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Local LowRank Matrix Approximation
"... Matrix approximation is a common tool in recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of lowrank. We propose a new matrix approximation model where we assume instead that the matrix is ..."
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Cited by 4 (1 self)
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Matrix approximation is a common tool in recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of lowrank. We propose a new matrix approximation model where we assume instead that the matrix
A Schur Method for LowRank Matrix Approximation
, 1996
"... This paper describes a much simpler generalized Schurtype algorithm to compute similar lowrank approximants. For a given matrix H which has d singular values larger than e, we find all rank d approximants H such that ..."
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Cited by 21 (8 self)
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This paper describes a much simpler generalized Schurtype algorithm to compute similar lowrank approximants. For a given matrix H which has d singular values larger than e, we find all rank d approximants H such that
Relative errors for deterministic lowrank matrix approximations
 In Proceedings of the 25th Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2014
"... ar ..."
Fast Computation of Low Rank Matrix Approximations
, 2001
"... In many practical applications, given an m n matrix A it is of interest to nd an approximation to A that has low rank. We introduce a technique that exploits spectral structure in A to accelerate Orthogonal Iteration and Lanczos Iteration, the two most common methods for computing such approximat ..."
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Cited by 161 (4 self)
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In many practical applications, given an m n matrix A it is of interest to nd an approximation to A that has low rank. We introduce a technique that exploits spectral structure in A to accelerate Orthogonal Iteration and Lanczos Iteration, the two most common methods for computing
A Scalable Approach to ColumnBased LowRank Matrix Approximation ∗
"... In this paper, we address the columnbased lowrank matrix approximation problem using a novel parallel approach. Our approach is based on the divideandcombine idea. We first perform column selection on submatrices of an original data matrix in parallel, and then combine the selected columns into t ..."
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In this paper, we address the columnbased lowrank matrix approximation problem using a novel parallel approach. Our approach is based on the divideandcombine idea. We first perform column selection on submatrices of an original data matrix in parallel, and then combine the selected columns
Low rank matrix approximation in linear time, manuscript
, 2006
"... Given a matrix M with n rows and d columns, and fixed k and ε, we present an algorithm that in linear time (i.e., O(N)) computes a krank matrix B with approximation error ‖M − B ‖ 2 F ≤ (1 + ε)µopt(M, k), where N = nd is the input size, and µopt(M, k) is the minimum error of a krank approximation ..."
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Cited by 25 (0 self)
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Given a matrix M with n rows and d columns, and fixed k and ε, we present an algorithm that in linear time (i.e., O(N)) computes a krank matrix B with approximation error ‖M − B ‖ 2 F ≤ (1 + ε)µopt(M, k), where N = nd is the input size, and µopt(M, k) is the minimum error of a krank approximation
Robust video restoration by joint sparse and low rank matrix approximation
 SIAM Journal on Imaging Sciences
"... Abstract. This paper presents a new video restoration scheme based on the joint sparse and lowrank matrix approximation. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and lowrank matrix approximation problem. The resulted nucl ..."
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Cited by 13 (2 self)
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Abstract. This paper presents a new video restoration scheme based on the joint sparse and lowrank matrix approximation. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and lowrank matrix approximation problem. The resulted
Low Rank Matrix Approximation Using The Lanczos Bidiagonalization Process With Applications
 SIAM J. Sci. Comput
, 2000
"... Low rank approximation of large and/or sparse matrices is important in many applications. We show that good low rank matrix approximations can be directly obtained from the Lanczos bidiagonalization process without computing singular value decomposition. We also demonstrate that a socalled oneside ..."
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Cited by 32 (1 self)
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Low rank approximation of large and/or sparse matrices is important in many applications. We show that good low rank matrix approximations can be directly obtained from the Lanczos bidiagonalization process without computing singular value decomposition. We also demonstrate that a socalled one
Sparse principal component analysis via regularized low rank matrix approximation
 Journal of Multivariate Analysis
"... Principal component analysis (PCA) is a widely used tool for data analysis and dimension reduction in applications throughout science and engineering. However, the principal components (PCs) can sometimes be difficult to interpret, because they are linear combinations of all the original variables. ..."
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Cited by 101 (3 self)
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) of the data matrix and extract the PCs through solving a low rank matrix approximation problem. Regularization penalties are introduced to the corresponding minimization problem to promote sparsity in PC loadings. An efficient iterative algorithm is proposed for computation. Two tuning parameter selection
LowRank Matrix Approximation Using PointWise Operators
"... Abstract—The problem of extracting lowdimensional structure from highdimensional data arises in many applications such as machine learning, statistical pattern recognition, wireless sensor networks, and data compression. If the data is restricted to a lower dimensional subspace, then simple algori ..."
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, the underlying lowrank matrix; i.e., we are reducing the dimensionality of by using pointwise operators. Moreover, the estimation algorithm does not need to know the rank of. We also provide bounds on the quality of the approximation and validate the stability of the proposed algorithm with simulations
Results 1  10
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