MDS Algorithms

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


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.


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


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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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