# Low Rank Approximation - Algorithms, Implementation, Applications

@inproceedings{Markovsky2012LowRA, title={Low Rank Approximation - Algorithms, Implementation, Applications}, author={Ivan Markovsky}, booktitle={Communications and Control Engineering}, year={2012} }

Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. Much of the text is devoted to describing the applications of the theory including: system and control theory; signal processing; computer algebra for approximate factorization and common divisor computation… Expand

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Software for weighted structured low-rank approximation

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A software package is presented that computes locally optimal solutions to low-rank approximation problems with the following features:osaic Hankel structure constraint on the approximating matrix, weighted 2-norm approximation criterion, and linear constraints on an approximation matrix's left kernel basis. Expand

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The proposed local optimization algorithm is able to solve the weighted structured low-rank approximation problem, as well as to deal with the cases of missing or fixed elements, and is designed to address the case of small targeted rank. Expand

Recent process on structured low-rank approximation

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Rank deficiency of a data matrix is equivalent to the existence of an exact linear model for the data. For the purpose of linear static modeling, the matrix is unstructured and the corresponding… Expand

Factorization Approach to Structured Low-Rank Approximation with Applications

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The proposed local optimization algorithm is able to solve the weighted structured low-rank approximation problem, as well as to deal with the cases of missing or fixed elements and compared to existing approaches on numerical examples of system identification, approximate greatest common divisor problem, and symmetric tensor decomposition. Expand

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It is shown how matrices from error correcting codes can be used to find such low rank approximations and matrix decompositions, and extended the framework to linear least squares regression problems. Expand

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Stochastic algorithms for solving structured low-rank matrix approximation problems

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This paper investigates the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develops a family of algorithms to solve this problem, which has the property of guaranteed convergence. Expand

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- 2019 IEEE 58th Conference on Decision and Control (CDC)
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The SLRA package is presented, C software with interface to MATLAB, Octave, and R for solving low-rank approximation problems with the following features: mosaic Hankel structured approximating matrix, weighted 2-norm approximation criterion, and fixed and missing elements in the approximation matrix. Expand

Structured Low-Rank Approximation with Missing Data

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This paper considers low-rank approximation of affinely structured matrices with missing elements, a singular linear least-norm problem, based on reformulation of the problem as inner and outer optimization. Expand

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This dissertation addresses some analytical and numerical aspects of a problem of weighted low-rank approximation of matrices. We propose and solve two different versions of weighted low-rank… Expand