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The tunneling method for global optimization in multidimensional scaling

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  • Patrick Groenen
  • Willem Heiser

Abstract

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Suggested Citation

  • 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.
  • Handle: RePEc:spr:psycho:v:61:y:1996:i:3:p:529-550
    DOI: 10.1007/BF02294553
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    References listed on IDEAS

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    1. Willem Heiser & Patrick Groenen, 1997. "Cluster differences scaling with a within-clusters loss component and a fuzzy successive approximation strategy to avoid local minima," Psychometrika, Springer;The Psychometric Society, vol. 62(1), pages 63-83, March.
    2. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    3. 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.
    4. 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.
    5. David Weeks & P. Bentler, 1982. "Restricted multidimensional scaling models for asymmetric proximities," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 201-208, June.
    6. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
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    Citations

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    Cited by:

    1. Leung, Pui Lam & Lau, Kin-nam, 2004. "Estimating the city-block two-dimensional scaling model with simulated annealing," European Journal of Operational Research, Elsevier, vol. 158(2), pages 518-524, October.
    2. S. Hess & E. Suárez & J. Camacho & G. Ramírez & B. Hernández, 2001. "Reliability of Coordinates Obtained by MINISSA Concerning the Order of Presented Stimuli," Quality & Quantity: International Journal of Methodology, Springer, vol. 35(2), pages 117-128, May.
    3. Marc Robini & Pierre-Jean Reissman, 2013. "From simulated annealing to stochastic continuation: a new trend in combinatorial optimization," Journal of Global Optimization, Springer, vol. 56(1), pages 185-215, May.
    4. Hua Zhou & Kenneth L. Lange, 2010. "On the Bumpy Road to the Dominant Mode," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 612-631.
    5. 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).
    6. Michael Brusco & Stephanie Stahl, 2005. "Optimal Least-Squares Unidimensional Scaling: Improved Branch-and-Bound Procedures and Comparison to Dynamic Programming," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 253-270, June.
    7. 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.
    8. Groenen, P.J.F. & Kaymak, U. & van Rosmalen, J.M., 2006. "Fuzzy clustering with Minkowski distance," Econometric Institute Research Papers EI 2006-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Groenen, Patrick J. F. & Franses, Philip Hans, 2000. "Visualizing time-varying correlations across stock markets," Journal of Empirical Finance, Elsevier, vol. 7(2), pages 155-172, August.
    10. Michael Brusco & Douglas Steinley, 2011. "A Tabu-Search Heuristic for Deterministic Two-Mode Blockmodeling of Binary Network Matrices," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 612-633, October.
    11. Malone, Samuel W. & Tarazaga, Pablo & Trosset, Michael W., 2002. "Better initial configurations for metric multidimensional scaling," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 143-156, November.
    12. Michael Brusco & Patrick Doreian, 2015. "An Exact Algorithm for the Two-Mode KL-Means Partitioning Problem," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 481-515, October.
    13. Michael Brusco & Stephanie Stahl, 2001. "An interactive multiobjective programming approach to combinatorial data analysis," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 5-24, March.
    14. 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.
    15. Michael Brusco & Hans-Friedrich Köhn & Stephanie Stahl, 2008. "Heuristic Implementation of Dynamic Programming for Matrix Permutation Problems in Combinatorial Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 503-522, September.

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