A Majorization Algorithm for Constrained Correlation Matrix Approximation

Daniel J. Simon; Jeff Abell

doi:10.1016/j.laa.2009.10.025

A Majorization Algorithm for Constrained Correlation Matrix Approximation

Research output: Contribution to journal › Article › peer-review

Abstract

We desire to find a correlation matrix of a given rank that is as close as possible to an input matrix R , subject to the constraint that specified elements in must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization algorithm to solve the problem. Although many correlation matrix approximation approaches have been proposed, this specific problem, with the rank specification and the constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples.

Original language	American English
Journal	Linear Algebra and its Applications
Volume	432
DOIs	https://doi.org/10.1016/j.laa.2009.10.025
State	Published - Feb 1 2010
Externally published	Yes

Keywords

Correlation matrix
Majorization
Constrained optimization

Disciplines

Applied Mathematics
Electrical and Computer Engineering

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10.1016/j.laa.2009.10.025License: CC BY

A Majorization Algorithm for Constrained Correlation Matrix ApproFinal published version, 1.14 MBLicense: CC BY

Cite this

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title = "A Majorization Algorithm for Constrained Correlation Matrix Approximation",

abstract = " We desire to find a correlation matrix of a given rank that is as close as possible to an input matrix R , subject to the constraint that specified elements in must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization algorithm to solve the problem. Although many correlation matrix approximation approaches have been proposed, this specific problem, with the rank specification and the constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples.",

keywords = "Correlation matrix, Majorization, Constrained optimization",

author = "Simon, \{Daniel J.\} and Jeff Abell",

note = "Dan Simon, Jeff Abell. (2010). A majorization algorithm for constrained correlation matrix approximation. Linear Algebra and its Applications, 432(5), 1152-1164, doi: 10.1016/j.laa.2009.10.025.",

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PY - 2010/2/1

Y1 - 2010/2/1

N2 - We desire to find a correlation matrix of a given rank that is as close as possible to an input matrix R , subject to the constraint that specified elements in must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization algorithm to solve the problem. Although many correlation matrix approximation approaches have been proposed, this specific problem, with the rank specification and the constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples.

AB - We desire to find a correlation matrix of a given rank that is as close as possible to an input matrix R , subject to the constraint that specified elements in must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization algorithm to solve the problem. Although many correlation matrix approximation approaches have been proposed, this specific problem, with the rank specification and the constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples.

KW - Correlation matrix

KW - Majorization

KW - Constrained optimization

UR - https://engagedscholarship.csuohio.edu/enece_facpub/139

U2 - 10.1016/j.laa.2009.10.025

DO - 10.1016/j.laa.2009.10.025

M3 - Article

VL - 432

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

A Majorization Algorithm for Constrained Correlation Matrix Approximation

Abstract

Keywords

Disciplines

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