IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v031i03.html
   My bibliography  Save this article

Multidimensional Scaling Using Majorization: SMACOF in R

Author

Listed:
  • de Leeuw, Jan
  • Mair, Patrick

Abstract

In this paper we present the methodology of multidimensional scaling problems (MDS) solved by means of the majorization algorithm. The objective function to be minimized is known as stress and functions which majorize stress are elaborated. This strategy to solve MDS problems is called SMACOF and it is implemented in an R package of the same name which is presented in this article. We extend the basic SMACOF theory in terms of configuration constraints, three-way data, unfolding models, and projection of the resulting configurations onto spheres and other quadratic surfaces. Various examples are presented to show the possibilities of the SMACOF approach offered by the corresponding package.

Suggested Citation

  • 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).
    • Handle: RePEc:jss:jstsof:v:031:i03
    DOI: http://hdl.handle.net/10.18637/jss.v031.i03
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v031i03/v31i03.pdf
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v031i03/smacof_1.0-0.tar.gz
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v031i03/v31i03.R.zip
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v031i03/v31i03-erratum.R
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v031i03/ciexyz31_1.txt
    Download Restriction: no
    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v031.i03?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. Roger Shepard, 1974. "Representation of structure in similarity data: Problems and prospects," Psychometrika, Springer;The Psychometric Society, vol. 39(4), pages 373-421, December.
    3. 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.
    4. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    5. Ingwer Borg & James Lingoes, 1980. "A model and algorithm for multidimensional scaling with external constraints on the distances," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 25-38, March.
    6. Jan Leeuw & Jacqueline Meulman, 1986. "A special Jackknife for Multidimensional Scaling," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 97-112, March.
    7. Peter Schönemann, 1972. "An algebraic solution for a class of subjective metrics models," Psychometrika, Springer;The Psychometric Society, vol. 37(4), pages 441-451, December.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:jss:jstsof:31:i03 is not listed on IDEAS
    2. 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.
    3. Forrest Young & Yoshio Takane & Rostyslaw Lewyckyj, 1978. "Three notes on ALSCAL," Psychometrika, Springer;The Psychometric Society, vol. 43(3), pages 433-435, September.
    4. Richard Sands & Forrest Young, 1980. "Component models for three-way data: An alternating least squares algorithm with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 39-67, March.
    5. J. Carroll, 1985. "Review," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 133-140, March.
    6. Aurea Grané & Rosario Romera, 2018. "On Visualizing Mixed-Type Data," Sociological Methods & Research, , vol. 47(2), pages 207-239, March.
    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. Akinori Okada & Tadashi Imaizumi, 1997. "Asymmetric multidimensional scaling of two-mode three-way proximities," Journal of Classification, Springer;The Classification Society, vol. 14(2), pages 195-224, September.
    9. 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.
    10. Douglas Clarkson & Richard Gonzalez, 2001. "Random effects diagonal metric multidimensional scaling models," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 25-43, March.
    11. Rolf Langeheine, 1982. "Statistical evaluation of measures of fit in the Lingoes-Borg procrustean individual differences scaling," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 427-442, December.
    12. 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.
    13. Michael C Hout & Stephen D Goldinger & Kyle J Brady, 2014. "MM-MDS: A Multidimensional Scaling Database with Similarity Ratings for 240 Object Categories from the Massive Memory Picture Database," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-11, November.
    14. 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.
    15. Jan Leeuw & Sandra Pruzansky, 1978. "A new computational method to fit the weighted euclidean distance model," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 479-490, December.
    16. J. Carroll, 1976. "Spatial, non-spatial and hybrid models for scaling," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 439-463, December.
    17. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    18. Kohn, Hans-Friedrich, 2006. "Combinatorial individual differences scaling within the city-block metric," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 931-946, November.
    19. 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.
    20. 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.
    21. Yoshio Takane & Forrest Young & Jan Leeuw, 1980. "An individual differences additive model: An alterating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 45(2), pages 183-209, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jss:jstsof:v:031:i03. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.