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 stress function which compares proximity values with Euclidian distances of the respective points. The corresponding minimization problem is non-convex and sensitive to local minima. We present a novel deterministic annealing algorithm for the frequently used objective SSTRESS and for Sammon mapping, derived in the framework of maximum entropy estimation. Experimental results demonstrate the superiority of our optimization technique compared to conventional gradient descent methods. 1 Introduction Visualizing experimental data arises as a fundamental pattern recognition problem for exploratory data analysis in empirical sciences. Data are quite frequently represented as vectors in an often high-dimensional Euclidian vector space. Visualization in this context requires to project high-dimensional ...

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