Algorithms in Multidimensional Scaling

The ideas described in this paper are motivated by a basic problem in Multidimensional Scaling which is solved not quite satisfactory up to now. Suppose that there are given pairwise dissimilarities δ_ij, 1 ≤ i, j ≤ n, as nonnegative real numbers between n objects. These originate from the special type of application and may be, for example in cartography, measurements of pairwise distances disturbed by additive random errors or, in psychology, individual assessments of the deviation in behaviour of n persons measured on a certain real scale. There are many other applications in a variety of fields, a structured overview may be obtained from de Leeuw & Heiser (1980, 1982).