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Constrained Optimization of the Stress Function for Multidimensional Scaling

  • Vydunas Saltenis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)

Abstract

Multidimensional Scaling (MDS) requires the multimodal Stress function optimization to estimate the model parameters, i.e. the coordinates of points in a lower-dimensional space. Therefore, finding the global optimum of the Stress function is very important for applications of MDS. The main idea of this paper is replacing the difficult multimodal problem by a simpler unimodal constrained optimization problem. A coplanarity measure of points is used as a constraint while the Stress function is minimized in the original high-dimensional space. Two coplanarity measures are proposed. A simple example presented illustrates and visualizes the optimization procedure. Experimental evaluation results with various data point sets demonstrate the potential ability to simplify MDS algorithms avoiding multidimodality.

Keywords

Local Optimization Multidimensional Scaling Conjugate Gradient Method Stress Function Optimal Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Vydunas Saltenis
    • 1
  1. 1.Institute of Mathematics and InformaticsVilniusLithuania

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