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102
Algorithms and applications for approximate nonnegative matrix factorization
 Computational Statistics and Data Analysis
, 2006
"... In this paper we discuss the development and use of lowrank approximate nonnegative matrix factorization (NMF) algorithms for feature extraction and identification in the fields of text mining and spectral data analysis. The evolution and convergence properties of hybrid methods based on both spars ..."
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Cited by 204 (8 self)
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In this paper we discuss the development and use of lowrank approximate nonnegative matrix factorization (NMF) algorithms for feature extraction and identification in the fields of text mining and spectral data analysis. The evolution and convergence properties of hybrid methods based on both
Structured lowrank approximation and its applications
, 2007
"... Fitting data by a bounded complexity linear model is equivalent to lowrank approximation of a matrix constructed from the data. The data matrix being Hankel structured is equivalent to the existence of a linear timeinvariant system that fits the data and the rank constraint is related to a bound ..."
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Cited by 33 (13 self)
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approximation criteria (e.g., weighted norm), constraints on the data matrix (e.g., nonnegativity), and data structures (e.g., kernel mapping). Related problems are rank minimization and structured pseudospectra. Keywords: Lowrank approximation, total least squares, system identification, errors
Parallel Gaussian process regression for big data: Lowrank representation meets Markov approximation. arXiv:1411.4510
"... The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a lowrankcumMarkov approximation (LMA) of the GP model that is novel in leveraging the dual computational advantages stemming from complement ..."
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Cited by 5 (5 self)
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complementing a lowrank approximate representation of the fullrank GP based on a support set of inputs with a Markov approximation of the resulting residual process; the latter approximation is guaranteed to be closest in the KullbackLeibler distance criterion subject to some constraint and is consid
NONNEGATIVE MATRIX FACTORIZATION WITHOUT NONNEGATIVITY CONSTRAINTS ON THE FACTORS
"... Abstract. We consider a new kind of low rank matrix approximation problem for nonnegative matrices: given a nonnegative matrix M, approximate it with a low rank product V.H such that V.H is nonnegative, but without nonnegativity constraints on V and H separately. The nonnegativity constraint on V.H ..."
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Abstract. We consider a new kind of low rank matrix approximation problem for nonnegative matrices: given a nonnegative matrix M, approximate it with a low rank product V.H such that V.H is nonnegative, but without nonnegativity constraints on V and H separately. The nonnegativity constraint on V
Approximate lowrank factorization with structured factors, Computational Statistics & Data Analysis
 in IEEE 11th Int. Conf. on Computer Vision
, 2007
"... An approximate rank revealing factorization problem with structure constraints on the normalized factors is considered. Examples of structure, motivated by an application in microarray data analysis, are sparsity, nonnegativity, periodicity, and smoothness. In general, the approximate rank revealing ..."
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Cited by 1 (0 self)
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An approximate rank revealing factorization problem with structure constraints on the normalized factors is considered. Examples of structure, motivated by an application in microarray data analysis, are sparsity, nonnegativity, periodicity, and smoothness. In general, the approximate rank
A Parallel Approximation Algorithm for Positive Linear Programming
, 1993
"... We introduce a fast parallel approximation algorithm for the positive linear programming optimization problem, i.e. the special case of the linear programming optimization problem where the input constraint matrix and constraint vector consist entirely of positive entries. The algorithm is elementar ..."
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Cited by 85 (0 self)
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We introduce a fast parallel approximation algorithm for the positive linear programming optimization problem, i.e. the special case of the linear programming optimization problem where the input constraint matrix and constraint vector consist entirely of positive entries. The algorithm
www.cosy.sbg.ac.at Technical Report SeriesNonnegative Matrix Factorization:
, 2010
"... Abstract. An alternative to singular value decomposition (SVD) in the information retrieval is the lowrank approximation of an original nonnegative matrix A by its nonnegative factors U and V. The columns of U are the feature vectors with no nonnegative components, and the columns of V store the ..."
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Abstract. An alternative to singular value decomposition (SVD) in the information retrieval is the lowrank approximation of an original nonnegative matrix A by its nonnegative factors U and V. The columns of U are the feature vectors with no nonnegative components, and the columns of V store
MULTIPLICATIVE UPDATE RULES FOR NONNEGATIVE MATRIX FACTORIZATION WITH COOCCURRENCE CONSTRAINTS
"... Nonnegative matrix factorization (NMF) is a widelyused tool for obtaining lowrank approximations of nonnegative data such as digital images, audio signals, textual data, financial data, and more. One disadvantage of the basic NMF formulation is its inability to control the amount of dependence amo ..."
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Cited by 1 (0 self)
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Nonnegative matrix factorization (NMF) is a widelyused tool for obtaining lowrank approximations of nonnegative data such as digital images, audio signals, textual data, financial data, and more. One disadvantage of the basic NMF formulation is its inability to control the amount of dependence
Generalized Low Rank Models
, 2014
"... Principal components analysis (PCA) is a wellknown technique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompa ..."
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Cited by 1 (1 self)
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Principal components analysis (PCA) is a wellknown technique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework
Linear and Nonlinear Projective Nonnegative Matrix Factorization
"... Abstract—A variant of nonnegative matrix factorization (NMF) which was proposed earlier is analyzed here. It is called Projective Nonnegative Matrix Factorization (PNMF). The new method approximately factorizes a projection matrix, minimizing the reconstruction error, into a positive lowrank matrix ..."
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Cited by 21 (3 self)
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Abstract—A variant of nonnegative matrix factorization (NMF) which was proposed earlier is analyzed here. It is called Projective Nonnegative Matrix Factorization (PNMF). The new method approximately factorizes a projection matrix, minimizing the reconstruction error, into a positive lowrank
Results 1  10
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102