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The Past, Present, and Future of Multidimensional Scaling

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  • Groenen, P.J.F.
  • Borg, I.

Abstract

Multidimensional scaling (MDS) has established itself as a standard tool for statisticians and applied researchers. Its success is due to its simple and easily interpretable representation of potentially complex structural data. These data are typically embedded into a 2-dimensional map, where the objects of interest (items, attributes, stimuli, respondents, etc.) correspond to points such that those that are near to each other are empirically similar, and those that are far apart are different. In this paper, we pay tribute to several important developers of MDS and give a subjective overview of milestones in MDS developments. We also discuss the present situation of MDS and give a brief outlook on its future.

Suggested Citation

  • Groenen, P.J.F. & Borg, I., 2013. "The Past, Present, and Future of Multidimensional Scaling," Econometric Institute Research Papers EI 2013-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:39177
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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. Nees Jan Eck & Ludo Waltman, 2010. "Software survey: VOSviewer, a computer program for bibliometric mapping," Scientometrics, Springer;Akadémiai Kiadó, vol. 84(2), pages 523-538, August.
    4. James Lingoes & Ingwer Borg, 1978. "A direct approach to individual differences scaling using increasingly complex transformations," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 491-519, December.
    5. Alex Murillo & J. Fernando Vera & Willem J. Heiser, 2005. "A Permutation-Translation Simulated Annealing Algorithm for L 1 and L 2 Unidimensional Scaling," Journal of Classification, Springer;The Classification Society, vol. 22(1), pages 119-138, June.
    6. de Leeuw, Jan & Mair, Patrick, 2009. "Multidimensional Scaling Using Majorization: SMACOF in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i03).
    7. Vadim Pliner, 1996. "Metric unidimensional scaling and global optimization," Journal of Classification, Springer;The Classification Society, vol. 13(1), pages 3-18, March.
    8. J. Fernando Vera & Willem J. Heiser & Alex Murillo, 2007. "Global Optimization in Any Minkowski Metric: A Permutation-Translation Simulated Annealing Algorithm for Multidimensional Scaling," Journal of Classification, Springer;The Classification Society, vol. 24(2), pages 277-301, September.
    9. Jacqueline Meulman, 1992. "The integration of multidimensional scaling and multivariate analysis with optimal transformations," Psychometrika, Springer;The Psychometric Society, vol. 57(4), pages 539-565, December.
    10. Patrick Groenen & Rudolf Mathar & Willem Heiser, 1995. "The majorization approach to multidimensional scaling for Minkowski distances," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 3-19, March.
    11. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. II," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 219-246, September.
    12. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    13. 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.
    14. Lawrence Hubert & Phipps Arabie & Matthew Hesson-Mcinnis, 1992. "Multidimensional scaling in the city-block metric: A combinatorial approach," Journal of Classification, Springer;The Classification Society, vol. 9(2), pages 211-236, December.
    15. J. Ramsay, 1977. "Maximum likelihood estimation in multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 241-266, June.
    16. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. I," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 125-140, June.
    17. Michael J. Brusco, 2001. "A Simulated Annealing Heuristic for Unidimensional and Multidimensional (City-Block) Scaling of Symmetric Proximity Matrices," Journal of Classification, Springer;The Classification Society, vol. 18(1), pages 3-33, January.
    18. C. Horan, 1969. "Multidimensional scaling: Combining observations when individuals have different perceptual structures," Psychometrika, Springer;The Psychometric Society, vol. 34(2), pages 139-165, June.
    19. Groenen, P.J.F. & Winsberg, S. & Rodriguez, O. & Diday, E., 2006. "I-Scal: Multidimensional scaling of interval dissimilarities," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 360-378, November.
    20. 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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    Keywords

    multidimensional scaling;

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