Results 1  10
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22,846
Probabilistic sparse matrix factorization
, 2004
"... Many kinds of data can be viewed as consisting of a set of vectors, each of which is a noisy combination of a small number of noisy prototype vectors. Physically, these prototype vectors may correspond to different hidden variables that play a role in determining the measured data. For example, a ge ..."
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Cited by 12 (3 self)
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as the problem of factorizing a data matrix, while taking into account hard constraints reflecting structural knowledge of the problem and probabilistic relationships between variables that are induced by known uncertainties in the problem. We present softdecision probabilistic sparse matrix factorization (PSMF
Convex sparse matrix factorizations
"... We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rankreducing term similar to the trace norm. In particular, our formulation introduces an explicit tradeoff b ..."
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Cited by 25 (13 self)
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We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rankreducing term similar to the trace norm. In particular, our formulation introduces an explicit trade
Highly scalable parallel algorithms for sparse matrix factorization
 IEEE Transactions on Parallel and Distributed Systems
, 1994
"... In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algo ..."
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Cited by 130 (27 self)
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In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our
On optimal tree traversals for sparse matrix factorization
 In IPDPS’2011, the 25th IEEE International Parallel and Distributed Processing Symposium. IEEE Computer
, 2011
"... Abstract—We study the complexity of traversing treeshaped workflows whose tasks require large I/O files. Such workflows typically arise in the multifrontal method of sparse matrix factorization. We target a classical twolevel memory system, where the main memory is faster but smaller than the seco ..."
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Cited by 11 (7 self)
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Abstract—We study the complexity of traversing treeshaped workflows whose tasks require large I/O files. Such workflows typically arise in the multifrontal method of sparse matrix factorization. We target a classical twolevel memory system, where the main memory is faster but smaller than
Sparse Matrix Factorization of Gene Expression Data
 Unpublished note, MIT Artificial Intelligence Laboratory. Available
, 2001
"... The Problem: Motivated by the analysis of gene expression data, wedevelop a new unsupervised modeling technique. Specifically, we study how data can be modeled as a sparse matrix factorization. Motivation: Gene expression data consists of expression level reads for thousands of genes across dozens o ..."
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Cited by 6 (0 self)
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The Problem: Motivated by the analysis of gene expression data, wedevelop a new unsupervised modeling technique. Specifically, we study how data can be modeled as a sparse matrix factorization. Motivation: Gene expression data consists of expression level reads for thousands of genes across dozens
Multifrontal Sparse Matrix Factorization on Graphics Processing Units
, 2012
"... For many finite element problems, when represented as sparse matrices, iterative solvers are found to be unreliable because they can impose computational bottlenecks. Early pioneering work by Duff et al, explored an alternative strategy called multifrontal sparse matrix factorization. This approac ..."
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For many finite element problems, when represented as sparse matrices, iterative solvers are found to be unreliable because they can impose computational bottlenecks. Early pioneering work by Duff et al, explored an alternative strategy called multifrontal sparse matrix factorization. This ap
Tight convex relaxations for sparse matrix factorization
, 2014
"... Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and lowrank sparse bilinear regre ..."
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Cited by 3 (0 self)
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Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and lowrank sparse bilinear
Sparse Matrix Factorization for Analyzing Gene Expression Patterns
"... Motivated by the analysis of gene expression data, we develop a new unsupervised modeling technique. Specifically, we study how such data can be modeled via sparse matrix factorization (SMF). Unsupervised modeling using constrained matrix factorization has been studied by Lee and Seung [1, 2, 3]. Un ..."
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Cited by 1 (0 self)
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Motivated by the analysis of gene expression data, we develop a new unsupervised modeling technique. Specifically, we study how such data can be modeled via sparse matrix factorization (SMF). Unsupervised modeling using constrained matrix factorization has been studied by Lee and Seung [1, 2, 3
Predicting Structure In Nonsymmetric Sparse Matrix Factorizations
 GRAPH THEORY AND SPARSE MATRIX COMPUTATION
, 1992
"... Many computations on sparse matrices have a phase that predicts the nonzero structure of the output, followed by a phase that actually performs the numerical computation. We study structure prediction for computations that involve nonsymmetric row and column permutations and nonsymmetric or nonsqu ..."
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Cited by 38 (10 self)
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square matrices. Our tools are bipartite graphs, matchings, and alternating paths. Our main new result concerns LU factorization with partial pivoting. We show that if a square matrix A has the strong Hall property (i.e., is fully indecomposable) then an upper bound due to George and Ng on the nonzero structure
Results 1  10
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22,846