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Low-rank approximation
Known as:
Low rank approximation
In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and…
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Related topics
Related topics
23 relations
Biconvex optimization
Biplot
Data compression
Factor analysis
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Broader (1)
Numerical linear algebra
Papers overview
Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2012
Highly Cited
2012
Low-Rank Approximation and Regression in Input Sparsity Time
K. Clarkson
,
David P. Woodruff
ArXiv
2012
Corpus ID: 14094215
We design a new distribution over m × n matrices S so that, for any fixed n × d matrix A of rank r, with probability at least 9…
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Highly Cited
2012
Highly Cited
2012
Low Rank Approximation - Algorithms, Implementation, Applications
I. Markovsky
Communications and Control Engineering
2012
Corpus ID: 46336784
Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation…
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Highly Cited
2008
Highly Cited
2008
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
Vin de Silva
,
Lek-Heng Lim
SIAM Journal on Matrix Analysis and Applications
2008
Corpus ID: 7159193
There has been continued interest in seeking a theorem describing optimal low-rank approximations to tensors of order 3 or higher…
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Highly Cited
2008
Highly Cited
2008
Improved Nyström low-rank approximation and error analysis
Kai Zhang
,
I. Tsang
,
J. Kwok
International Conference on Machine Learning
2008
Corpus ID: 10651609
Low-rank matrix approximation is an effective tool in alleviating the memory and computational burdens of kernel methods and…
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Highly Cited
2006
Highly Cited
2006
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
P. Drineas
,
R. Kannan
,
Michael W. Mahoney
SIAM journal on computing (Print)
2006
Corpus ID: 5453786
In many applications, the data consist of (or may be naturally formulated as) an $m \times n$ matrix $A$. It is often of interest…
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Highly Cited
2005
Highly Cited
2005
Generalized Low Rank Approximations of Matrices
Jieping Ye
Machine-mediated learning
2005
Corpus ID: 490977
The problem of computing low rank approximations of matrices is considered. The novel aspect of our approach is that the low rank…
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Highly Cited
2003
Highly Cited
2003
Adaptive Low-Rank Approximation of Collocation Matrices
M. Bebendorf
,
S. Rjasanow
Computing
2003
Corpus ID: 16501661
This article deals with the solution of integral equations using collocation methods with almost linear complexity. Methods such…
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Highly Cited
2003
Highly Cited
2003
Weighted Low-Rank Approximations
Nathan Srebro
,
T. Jaakkola
International Conference on Machine Learning
2003
Corpus ID: 5815325
We study the common problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM…
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Highly Cited
2001
Highly Cited
2001
Rank-One Approximation to High Order Tensors
Tong Zhang
,
G. Golub
SIAM Journal on Matrix Analysis and Applications
2001
Corpus ID: 22258700
The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was…
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Highly Cited
2001
Highly Cited
2001
Fast computation of low rank matrix approximations
D. Achlioptas
,
Frank McSherry
Symposium on the Theory of Computing
2001
Corpus ID: 2683832
Given a matrix <italic>A</italic> it is often desirable to find an approximation to <italic>A</italic> that has low rank. We…
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