Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis

J. B. Kruskal

doi:10.1007/bf02289565

journal article Mar 01, 1964

Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis

J. B. Kruskal

Psychometrika Vol. 29 No. 1 pp. 1-27 · Cambridge University Press (CUP)

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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.

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Details

Published: Mar 01, 1964
Vol/Issue: 29(1)
Pages: 1-27
License: View

Authors

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J. B. Kruskal

Cite This Article

J. B. Kruskal (1964). Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis. Psychometrika, 29(1), 1-27. https://doi.org/10.1007/bf02289565

Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis

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