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Convergence of the majorization method for multidimensional scaling

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  • Jan Leeuw

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  • 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.
    • Handle: RePEc:spr:jclass:v:5:y:1988:i:2:p:163-180
    DOI: 10.1007/BF01897162
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    References listed on IDEAS

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    1. Louis Guttman, 1968. "A general nonmetric technique for finding the smallest coordinate space for a configuration of points," Psychometrika, Springer;The Psychometric Society, vol. 33(4), pages 469-506, December.
    2. J. Kruskal, 1971. "Monotone regression: Continuity and differentiability properties," Psychometrika, Springer;The Psychometric Society, vol. 36(1), pages 57-62, March.
    3. 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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    Citations

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    Cited by:

    1. Marc C. Robini & Lihui Wang & Yuemin Zhu, 2024. "The appeals of quadratic majorization–minimization," Journal of Global Optimization, Springer, vol. 89(3), pages 509-558, July.
    2. 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.
    3. Robert Schneider, 1992. "A uniform approach to multidimensional scaling," Journal of Classification, Springer;The Classification Society, vol. 9(2), pages 257-273, December.
    4. 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.
    5. Michael J. Greenacre & Patrick J. F. Groenen, 2016. "Weighted Euclidean Biplots," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 442-459, October.
    6. 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.
    7. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
    8. Hanafi, Mohamed & Kiers, Henk A.L., 2006. "Analysis of K sets of data, with differential emphasis on agreement between and within sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1491-1508, December.
    9. Gruenhage, Gina & Opper, Manfred & Barthelme, Simon, 2016. "Visualizing the effects of a changing distance on data using continuous embeddings," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 51-65.
    10. Kagie, M. & van Wezel, M.C. & Groenen, P.J.F., 2007. "A graphical shopping interface bases on product attributes," Econometric Institute Research Papers EI 2007-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. 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.
    12. Husson, F. & Pages, J., 2006. "INDSCAL model: geometrical interpretation and methodology," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 358-378, January.
    13. 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).
    14. repec:jss:jstsof:31:i03 is not listed on IDEAS
    15. Wei Liu & Li Yang & Bo Yu, 2020. "A Lifting-Penalty Method for Quadratic Programming with a Quadratic Matrix Inequality Constraint," Mathematics, MDPI, vol. 8(2), pages 1-11, January.
    16. Linghao Zhang & Bo Pang & Haitao Tang & Hongjun Wang & Chongshou Li & Zhipeng Luo, 2022. "Pairwise Constraints Multidimensional Scaling for Discriminative Feature Learning," Mathematics, MDPI, vol. 10(21), pages 1-16, November.
    17. Simon J. L. Billinge & Phillip M. Duxbury & Douglas S. Gonçalves & Carlile Lavor & Antonio Mucherino, 2018. "Recent results on assigned and unassigned distance geometry with applications to protein molecules and nanostructures," Annals of Operations Research, Springer, vol. 271(1), pages 161-203, December.
    18. Noga Ram & Shoham Sabach, 2024. "A Globally Convergent Inertial First-Order Optimization Method for Multidimensional Scaling," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 949-974, August.
    19. Kagie, M. & van Wezel, M.C. & Groenen, P.J.F., 2009. "Map Based Visualization of Product Catalogs," ERIM Report Series Research in Management ERS-2009-010-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    20. 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.
    21. Peter Verboon & Willem Heiser, 1992. "Resistant orthogonal procrustes analysis," Journal of Classification, Springer;The Classification Society, vol. 9(2), pages 237-256, December.
    22. van den Burg, G.J.J. & Groenen, P.J.F., 2014. "GenSVM: A Generalized Multiclass Support Vector Machine," Econometric Institute Research Papers EI 2014-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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