is relatively small, so that it is possible to evaluate each model in the set separately. The second part deals with sparse models, i.e., models sharing the same parameter vector, but for which any combination of zero valued and nonzero valued parameters is possible. Sparse models appear in a variety
A View Of The Em Algorithm That Justifies Incremental, Sparse, And Other Variants
 Learning in Graphical Models
, 1998
"... . The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the d ..."
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Cited by 988 (18 self)
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. The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect
KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
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Cited by 930 (41 self)
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In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many
Collaborative hierarchical sparse modeling
, 2010
"... Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an â„“1regularized linear regression problem, usually called Lasso. In this work we first combine the sparsityinducing property of the Lasso model, at the individual ..."
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Cited by 17 (2 self)
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Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an â„“1regularized linear regression problem, usually called Lasso. In this work we first combine the sparsityinducing property of the Lasso model, at the individual
Estimation of probabilities from sparse data for the language model component of a speech recognizer
 IEEE Transactions on Acoustics, Speech and Signal Processing
, 1987
"... AbstractThe description of a novel type of rngram language model is given. The model offers, via a nonlinear recursive procedure, a computation and space efficient solution to the problem of estimating probabilities from sparse data. This solution compares favorably to other proposed methods. Wh ..."
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Cited by 790 (2 self)
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AbstractThe description of a novel type of rngram language model is given. The model offers, via a nonlinear recursive procedure, a computation and space efficient solution to the problem of estimating probabilities from sparse data. This solution compares favorably to other proposed methods
Results 1  10
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364,574