MDS Algorithms

  • Ingwer Borg
  • Patrick J. F. Groenen
  • Patrick Mair
Chapter
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Abstract

Two types of solutions for MDS are discussed. If the proximities are Euclidean distances, classical MDS yields an easy algebraic solution. In most MDS applications, iterative methods are needed, because they admit many types of data and distances. They use a two-phase optimization algorithm, moving the points in MDS space in small steps while holding the data and their transforms fixed, and vice versa, until convergence is reached.

Keywords

Classical MDS Iterative MDS algorithm Disparity Two-phase algorithm Rational starting configuration Majorization smacof 

References

  1. Basalaj, W. (2001). Proximity visualisation of abstract data, Unpublished doctoral dissertation, Cambridge University, U.K.Google Scholar
  2. Borg, I., & Groenen, P. J. F. (2005). Modern multidimensional scaling (2nd ed.). New York: Springer.MATHGoogle Scholar
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  4. De Leeuw, J., & Mair, P. (2009). Multidimensional scaling using majorization: SMACOF in R. Journal of Statistical Software, 31(3), 1-30. Retrieved from http://www.jstatsoft.org/v31/i03/.
  5. De Leeuw, J., & Heiser, W. J. (1980). Multidimensional scaling with restrictions on the configuration. In P. R. Krishnaiah (Ed.), Multivariate Analysis (Vol. V, pp. 501–522). Amsterdam: North-Holland.Google Scholar
  6. Groenen, P. J. F. (1993). The majorization approach to multidimensional scaling: some problems and extensions, Unpublished doctoral dissertation, University of Leiden.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Ingwer Borg
    • 1
  • Patrick J. F. Groenen
    • 2
  • Patrick Mair
    • 3
  1. 1.Westfälische Wilhelms-UniversitätMuensterGermany
  2. 2.Econometric InstituteErasmus University RotterdamRotterdamThe Netherlands
  3. 3.Department of PsychologyHarvard UniversityCambridgeUSA

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