Multidimensional Scaling Using Majorization: SMACOF in R
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Patrick Groenen & Willem Heiser, 1996. "The tunneling method for global optimization in multidimensional scaling," Psychometrika, Springer, vol. 61(3), pages 529-550, September.
- Jan Leeuw, 1988. "Convergence of the majorization method for multidimensional scaling," Journal of Classification, Springer, vol. 5(2), pages 163-180, September.
- Ingwer Borg & James Lingoes, 1980. "A model and algorithm for multidimensional scaling with external constraints on the distances," Psychometrika, Springer, vol. 45(1), pages 25-38, March.
- Jacqueline Meulman, 1992. "The integration of multidimensional scaling and multivariate analysis with optimal transformations," Psychometrika, Springer, vol. 57(4), pages 539-565, December.
- J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer, vol. 35(3), pages 283-319, September.
- Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer, vol. 42(1), pages 7-67, March.
- Roger Shepard, 1974. "Representation of structure in similarity data: Problems and prospects," Psychometrika, Springer, vol. 39(4), pages 373-421, December.
- Jan Leeuw & Jacqueline Meulman, 1986. "A special Jackknife for Multidimensional Scaling," Journal of Classification, Springer, vol. 3(1), pages 97-112, March.
- Peter Schönemann, 1972. "An algebraic solution for a class of subjective metrics models," Psychometrika, Springer, vol. 37(4), pages 441-451, December.
When requesting a correction, please mention this item's handle: RePEc:jss:jstsof:31:i03. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.