A majorization algorithm for constrained correlation matrix approximation

作者：Simon Dan^*; Abell Jeff

来源：Linear Algebra and Its Applications, 2010, 432(5): 1152-1164.

DOI：10.1016/j.laa.2009.10.025

• Correlation matrix
• Majorization
• Constrained optimization

We desire to find a correlation matrix (R) over cap of a given rank that is as close as possible to an input matrix R, subject to the constraint that specified elements in (R) over cap 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 (R) over cap (ij) = 0 constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples.

• 出版日期2010-2-15