Abstract
A computer program is described that is designed to reconstruct the metric configuration of a set of points in Euclidean space on the basis of essentially nonmetric information about that configuration. A minimum set of Cartesian coordinates for the points is determined when the only available information specifies for each pair of those points—not the distance between them—but some unknown, fixed monotonic function of that distance. The program is proposed as a tool for reductively analyzing several types of psychological data, particularly measures of interstimulus similarity or confusability, by making explicit the multidimensional structure underlying such data.
Keywords
Multidimensional scalingSimilarity (geometry)Euclidean distanceSet (abstract data type)Metric (unit)Monotonic functionScalingEuclidean spaceFunction (biology)Basis (linear algebra)MathematicsComputer scienceCartesian coordinate systemEuclidean geometryMetric spaceAlgorithmTheoretical computer scienceArtificial intelligenceDiscrete mathematicsStatisticsPure mathematicsMathematical analysisImage (mathematics)Geometry
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Publication Info
- Year
- 1962
- Type
- article
- Volume
- 27
- Issue
- 2
- Pages
- 125-140
- Citations
- 2518
- Access
- Closed
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Cite This
Roger N. Shepard
(1962).
The Analysis of Proximities: Multidimensional Scaling with an Unknown Distance Function. I..
Psychometrika
, 27
(2)
, 125-140.
https://doi.org/10.1007/bf02289630
Identifiers
- DOI
- 10.1007/bf02289630