Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-08T10:32:12.578Z Has data issue: false hasContentIssue false
  • English
  • Français

Extended Similarity Trees

Published online by Cambridge University Press:  01 January 2025

James E. Corter  and
Amos Tversky
James E. Corter*
Affiliation:
Teachers College, Columbia University
Amos Tversky
Affiliation:
Stanford University
*
Requests for reprints should be sent to James E. Corter, Box 41, Teachers College, Columbia University, New York, NY 10027.
Get access Rights & Permissions [Opens in a new window]

Abstract

Proximity data can be represented by an extended tree, which generalizes traditional trees by including marked segments that correspond to overlapping clusters. An extended tree is a graphical representation of the distinctive features model. A computer program (EXTREE) that constructs extended trees is described and applied to several sets of conceptual and perceptual proximity data.

Keywords

proximitiesnonhierarchical clusteringadditive treesfeature models
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 3 , September 1986 , pp. 429 - 451
Copyright
Copyright © 1986 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was supported in part by a National Science Foundation Pre-doctoral Fellowship to the first author.

A magnetic tape containing both the EXTREE program described in the article and ADDTREE/P program for fitting additive trees can also be obtained from the above address. Requests for the program should be accompanied by a check for $25 made out to Teachers College, to cover the costs of the tape and postage.

References

Arabie, P., Carroll, J. D. (1980). MAPCLUS: A mathematical programming approach to fitting the ADCLUS model. Psychometrika, 45, 211–235.CrossRefGoogle Scholar
Buneman, P. (1971). The recovery of trees from measures of dissimilarity. In Hodson, F. R., Kendall, D. G., Tautu, P. (Eds.), Mathematics in the archeological and historical sciences, Edinburgh: Edinburgh University Press.Google Scholar
Bynon, T. (1980). Historical linguistics, Cambridge: Cambridge University Press.Google Scholar
Chernoff, H. (1973). The use of faces to represent points ink-dimensional space graphically. Journal of the American Statistical Association, 68, 361–368.CrossRefGoogle Scholar
Corter, J. E. (1982). ADDTREE/P: A PASCAL program for fitting additive trees based on Sattath and Tversky's ADDTREE algorithm. Behavior Research Methods and Instrumentation, 14(3), 353–354.CrossRefGoogle Scholar
Cunningham, J. P. (1978). Free trees and bidirectional trees as representations of psychological distance. Journal of Mathematical Psychology, 17, 165–188.CrossRefGoogle Scholar
Freedman, D., Lane, D. (1983). Significance testing in a nonstochastic setting. In Bickel, P., Doksum, K., Hodges, J. L. Jr. (Eds.), Lehmann Festschrift, Belmont, CA: Wadsworth.Google Scholar
Freedman, D., Lane, D. (1983). A nonstochastic interpretation of reported significance levels. Journal of Business & Economic Statistics, 1, 292–298.CrossRefGoogle Scholar
Jardine, N., Sibson, R. (1971). Mathematical taxonomy, London: Wiley.Google Scholar
Johnson, S. C. (1967). Hierarchical clustering schemes. Psychometrika, 32, 241–254.CrossRefGoogle ScholarPubMed
Keren, G., Baggen, S. (1981). Recognition models of alphanumeric characters. Perception & Psychophysics, 29, 234–246.CrossRefGoogle ScholarPubMed
Kruskal, J. B., Young, F. W., & Seery, J. B. (1977). How to use KYST-2A, a very flexible program to do multidimensional scaling and unfolding. Unpublished manuscript, AT&T Bell laboratories.Google Scholar
Mervis, C. B., Rips, L. J., Rosch, E., Shoben, E. J., & Smith, E. E. (1975). Unpublished data.Google Scholar
Pruzansky, S., Tversky, A., Carroll, J. D. (1982). Spatial versus tree representation of proximity data. Psychometrika, 47, 3–24.CrossRefGoogle Scholar
Restle, F. (1959). A metric and an ordering on sets. Psychometrika, 24, 207–220.CrossRefGoogle Scholar
Rosch, E., Mervis, C. B. (1975). Family resemblances: Studies in the internal structure of categories. Cognitive Psychology, 7, 573–605.CrossRefGoogle Scholar
Sattath, S., Tversky, A. (1977). Additive similarity trees. Psychometrika, 42, 319–345.CrossRefGoogle Scholar
Sattath, S., & Tversky, A. (1985). On the relation between common and distinctive feature models. Unpublished manuscript, Stanford University.Google Scholar
Shepard, R. N., Arabie, P. (1979). Additive clustering: Representation of similarities as combinations of discrete overlapping properties. Psychological Review, 86, 87–123.CrossRefGoogle Scholar
Shepard, R. N., Kilpatric, D. W., Cunningham, J. P. (1975). The internal representation of numbers. Cognitive Psychology, 7, 82–138.CrossRefGoogle Scholar
Sokal, R. R., Sneath, P. H. A. (1963). Principles of numerical taxonomy, San Francisco: W. H. Freeman.Google Scholar
Tischler, J. (1973). Glottochronologie und lexikostatistik, Innsbruck: Innsbrucker Beitrage zur Sprachwissenschaft.Google Scholar
Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327–352.CrossRefGoogle Scholar
Tversky, A., Sattath, S. (1979). Preference trees. Psychological Review, 86, 542–573.CrossRefGoogle Scholar