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495
Partitioning of Unstructured Problems for Parallel Processing
, 1991
"... Many large scale computational problems are based on unstructured computational domains. Primary examples are unstructured grid calculations based on finite volume methods in computational fluid dynamics, or structural analysis problems based on finite element approximations. Here we will address th ..."
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Cited by 344 (16 self)
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the question of how to distribute such unstructured computational domains over a large number of processors in a MIMD machine with distributed memory. A graph theoretical framework for these problems will be established. Based on this framework three decomposition algorithms will be introduced. In particular
FINDING STRUCTURE WITH RANDOMNESS: PROBABILISTIC ALGORITHMS FOR CONSTRUCTING APPROXIMATE MATRIX DECOMPOSITIONS
"... Lowrank matrix approximations, such as the truncated singular value decomposition and the rankrevealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for ..."
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Cited by 253 (6 self)
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Lowrank matrix approximations, such as the truncated singular value decomposition and the rankrevealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool
Optimal Boolean Matrix Decomposition: Application to Role Engineering
"... A decomposition of a binary matrix into two matrices gives a set of basis vectors and their appropriate combination to form the original matrix. Such decomposition solutions are useful in a number of application domains including text mining, role engineering as well as knowledge discovery. While a ..."
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Cited by 26 (6 self)
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. In this paper, we first present a number of variants to the optimal Boolean matrix decomposition problem that have pragmatic implications. We then present a unified framework for modeling the optimal binary matrix decomposition and its variants using binary integer programming. Such modeling allows us
A Sparse Signal Reconstruction Perspective for Source Localization With Sensor Arrays
, 2005
"... We present a source localization method based on a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold. We enforce sparsity by imposing penalties based on the 1norm. A number of recent theoretical results on sparsifying properties of ..."
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Cited by 231 (6 self)
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of 1 penalties justify this choice. Explicitly enforcing the sparsity of the representation is motivated by a desire to obtain a sharp estimate of the spatial spectrum that exhibits superresolution. We propose to use the singular value decomposition (SVD) of the data matrix to summarize multiple time
BOOLEAN MATRIX DECOMPOSITION AND EXTENSION WITH APPLICATIONS
, 2011
"... Boolean matrix decomposition (BMD) refers to decomposing of an input Boolean matrix into a product of two Boolean matrices, where the first matrix represents a set of meaningful concepts, and the second describes how the observed data can be expressed as combinations of those concepts. As opposed to ..."
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Boolean matrix decomposition (BMD) refers to decomposing of an input Boolean matrix into a product of two Boolean matrices, where the first matrix represents a set of meaningful concepts, and the second describes how the observed data can be expressed as combinations of those concepts. As opposed
Multilinear Analysis of Image Ensembles: TensorFaces
 IN PROCEEDINGS OF THE EUROPEAN CONFERENCE ON COMPUTER VISION
, 2002
"... Natural images are the composite consequence of multiple factors related to scene structure, illumination, and imaging. Multilinear algebra, the algebra of higherorder tensors, offers a potent mathematical framework for analyzing the multifactor structure of image ensembles and for addressing the d ..."
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Cited by 188 (7 self)
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the difficult problem of disentangling the constituent factors or modes. Our multilinear modeling technique employs a tensor extension of the conventional matrix singular value decomposition (SVD), known as the Nmode SVD.As a concrete example, we consider the multilinear analysis of ensembles of facial images
Probability matrix decomposition models
 Psychometrika
, 1996
"... In this paper, we consider a class of models for twoway matrices with binary entries of 0 and l. First, we consider Boolean matrix decomposition, conceptualize it as a latent response model (LRM) and, by making use of this conceptualization, generalize it to a larger class of matrix decomposition m ..."
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Cited by 11 (7 self)
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In this paper, we consider a class of models for twoway matrices with binary entries of 0 and l. First, we consider Boolean matrix decomposition, conceptualize it as a latent response model (LRM) and, by making use of this conceptualization, generalize it to a larger class of matrix decomposition
Constraintaware role mining via extended Boolean matrix decomposition
 IEEE TRANS. DEPENDABLE SEC. COMPUT
, 2012
"... The role mining problem has received considerable attention recently. Among the many solutions proposed, the Boolean matrix decomposition (BMD) formulation has stood out, which essentially discovers roles by decomposing the binary matrix representing usertopermission assignment (UPA) into two mat ..."
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Cited by 2 (0 self)
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propose a novel approach, extended Boolean matrix decomposition (EBMD), which addresses the ineffectiveness of BMD in its ability of capturing underlying constraints. We analyze the computational complexity for each of CRM variants and present heuristics for problems that are proven to be NPhard.
HypergraphPartitioning Based Decomposition for Parallel SparseMatrix Vector Multiplication
 IEEE Trans. on Parallel and Distributed Computing
"... In this work, we show that the standard graphpartitioning based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrixvector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph mo ..."
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Cited by 70 (34 self)
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model. The proposed models reduce the decomposition problem to the wellknown hypergraph partitioning problem. The recently proposed successful multilevel framework is exploited to develop a multilevel hypergraph partitioning tool PaToH for the experimental verification of our proposed hypergraph models
Structural graph matching using the em algorithm and singular value decomposition
 IEEE Trans. PAMI
, 2001
"... AbstractÐThis paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is to say, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions. Commencing from a probability distri ..."
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Cited by 99 (9 self)
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distribution for matching errors, we show how the problem of graph matching can be posed as maximumlikelihood estimation using the apparatus of the EM algorithm. Our second contribution is to cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows us
Results 1  10
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495