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Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis

Published online by Cambridge University Press:  01 January 2025

J. B. Kruskal
J. B. Kruskal*
Affiliation:
Bell Telephone Laboratories, Murray Hill, N. J.
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Abstract

Multidimensional scaling is the problem of representing n objects geometrically by n 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.

Information

Type
Original Paper
Information
Psychometrika , Volume 29 , Issue 1 , March 1964 , pp. 1 - 27
Copyright
Copyright © 1964 Psychometric Society

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