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Convex and SemiNonnegative Matrix Factorizations
, 2008
"... We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X = F GT, we focus on algorithms in which G is restricted to contain nonnegative entries, but allow the data matrix X to have mixed signs, thus extending the applicable ra ..."
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Cited by 112 (10 self)
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We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X = F GT, we focus on algorithms in which G is restricted to contain nonnegative entries, but allow the data matrix X to have mixed signs, thus extending the applicable
On the complexity of nonnegative matrix factorization
 SIAM Journal on Optimization
"... Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases and other information retrieval and clustering applications. In this report, we define an exact version of NMF. Then we establish several results about exact NMF: (1) that it i ..."
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Cited by 73 (2 self)
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Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases and other information retrieval and clustering applications. In this report, we define an exact version of NMF. Then we establish several results about exact NMF: (1
Nonnegative sparse coding
 PROC. IEEE WORKSHOP ON NEURAL NETWORKS FOR SIGNAL PROCESSING (NNSP’2002), 2002
, 2002
"... Nonnegative sparse coding is a method for decomposing multivariate data into nonnegative sparse components. In this paper we briefly describe the motivation behind this type of data representation and its relation to standard sparse coding and nonnegative matrix factorization. We then give a sim ..."
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Cited by 166 (3 self)
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Nonnegative sparse coding is a method for decomposing multivariate data into nonnegative sparse components. In this paper we briefly describe the motivation behind this type of data representation and its relation to standard sparse coding and nonnegative matrix factorization. We then give a
Nonnegative Matrix Factorization with Quadratic Programming
, 2006
"... Nonnegative Matrix Factorization (NMF) solves the following problem: find such nonnegative matrices A ∈ R I×J + and X ∈ R J×K + that Y ∼ = AX, given only Y ∈ R I×K and the assigned index J (K>> I ≥ J). Basically, the factorization is achieved by alternating minimization of a given cost functi ..."
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Cited by 9 (2 self)
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Nonnegative Matrix Factorization (NMF) solves the following problem: find such nonnegative matrices A ∈ R I×J + and X ∈ R J×K + that Y ∼ = AX, given only Y ∈ R I×K and the assigned index J (K>> I ≥ J). Basically, the factorization is achieved by alternating minimization of a given cost
Orthogonal nonnegative matrix trifactorizations for clustering
 In SIGKDD
, 2006
"... Currently, most research on nonnegative matrix factorization (NMF) focus on 2factor X = FG T factorization. We provide a systematic analysis of 3factor X = FSG T NMF. While unconstrained 3factor NMF is equivalent to unconstrained 2factor NMF, constrained 3factor NMF brings new features to constr ..."
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Cited by 117 (22 self)
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Currently, most research on nonnegative matrix factorization (NMF) focus on 2factor X = FG T factorization. We provide a systematic analysis of 3factor X = FSG T NMF. While unconstrained 3factor NMF is equivalent to unconstrained 2factor NMF, constrained 3factor NMF brings new features
Nonnegative Matrix Factorization: A Comprehensive Review
 IEEE TRANS. KNOWLEDGE AND DATA ENG
, 2013
"... Nonnegative Matrix Factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception. It incorporates the nonnegativity constraint and thus obtains the partsbased representation as well as enhancing the interpretability of the issue corres ..."
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Cited by 17 (2 self)
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Nonnegative Matrix Factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception. It incorporates the nonnegativity constraint and thus obtains the partsbased representation as well as enhancing the interpretability of the issue
Nonsmooth nonnegative matrix factorization (nsnmf
 IEEE transactions on
, 2006
"... Abstract—We propose a novel nonnegative matrix factorization model that aims at finding localized, partbased, representations of nonnegative multivariate data items. Unlike the classical nonnegative matrix factorization (NMF) technique, this new model, denoted “nonsmooth nonnegative matrix factoriz ..."
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Cited by 66 (4 self)
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Abstract—We propose a novel nonnegative matrix factorization model that aims at finding localized, partbased, representations of nonnegative multivariate data items. Unlike the classical nonnegative matrix factorization (NMF) technique, this new model, denoted “nonsmooth nonnegative matrix
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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. Enforcing orthonormality to the basic objective is shown to lead to an even more efficient update rule, which is also readily extended to nonlinear cases. The formulation of the PNMF objective is shown to be connected to a variety of existing nonnegative matrix factorization methods and clustering
Results 11  20
of
2,263