Advertisement

Psychometrika

, Volume 27, Issue 2, pp 125–140 | Cite as

The analysis of proximities: Multidimensional scaling with an unknown distance function. I.

  • Roger N. Shepard
Article
Received:
Revised:

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.

Keywords

Computer Program Public Policy Euclidean Space Distance Function Statistical Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Abelson, R. P. and Sermat, V. Multidimensional scaling of facial expressions.J. exp. Psychol, in press.Google Scholar
  2. [2]
    Attneave, F. Dimensions of similarity.Amer. J. Psychol, 1950,63, 516–556.Google Scholar
  3. [3]
    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.Google Scholar
  4. [4]
    Bennett, J. F. and Hays, W. L. Multidimensional unfolding: Determining the dimensionality of ranked preference data.Psychometrika, 1960,25, 27–43.Google Scholar
  5. [5]
    Coxeter, H. S. M.Regular polytopes. London: Methuen, 1948.Google Scholar
  6. [6]
    Ekman, G. Dimensions of color vision.J. Psychol., 1954,38, 467–474.Google Scholar
  7. [7]
    Green, B. F. and Anderson, L. K. The tactual identification of shapes for coding switch handles.J. appl. Psychol., 1955,39, 219–226.Google Scholar
  8. [8]
    Hammersley, J. M. The distribution of distances in a hypersphere.Ann. math. Statist., 1950,21, 447–452.Google Scholar
  9. [9]
    Harman, H. H.Modern factor analysis. Chicago: Univ. Chicago Press, 1960.Google Scholar
  10. [10]
    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.Google Scholar
  11. [11]
    Lord, R. D. The distribution of distance in a hypersphere.Ann. math. Statist., 1954,25, 794–798.Google Scholar
  12. [12]
    Plotkin, L. Stimulus generalization in morse code learning.Arch. Psychol., 1943,40, No. 287.Google Scholar
  13. [13]
    Rothkopf, E. Z. Signal similarity and reception errors in early morse code training. In G. Finch and F. Cameron (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
  14. [14]
    Rothkopf, E. Z. A measure of stimulus similarity and errors in some paired-associate learning tasks.J. exp. Psychol., 1957,53, 94–101.Google Scholar
  15. [15]
    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
  16. [16]
    Shepard, R. N. Multidimensional scaling of concepts based upon sequences of restricted associative responses.Amer. Psychologist, 1957,12, 440–441. (Abstract)Google Scholar
  17. [17]
    Shepard, R. N. Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space.Psychometrika, 1957,22, 325–345.Google Scholar
  18. [18]
    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.Google Scholar
  19. [19]
    Shepard, R. N. Stimulus and response generalization: Deduction of the generalization gradient from a trace model.Psychol. Rev., 1958,65, 242–256.Google Scholar
  20. [20]
    Shepard, R. N. Similarity of stimuli and metric properties of behavioral data. In H. Gulliksen and S. Messick (Eds.),Psychological scaling: theory and method. New York: Wiley, 1960. Pp. 33–43.Google Scholar
  21. [21]
    Torgerson, W. S.Theory and methods of scaling. New York: Wiley, 1958.Google Scholar

Copyright information

© Psychometric Society 1962

Authors and Affiliations

  • Roger N. Shepard
    • 1
  1. 1.Bell Telephone LaboratoriesUSA

Personalised recommendations