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Additive Similarity Trees

Published online by Cambridge University Press:  01 January 2025

Shmuel Sattath  and
Amos Tversky
Shmuel Sattath
Affiliation:
Hebrew University of Jerusalem
Amos Tversky*
Affiliation:
Hebrew University of Jerusalem
*
Requests for reprints should be sent to Prof. Amos Tversky, Dept. of Psychology, The Hebrew University, Jerusalem, Israel.
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Abstract

Similarity data can be represented by additive trees. In this model, objects are represented by the external nodes of a tree, and the dissimilarity between objects is the length of the path joining them. The additive tree is less restrictive than the ultrametric tree, commonly known as the hierarchical clustering scheme. The two representations are characterized and compared. A computer program, ADDTREE, for the construction of additive trees is described and applied to several sets of data. A comparison of these results to the results of multidimensional scaling illustrates some empirical and theoretical advantages of tree representations over spatial representations of proximity data.

Keywords

proximityclusteringmultidimensional scaling
Type
Original Paper
Information
Psychometrika , Volume 42 , Issue 3 , September 1977 , pp. 319 - 345
Copyright
Copyright © 1977 The Psychometric Society

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Footnotes

We thank Nancy Henley and Vered Kraus for providing us with data, and Jan deLeeuw for calling our attention to relevant literature. The work of the first author was supported in part by the Psychology Unit of the Israel Defense Forces.

References

Reference Notes

Holman, E. W. A test of the hierarchical clustering model for dissimilarity data. Unpublished manuscript, University of California at Los Angeles, 1975.Google Scholar
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Kraus, personal communication, 1976.Google Scholar

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