A RESTRAINED CONDITION NUMBER LEAST SQUARES TECHNIQUE WITH ITS APPLICATIONS TO AVOIDING RANK DEFICIENCY

Abstract

An algorithm for the constrained least squares problem is proposed in which the upper bound of the condition number of a parameter matrix is predetermined. In the algorithm, the parameter matrix to be obtained is reparameterized using its singular value decomposition, and the loss function is minimized alternately over the singular vector matrices and the singular values with condition number constraint. It was demonstrated that the algorithm recovered full rank matrices in simulated reverse component analysis, in which the matrices were estimated from their reduced rank counterparts. The proposed algorithm is useful for avoiding degenerate solutions in which parameter matrices become rank de(cid:12)cient, which is illustrated in its application to generalized oblique Procrustes rotation and three-mode Parafac component analysis.