, Volume 29, Issue 1, pp 1–27 | Cite as

Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

  • J. B. Kruskal


Multidimensional scaling is the problem of representingn objects geometrically byn points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that configuration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a companion paper.


Computer Program Public Policy Statistical Theory Multidimensional Scaling Companion Paper 
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

© Psychometric Society 1964

Authors and Affiliations

  • J. B. Kruskal
    • 1
  1. 1.Bell Telephone LaboratoriesMurray Hill

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