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.
Keywords
Goodness of fitMultidimensional scalingMathematicsScalingMonotonic functionMeasure (data warehouse)Multidimensional analysisStatisticsComputer scienceMathematical analysisGeometryData mining
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Publication Info
- Year
- 1964
- Type
- article
- Volume
- 29
- Issue
- 1
- Pages
- 1-27
- Citations
- 7274
- Access
- Closed
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Cite This
Joseph 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
Identifiers
- DOI
- 10.1007/bf02289565