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Multidimensional scaling

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  • Groenen, P.J.F.
  • van de Velden, M.

Abstract

Multidimensional scaling is a statistical technique to visualize dissimilarity data. In multidimensional scaling, objects are represented as points in a usually two dimensional space, such that the distances between the points match the observed dissimilarities as closely as possible. Here, we discuss what kind of data can be used for multidimensional scaling, what the essence of the technique is, how to choose the dimensionality, transformations of the dissimilarities, and some pitfalls to watch out for when using multidimensional scaling.

Suggested Citation

  • Groenen, P.J.F. & van de Velden, M., 2004. "Multidimensional scaling," Econometric Institute Research Papers EI 2004-15, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1274
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    References listed on IDEAS

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    1. Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 7-67, March.
    2. Patrick Groenen & Willem Heiser, 1996. "The tunneling method for global optimization in multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 529-550, September.
    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.
    5. P. J. F. Groenen & W. J. Heiser & J. J. Meulman, 1999. "Global Optimization in Least-Squares Multidimensional Scaling by Distance Smoothing," Journal of Classification, Springer;The Classification Society, vol. 16(2), pages 225-254, July.
    6. Jan Leeuw, 1988. "Convergence of the majorization method for multidimensional scaling," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 163-180, September.
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    Cited by:

    1. Vivien Kana Zeumo & Alexis Tsoukiàs & Blaise Some, 2012. "A new methodology for multidimensional poverty measurement based on the capability approach," Working Papers hal-00874627, HAL.

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