Multidimensional scaling with restrictions using simulated annealing

Multidimensional Scaling (MDS) with restriction on the configuration (MDSR) aims to minimize Stress subject to some restrictions on the configuration matrix. De Leeuw & Heiser propose an algorithm to compute the minimum of Stress with restrictions on the configuration. Our objective is to show an alternate procedure based on Simulated Annealing, in the case that restrictions are linear. Using the ‘Facil Expressions’ data, presented in Borg & Groenen, we calculate Stress with both methods, and the corresponding configuration. We repeat the computations in a set of 20 data obtained from a modification of the preceding data. In all cases we obtained, with both algorithms, the same Stress and identical configuration (except for rotations). Moreover, with the ‘Bacterial Strain’ data we obtained for Simulated Annealing better results than Smacof in 10% of the cases.