, Volume 29, Issue 1, pp 1–27

Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

  • J. B. Kruskal

DOI: 10.1007/BF02289565

Cite this article as:
Kruskal, J.B. Psychometrika (1964) 29: 1. doi:10.1007/BF02289565


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.


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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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