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Multidimensional Scaling and Genetic Algorithms : A Solution Approach to Avoid Local Minima

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  • Etschberger, Stefan
  • Hilbert, Andreas

Abstract

Multidimensional scaling is very common in exploratory data analysis. It is mainly used to represent sets of objects with respect to their proximities in a low dimensional Euclidean space. Widely used optimization algorithms try to improve the representation via shifting its coordinates in direction of the negative gradient of a corresponding fit function. Depending on the initial configuration, the chosen algorithm and its parameter settings there is a possibility for the algorithm to terminate in a local minimum. This article describes the combination of an evolutionary model with a non-metric gradient solution method to avoid this problem. Furthermore a simulation study compares the results of the evolutionary approach with one classic solution method.

Suggested Citation

  • Etschberger, Stefan & Hilbert, Andreas, 2002. "Multidimensional Scaling and Genetic Algorithms : A Solution Approach to Avoid Local Minima," Arbeitspapiere zur mathematischen Wirtschaftsforschung 181, Universität Augsburg, Institut für Statistik und Mathematische Wirtschaftstheorie.
    • Handle: RePEc:zbw:augamw:181
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    3. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    4. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
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