A new approach to the discretization of Multidimensional Scaling

Given a set of points in a Euclidean space having dimension K > 0, we are interested in the problem of finding a realization of the same set in a Euclidean space having a lower dimension. In most situations, it is not possible to preserve all available interpoint distances in the new space, so that the best possible realization, which gives the minimal error on the distances, needs to be searched. This problem is known in the scientific literature as the Multidimensional Scaling (MDS). We propose a new methodology to discretize the search space of MDS instances, with the aim of performing an efficient enumeration of their solution sets. Some preliminary computational experiments on a set of artificially generated instances are presented. We conclude our paper with some future research directions.