The analysis of proximities: Multidimensional scaling with an unknown distance function. I.
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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.
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References
- [1]Abelson, R. P. and Sermat, V. Multidimensional scaling of facial expressions.J. exp. Psychol, in press.Google Scholar
- [2]Attneave, F. Dimensions of similarity.Amer. J. Psychol, 1950,63, 516–556.Google Scholar
- [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]Bennett, J. F. and Hays, W. L. Multidimensional unfolding: Determining the dimensionality of ranked preference data.Psychometrika, 1960,25, 27–43.Google Scholar
- [5]Coxeter, H. S. M.Regular polytopes. London: Methuen, 1948.Google Scholar
- [6]Ekman, G. Dimensions of color vision.J. Psychol., 1954,38, 467–474.Google Scholar
- [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]Hammersley, J. M. The distribution of distances in a hypersphere.Ann. math. Statist., 1950,21, 447–452.Google Scholar
- [9]Harman, H. H.Modern factor analysis. Chicago: Univ. Chicago Press, 1960.Google Scholar
- [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]Lord, R. D. The distribution of distance in a hypersphere.Ann. math. Statist., 1954,25, 794–798.Google Scholar
- [12]Plotkin, L. Stimulus generalization in morse code learning.Arch. Psychol., 1943,40, No. 287.Google Scholar
- [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]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]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]Shepard, R. N. Multidimensional scaling of concepts based upon sequences of restricted associative responses.Amer. Psychologist, 1957,12, 440–441. (Abstract)Google Scholar
- [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]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]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]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]Torgerson, W. S.Theory and methods of scaling. New York: Wiley, 1958.Google Scholar
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