A NEW FORMULATION OF THE NONMETRIC STRAIN PROBLEM IN MULTIDIMENSIONAL-SCALING

A natural extension of classical metric multidimensional scaling is pr oposed. The result is a new formulation of nonmetric multidimensional scaling in which the strain criterion is minimized subject to order co nstraints on the disparity variables. Innovative features of the new f ormulation include: the parametrization of the p-dimensional distance matrices by the positive semidefinite matrices of rank less than or eq ual to p; optimization of the (squared) disparity variables, rather th an the configuration coordinate variables; and a new nondegeneracy con straint, which restricts the set of (squared) disparities rather than the set of distances. Solutions are obtained using an easily implement ed gradient projection method for numerical optimization. The method i s applied to two published data sets.