Better initial configurations for metric multidimensional scaling

Multidimensional scaling (MDS) is a collection of data analytic techniques for constructing con$gurations of points from dissimilarity information about interpoint distances. Two popular measures of how well the constructed distances $t the observed dissimilarities are the raw stress and sstress criteria, each of which must be minimized by numerical optimization. Because iterative procedures for numerical optimization typically $nd local minimizers that may not be global minimizers, the choice of an initial con$guration from which to begin searching for an optimal con$guration is crucial. A popular choice of initial con$guration is the classical solution of Torgerson (Psychometrika 17 (1952) 401). Results from the theory of distance matrices are exploited to derive two alternatives, each guaranteed to be at least as good as the classical solution, and empirical evidence is presented that they are usually substantially better. c © 2002 Elsevier Science B.V. All rights reserved. MSC: 62H25; 51K99; 15A18