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.
Similar content being viewed by others
References
Arabie, P., & Carroll, J. D. (1980). MAPCLUS: A mathematical programming approach to fitting the ADCLUS model.Psychometrika, 45, 211–235.
Buneman, P. (1971). The recovery of trees from measures of dissimilarity. In F. R. Hodson, D. G. Kendall, & P. Tautu (Eds.),Mathematics in the archeological and historical sciences. Edinburgh: Edinburgh University Press.
Bynon, T. (1980).Historical linguistics. Cambridge: Cambridge University Press.
Chernoff, H. (1973). The use of faces to represent points ink-dimensional space graphically.Journal of the American Statistical Association, 68, 361–368.
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.
Cunningham, J. P. (1978). Free trees and bidirectional trees as representations of psychological distance.Journal of Mathematical Psychology, 17, 165–188.
Freedman, D., & Lane, D. (1983a). Significance testing in a nonstochastic setting. In P. Bickel, K. Doksum, & J. L. Hodges, Jr. (Eds.),Lehmann Festschrift. Belmont, CA: Wadsworth.
Freedman, D., & Lane, D. (1983b). A nonstochastic interpretation of reported significance levels.Journal of Business & Economic Statistics, 1, 292–298.
Jardine, N., & Sibson, R. (1971).Mathematical taxonomy. London: Wiley.
Johnson, S. C. (1967). Hierarchical clustering schemes.Psychometrika, 32, 241–254.
Keren, G., & Baggen, S. (1981). Recognition models of alphanumeric characters.Perception & Psychophysics, 29, 234–246.
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 Unpublished manuscript, AT&T Bell laboratories.
Mervis, C. B., Rips, L. J., Rosch, E., Shoben, E. J., & Smith, E. E. (1975). Unpublished data.
Pruzansky, S., Tversky, A., & Carroll, J. D. (1982). Spatial versus tree representation of proximity data.Psychometrika, 47, 3–24.
Restle, F. (1959). A metric and an ordering on sets.Psychometrika, 24, 207–220.
Rosch, E., & Mervis, C. B. (1975). Family resemblances: Studies in the internal structure of categories.Cognitive Psychology, 7, 573–605.
Sattath, S., & Tversky, A. (1977). Additive similarity trees.Psychometrika, 42, 319–345.
Sattath, S., & Tversky, A. (1985). On the relation between common and distinctive feature models. Unpublished manuscript, Stanford University.
Shepard, R. N., & Arabie, P. (1979). Additive clustering: Representation of similarities as combinations of discrete overlapping properties.Psychological Review, 86, 87–123.
Shepard, R. N., Kilpatric, D. W., & Cunningham, J. P. (1975). The internal representation of numbers.Cognitive Psychology, 7, 82–138.
Sokal, R. R., & Sneath, P. H. A. (1963).Principles of numerical taxonomy. San Francisco: W. H. Freeman.
Tischler, J. (1973).Glottochronologie und lexikostatistik. Innsbruck: Innsbrucker Beitrage zur Sprachwissenschaft.
Tversky, A. (1977). Features of similarity.Psychological Review, 84, 327–352.
Tversky, A., & Sattath, S. (1979). Preference trees.Psychological Review, 86, 542–573.
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
Corter, J.E., Tversky, A. Extended similarity trees. Psychometrika 51, 429–451 (1986). https://doi.org/10.1007/BF02294065
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294065