Molecular dynamics multidimensional scaling

Abstract

We discuss a molecular dynamics approach to the problem of multidimensional scaling, which is a statistical method used for the visualization of dissimilarities in multidimensional data. Numerical estimates of dissimilarities between pairs of objects from a high dimensional data collection are approximated by distances between corresponding pairs of objects in a low dimensional visual representation. The quality of this approximation is expressed as an energy function, which yields the optimal arrangement at its minimum. We show how this optimal arrangement can be efficiently computed using the molecular dynamics approach. The numerical estimates show that the proposed molecular dynamics method is more accurate and about an order of magnitude faster than the simulated annealing method.