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Spatial Versus Tree Representations of Proximity Data

Published online by Cambridge University Press:  01 January 2025

Sandra Pruzansky ,
Amos Tversky  and
J. Douglas Carroll
Sandra Pruzansky*
Affiliation:
Bell Laboratories
Amos Tversky
Affiliation:
Stanford University
J. Douglas Carroll
Affiliation:
Bell Laboratories
*
Requests for reprints should be sent to Sandra Pruzansky, Bell Laboratories, 2C-552, Murray Hill, New Jersey 07974.
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Abstract

In this paper we investigated two of the most common representations of proximities, two-dimensional euclidean planes and additive trees. Our purpose was to develop guidelines for comparing these representations, and to discover properties that could help diagnose which representation is more appropriate for a given set of data. In a simulation study, artificial data generated either by a plane or by a tree were scaled using procedures for fitting either a plane (KYST) or a tree (ADDTREE). As expected, the appropriate model fit the data better than the inappropriate model for all noise levels. Furthermore, the two models were roughly comparable: for all noise levels, KYST accounted for plane data about as well as ADDTREE accounted for tree data. Two properties of the data proved useful in distinguishing between the models: the skewness of the distribution of distances, and the proportion of elongated triangles, which measures departures from the ultrametric inequality, Applications of KYST and ADDTREE to some twenty sets of real data, collected by other investigators, showed that most of these data could be classified clearly as favoring either a tree or a two-dimensional representation.

Keywords

multidimensional scalingclusteringtree structuresadditive trees
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 1 , March 1982 , pp. 3 - 24
Copyright
Copyright © 1982 The Psychometric Society

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Footnotes

A portable PASCAL program implementing the Sattath and Tversky [1977] ADDTREE algorithm is available from J. Corter, Department of Psychology, Stanford University, Stanford, California 94305.

References

Reference Notes

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