A metric multidimensional scaling method for large objects sets and its Monte Carlo evaluation

Multidimensional scaling (MDS) techniques always pose the problem of analysing a large number n of points, without collecting all (N(N-1))/2 possible interstimuli dissimilarities and while keeping satisfactory solutions. In the case of metric MDS it was found that a theoretical minimum of appropriate 2N-3 exact Euclidean distances are sufficient for the unique representation of N points in a 2-dimensional Euclidean space. On the one hand this paper proposes a generalization of this approach to greater dimensions. Thus it was found that by this method, d(N-2)+1 is the theoretical minimum number of appropriate exact distances for the unique representation of N points in a d-dimensional Euclidean space. On the other hand the method is evaluated by a Monte Carlo study on the basis of basic parameters.