Least Squares Multidimensional Scaling with Transformed Distances

  • Patrick J. F. Groenen
  • Jan de Leeuw
  • Rudolf Mathar
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


We consider a general least squares loss function for multidimensional scaling. Special cases of this loss function are STRESS, S-STRESS, and MULTISCALE. Several analytic results are presented. In particular, we present the gradient and Hessian, and look at the differentiability at a local minimum. We also consider fulldimensional scaling and indicate when a global minimum can be obtained. Furthermore, we treat the problem of inverse multidimensional scaling, where the aim is to find those dissimilarity matrices for which a fixed configuration is a stationary point.


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Copyright information

© Springer-Verlag Berlin · Heidelberg 1996

Authors and Affiliations

  • Patrick J. F. Groenen
    • 1
  • Jan de Leeuw
    • 2
  • Rudolf Mathar
    • 3
  1. 1.Department of Data TheoryUniversity of LeidenLeidenThe Netherlands
  2. 2.Interdivisional Program in statisticsUCLAUSA
  3. 3.Institute of StatisticsAachen University of TechnologyAachenGermany

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