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.
A Majorization Algorithm for Constrained Correlation Matrix ApproximationLinear Algebra and its Applications
Publisher's StatementNOTICE: this is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, 432, 5, (02-01-2010); 10.1016/j.laa.2009.10.025
Citation InformationDan 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.