A Majorization Algorithm for Solving MDS

  • Ingwer Borg
  • Patrick Groenen
Part of the Springer Series in Statistics book series (SSS)


An elegant algorithm for computing an MDS solution is discussed in this chapter. We reintroduce the Stress function that measures the deviance of the distances between points in a geometric space and their corresponding dissimilarities. Then, we focus on how a function can be minimized An easy and powerful minimization strategy is the principle of minimizing a function by iterative majorization. This method is applied in the SMACOF algorithm for minimizing Stress.


Auxiliary Function Stress Function Concave Function Supporting Point Matrix Trace 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ingwer Borg
    • 1
  • Patrick Groenen
    • 2
  1. 1.Zentrum für Umfragen, Methoden und AnalysenMannheimGermany
  2. 2.Department of Data TheoryLeiden UniversityLeidenThe Netherlands

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