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Three-Way MDS Models

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

Abstract

In the Procrustean context, the dimension-weighting model was used in order to better match a set of K given configurations X k to each other. We now ask how a solution of the dimension-weighting model can be found directly from the set of K proximity matrices without first deriving individual MDS spaces X k for each individual k. We discuss how dimension weighting can be incorporated into a framework for minimizing Stress. Another popular algorithm for solving this problem, indscal, is considered in some detail. Then, some algebraic properties of dimension-weighting models are investigated. Finally, matrix-conditional and -unconditional approaches are distinguished, and some general comments on dimension-weighting models are made. Table 21.1 gives an overview of the (three-way) Procrustean models discussed so far and the three-way MDS models of this chapter.

Keywords

Dimension Weight Weighted Euclidean Distance Subject Space Proximity Matrice Euclidean Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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