Recent Experimentation on Euclidean Approximations of Biased Euclidean Distances

Given a set of 16 points on a grid, a set of randomly biased distances matrices is built and ten methods for their Euclidean approximantion are compared to identify which minimize the stress. The Principal Coordinates Analysis of Torgerson’s (1958) matrix of biased distances, limited to positive eigenvalues proved to be more effective than methods based on monotonous transformations’ aiming at getting the corresponding Torgerson’s (1958) matrix positive semidefinitè prior to PCoA. Its behaviour resulted close to Kruskal Non-Metric Multidimensional Scaling and Bennani Dosse (1998) Optimal Scaling, with the advantage of the identification a posteriori of the suitable dimension.