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

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  • Etschberger, Stefan
  • Hilbert, Andreas
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    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. --

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    Paper provided by Universität Augsburg, Institut für Statistik und Mathematische Wirtschaftstheorie in its series Arbeitspapiere zur mathematischen Wirtschaftsforschung with number 181.

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    Date of creation: 2002
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    Handle: RePEc:zbw:augamw:181

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    Web page: http://www.wiwi.uni-augsburg.de/bwl/bamberg/
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    1. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer, Springer, vol. 29(2), pages 115-129, June.
    2. Jacqueline Meulman & Peter Verboon, 1993. "Points of view analysis revisited: Fitting multidimensional structures to optimal distance components with cluster restrictions on the variables," Psychometrika, Springer, Springer, vol. 58(1), pages 7-35, March.
    3. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer, Springer, vol. 29(1), pages 1-27, March.
    4. Richard Johnson, 1973. "Pairwise nonmetric multidimensional scaling," Psychometrika, Springer, Springer, vol. 38(1), pages 11-18, March.
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