The Solution of the Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newton's Method

: This paper considers numerical algorithms for finding local minimizers of metric multidimensional scaling problems. The two most common optimality criteria (STRESS and SSTRESS) are considered, the leading algorithms for each are carefully explicated, and a new algorithm is proposed. The new algorithm is based on Newton's method and relies on a parametrization that has not previously been used in multidimensional scaling algorithms. In contrast to previous algorithms, a very pleasant feature of the new algorithm is that it can be used with either the STRESS or the SSTRESS criterion. Numerical results are presented for the metric STRESS problem. These results are quite satisfying and, among other things, suggest that the well-known SMACOF-I algorithm tends to stop prematurely.