Journal ArticleDOI
Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
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TLDR
The fundamental hypothesis is that dissimilarities and distances are monotonically related, and a quantitative, intuitively satisfying measure of goodness of fit is defined to this hypothesis.Abstract:
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.read more
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References
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Journal ArticleDOI
Nonmetric multidimensional scaling: A numerical method
TL;DR: The numerical methods required in the approach to multi-dimensional scaling are described and the rationale of this approach has appeared previously.
Journal ArticleDOI
The analysis of proximities: Multidimensional scaling with an unknown distance function. I.
TL;DR: The results of two kinds of test applications of a computer program for multidimensional scaling on the basis of essentially nonmetric data are reported to measures of interstimulus similarity and confusability obtained from some actual psychological experiments.
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