Metric and Nonmetric MDS

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


In the previous chapter, we derived a majorization algorithm for fixed dissimilarities. However, in practical research we often have only rank-order information of the dissimilarities (or proximities), so that transformations that preserve the rank-order of the dissimilarities become admissible. In this chapter, we discuss optimal ways of estimating this and other transformations. One strategy for ordinal MDS is to use monotone regression. A different strategy, rank-images, is not optimal for minimizing Stress, but it has other properties that can be useful in MDS. An attractive group of transformations are spline transformations, which contain ordinal and linear transformations as special cases.


Primary Approach Alternate Little Square Monotone Regression Secondary Approach Interval Transformation 
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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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