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The Analysis of Proximities: Multidimensional Scaling with an Unknown Distance Function. I.

Published online by Cambridge University Press:  01 January 2025

Roger N. Shepard
Roger N. Shepard*
Affiliation:
Bell Telephone Laboratories
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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.

Information

Type
Original Paper
Information
Psychometrika , Volume 27 , Issue 2 , June 1962, pp. 125 - 140
Copyright
Copyright © 1962 The Psychometric Society

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References

Abelson, R. P. and Sermat, V. Multidimensional scaling of facial expressions. J. exp. Psychol, in press.Google Scholar
Attneave, F. Dimensions of similarity. Amer. J. Psychol, 1950, 63, 516–556.10.2307/1418869CrossRefGoogle ScholarPubMed
Bales, R. F., Strodtbeck, F. L., Mills, T. M., and Roseborough, M. E. Channels of communication in small groups. Amer. sociol. Rev., 1951, 16, 461–468.10.2307/2088276CrossRefGoogle Scholar
Bennett, J. F. and Hays, W. L. Multidimensional unfolding: Determining the dimensionality of ranked preference data. Psychometrika, 1960, 25, 27–43.10.1007/BF02288932CrossRefGoogle Scholar
Coxeter, H. S. M. Regular polytopes, London: Methuen, 1948.Google Scholar
Ekman, G. Dimensions of color vision. J. Psychol., 1954, 38, 467–474.10.1080/00223980.1954.9712953CrossRefGoogle Scholar
Green, B. F. and Anderson, L. K. The tactual identification of shapes for coding switch handles. J. appl. Psychol., 1955, 39, 219–226.10.1037/h0042925CrossRefGoogle Scholar
Hammersley, J. M. The distribution of distances in a hypersphere. Ann. math. Statist., 1950, 21, 447–452.10.1214/aoms/1177729805CrossRefGoogle Scholar
Harman, H. H. Modern factor analysis, Chicago: Univ. Chicago Press, 1960.Google Scholar
Keller, F. S. and Taubman, R. E. Studies in international morse code. II. Errors made in code reception. J. appl. Psychol., 1943, 27, 504–509.10.1037/h0057661CrossRefGoogle Scholar
Lord, R. D. The distribution of distance in a hypersphere. Ann. math. Statist., 1954, 25, 794–798.10.1214/aoms/1177728669CrossRefGoogle Scholar
Plotkin, L. Stimulus generalization in morse code learning. Arch. Psychol., 1943, 40, 287.Google Scholar
Rothkopf, E. Z. Signal similarity and reception errors in early morse code training. In Finch, G. and Cameron, F. (Eds.), Symposium on Air Force human engineering, personnel, and training research. Washington: National Academy of Sciences—National Research Council Publication 455, 1956. Pp. 229–235..Google Scholar
Rothkopf, E. Z. A measure of stimulus similarity and errors in some paired-associate learning tasks. J. exp. Psychol., 1957, 53, 94–101.10.1037/h0041867CrossRefGoogle ScholarPubMed
Seashore, H. and Kurtz, A. K. Analysis of errors in copying code. Washington, D. C.: Office of Scientific Research and Development, Rep. No. 4010, 1944.Google Scholar
Shepard, R. N. Multidimensional scaling of concepts based upon sequences of restricted associative responses. Amer. Psychologist, 1957, 12, 440–441. (Abstract).Google Scholar
Shepard, R. N. Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space. Psychometrika, 1957, 22, 325–345.10.1007/BF02288967CrossRefGoogle Scholar
Shepard, R. N. Stimulus and response generalization: Tests of a model relating generalization to distance in psychological space. J. exp. Psychol., 1958, 55, 509–523.10.1037/h0042354CrossRefGoogle Scholar
Shepard, R. N. Stimulus and response generalization: Deduction of the generalization gradient from a trace model. Psychol. Rev., 1958, 65, 242–256.10.1037/h0043083CrossRefGoogle ScholarPubMed
Shepard, R. N. Similarity of stimuli and metric properties of behavioral data. In Gulliksen, H. and Messick, S. (Eds.), Psychological scaling: theory and method. New York: Wiley, 1960, 33–43..Google Scholar
Torgerson, W. S. Theory and methods of scaling, New York: Wiley, 1958.Google Scholar