Multidimensional Scaling by Deterministic Annealing with Iterative Majorization Algorithm

Abstract

Multidimensional Scaling (MDS) is a dimension reduction method for information visualization, which is set up as a non-linear optimization problem. It is applicable to many data intensive scientific problems including studies of DNA sequences but tends to get trapped in local minima. Deterministic Annealing (DA) has been applied to many optimization problems to avoid local minima. We apply DA approach to MDS problem in this paper and show that our proposed DA approach improves the mapping quality and shows high reliability in a variety of experimental results. Further its execution time is similar to that of the un-annealed approach. We use different data sets for comparing the proposed DA approach with both a well known algorithm called SMACOF and a MDS with distance smoothing method which aims to avoid local optima. Our proposed DA method outperforms SMACOF algorithm and the distance smoothing MDS algorithm in terms of the mapping quality and shows much less sensitivity with respect to initial configurations and stopping condition. We also investigate various temperature cooling parameters for our deterministic annealing method within an exponential cooling scheme.