COMPONENT ANALYSIS WITH DIFFERENT SETS OF CONSTRAINTS ON DIFFERENT DIMENSIONS

Many of the ''classical'' multivariate data analysis and multidimensio nal scaling techniques call far approximations by lower dimensional co nfigurations. A model is proposed, in which different sets of linear c onstraints are imposed on different dimensions in component analysis a nd ''classical'' multidimensional scaling frameworks. A simple, effici ent, and monotonically convergent algorithm is presented for fitting t he model to the data by least squares. The basic algorithm is extended to cover across-dimension constraints imposed in addition to the dime nsionwise constraints, and to the case of a symmetric data matrix. Exa mples are given to demonstrate the use of the method.