Multidimensional scaling by deterministic annealing

Abstract

Multidimensional scaling addresses the problem how proximity data can be faithfully visualized as points in a low-dimensional Euclidian space. The quality of a data embedding is measured by a cost function called stress which compares proximity values with Euclidian distances of the respective points. We present a novel deterministic annealing algorithm to efficiently determine embedding coordinates for this continuous optimization problem. Experimental results demonstrate the superiority of the optimization technique compared to conventional gradient descent methods. Furthermore, we propose a transformation of dissimilarities to reduce the mismatch between a high-dimensional data space and a low-dimensional embedding space.