Multidimensional Scaling by Deterministic Annealing

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 an-nealing algorithm to eeciently 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.