Groupe d’études et de recherche en analyse des décisions

Identification of the Minkowski Parameter for Multidimensional Scaling

Gilles Caporossi

Based upon a robust optimization technique, Variable Neighborhood Search (VNS), we use simulation to find rules for identifying the correct Minkowski parameter $r$ to use in Multidimensional Scaling (MDS). Claims from the paper of Shepard (1974) are confirmed, and others are nuanced. We confirm the value of r cannot be defined precisely, that the proper r value cannot be found in dimension 2 or when the data is too noised, but it is possible to find good estimates in the other cases.

, 17 pages