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Structured low-rank approximation with missing data

Structured low-rank approximation with missing data
Structured low-rank approximation with missing data
The approach of SIAM J. Matrix Anal. Appl., 26(4):1083--1099 for solving structured total least squares problems is generalized to weighted structured low-rank approximation with missing data. The method proposed is based on elimination of the correction matrix and solution of the resulting nonlinear least squares problem by local optimization methods. The elimination step is a singular linear least-norm problem, which admits an analytic solution. Two approaches are proposed for the nonlinear least-squares minimization: minimization subject to equality constraints and unconstrained minimization with regularized cost function. The method is generalized to weighted low-rank approximation with singular weight matrix and is illustrated on matrix completion, system identification, and data-driven simulation problems. An extended version of the paper is a literate program, implementing the method and reproducing the presented results.
0895-4798
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Usevich, Konstantin
1ab9effb-9945-40b6-94d7-f94dd0339110
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Usevich, Konstantin
1ab9effb-9945-40b6-94d7-f94dd0339110

Markovsky, Ivan and Usevich, Konstantin (2012) Structured low-rank approximation with missing data. SIAM Journal on Matrix Analysis and Applications. (Submitted)

Record type: Article

Abstract

The approach of SIAM J. Matrix Anal. Appl., 26(4):1083--1099 for solving structured total least squares problems is generalized to weighted structured low-rank approximation with missing data. The method proposed is based on elimination of the correction matrix and solution of the resulting nonlinear least squares problem by local optimization methods. The elimination step is a singular linear least-norm problem, which admits an analytic solution. Two approaches are proposed for the nonlinear least-squares minimization: minimization subject to equality constraints and unconstrained minimization with regularized cost function. The method is generalized to weighted low-rank approximation with singular weight matrix and is illustrated on matrix completion, system identification, and data-driven simulation problems. An extended version of the paper is a literate program, implementing the method and reproducing the presented results.

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Submitted date: June 2012
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 340718
URI: http://eprints.soton.ac.uk/id/eprint/340718
ISSN: 0895-4798
PURE UUID: 1dc5e040-6746-48c1-ae82-26b312f1a56e

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Date deposited: 02 Jul 2012 09:26
Last modified: 14 Mar 2024 11:28

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Contributors

Author: Ivan Markovsky
Author: Konstantin Usevich

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