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.