A comparative study of techniques for multidimensional scaling using simulated data

Multidimensional Scaling (MDS) is a collection of techniques that construct geometric configurations of points from the initial information among objects measured through dissimilarity coefficients. To find these points there are two strategies: the metric and the non metric MDS. In this work, a simulation study is done to compare the ACE's new metric technique and Kruskal's non metric with two minimization methods: steepest descent and Broyden's quasi Newton method. For this purpose, one hundred random configurations of points are generated in R² using distribution U[0,1]. The Euclidean distances associated to these configurations are called perfect distances. If the configurations are modified by certain random error, the new distances associated to each configuration are called perturbed distances. Using these configurations a comparative study is done among the four possible combinations of technique and minimization method with two comparison criteria: the stress and the loss function.