Perception & Psychophysics

, Volume 26, Issue 1, pp 1–19 | Cite as

On the prediction of confusion matrices from similarity judgments

  • David J. Getty
  • John A. Swets
  • Joel B. Swets
  • David M. Green
Article
  • 405 Downloads

Abstract

Three observers viewed visual representations of eight complex sounds in both a pairwise similarity-judgment task and an identification task. A multidimensional scaling procedure applied to the similarity judgments yielded a three-dimensional perceptual space and the relative positions of the stimuli in that space. A probabilistic decision model based on weighted interstimulus distances served to predict well the confusion matrices of the identification task. Three conditions of the identification task, calling for identification of different subsets of the eight stimuli, led the observers to vary the weights they placed on the dimensions; they apparently adjusted the weights to maximize the percent correct identification. An additional group of 14 subjects, participating only in the similarity-judgment task, manifested the same three dimensions as the observers (corresponding to the locus of low-frequency energy, the locus of midfrequency energy, and visual contrast), and also a fourth dimension (corresponding to the periodicity, or waxing and waning, of the sound). Although not evident in the scaling analysis for the three observers, our utilization of the additional dimension increased significantly the variance accounted for in their identification responses. The overall accuracy of the predictions from a perceptual space to identification responses supplies a substantial validation of the use of multidimensional scaling procedures to reveal perceptual structure in demonstrating the ability of that structure to account for behavior in an independent task. The empirical success of this approach, furthermore, suggests a relatively simple and practical means of predicting, and possibly enhancing, identification performance for a given set of visual or auditory stimuli.

Reference Note

  1. Hardzinski, M., & Pachella, R. G.A psychophysical analysis of complex integrated displays. [Technical Report 59 (014523-2-T)]. Ann Arbor, Michigan: University of Michigan, February 1977.Google Scholar

References

  1. Carroll, J. D. Individual differences and multidimensional scaling. In R. N. Shepard, A. K. Romney, & S. Nerlove (Eds.),Multidimensional scaling: Theory and applications in the behavioral sciences. New York: Seminar Press, 1972.Google Scholar
  2. Carroll, J. D., &Chang, J. J. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition.Psychometrika, 1970,35, 288–319.CrossRefGoogle Scholar
  3. Carroll, J. D., &Wish, M. Models and methods for three-way multidimensional scaling. In R. C. Atkinson, D. H. Krantz, R. D. Luce, & P. Suppes (Eds.),Contemporary developments in mathematical psychology. San Francisco: Freeman, 1973.Google Scholar
  4. Howard, J. H., Jr. The psychophysical structure of eight complex underwater sounds.Journal of the Acoustical Society of America, 1977,62, 149–156.CrossRefPubMedGoogle Scholar
  5. Howard, J. H., Jr., &Silverman, E. G. A multidimensional scaling analysis of 16 complex sounds.Perception & Psychophysics, 1976,19, 193–200.CrossRefGoogle Scholar
  6. Klein, W., Plomp, R., &Pols, L. C. W. Vowel spectra, vowel spaces, and vowel identification.Journal of the Acoustical Society of America, 1970,48, 999–1009.CrossRefPubMedGoogle Scholar
  7. Luce, R. D. Detection and recognition. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.),Handbook of Mathematical Psychology. New York: Wiley, 1963.Google Scholar
  8. Miller, J. R., &Carterette, E. C. Perceptual space for musical structures.Journal of the Acoustical Society of America, 1975,58, 711–720.CrossRefPubMedGoogle Scholar
  9. Morgan, B. J. T., Woodhead, M. M., &Webster, J. C. On the recovery of physical dimensions of stimuli, using multidimensional scaling.Journal of the Acoustical Society of America, 1976,60, 186–189.CrossRefGoogle Scholar
  10. Pachella, R. G., & Somers, P. The development of integrated multidimensional displays.Naval Research Reviews, in press.Google Scholar
  11. Plomp, R., &Steeneken, H. J. M. Effect of phase on the timbre of complex tones.Journal of the Acoustical Society of America, 1969,46, 409–421.CrossRefPubMedGoogle Scholar
  12. Pols, L. C. W., Van Der Kamp, L. J. Th., &Plomp, R. Perceptual and physical space of vowel sounds.Journal of the Acoustical Society of America, 1969,46, 458–467.CrossRefPubMedGoogle Scholar
  13. Romney, A. K., Shepand, R. N., &Nerlove, S. B. (Eds.).Multidimensional scaling: Theory and applications in the behavioral sciences (Vol. II). New York: Seminar Press, 1972.Google Scholar
  14. Shaw, D. J. A phonological interpretation of two acoustic confusion matrices.Perception & Psychophysics, 1975,17, 537–542.CrossRefGoogle Scholar
  15. Shepard, R. N. Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space.Psychometrika, 1957,22, 325–345.CrossRefGoogle Scholar
  16. Shepard, R. N. Stimulus and response generalization: Deduction of the generalization gradient from a trace model.Psychological Review, 1958,65, 242–256. (a)CrossRefPubMedGoogle Scholar
  17. Shepard, R. N. Stimulus and response generalization: Tests of a model relating generalization to distance in psychological space.Journal of Experimental Psychology, 1958,55, 509–523. (b)CrossRefPubMedGoogle Scholar
  18. Shepard, R. N. Psychological representation of speech sounds. In E. David & P. Denes (Eds.),Human communication: A unified view. New York: McGraw-Hill, 1972.Google Scholar
  19. Shepard, R. N., &Chipman, S. Second-order isomorphism of internal representations: Shapes of states.Cognitive Psychology, 1970,1, 1–17.CrossRefGoogle Scholar
  20. Shepard, R. N., Romney, A. K., &Nealove, S. B. (Eds.),Multidimensional scaling: Theory and applications in the behavioral sciences (Vol. I). New York: Seminar Press, 1972.Google Scholar
  21. Stenson, H. H. The psychophysical dimensions of similarity among random shapes.Perception & Psychophysics, 1968,3, 201–214.CrossRefGoogle Scholar
  22. Swets, J. A., Green, D. A., Getty, D. J., &Swets, J. B. Signal detection and identification at successive stages of observation.Perception & Psychophysics, 1978,23, 275–289.CrossRefGoogle Scholar
  23. Tversky, A., &Krantz, D. H. The dimensional representation and the metric structure of similarity data.Journal of Mathematical Psychology, 1970,7, 572–596.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 1979

Authors and Affiliations

  • David J. Getty
    • 1
  • John A. Swets
    • 1
  • Joel B. Swets
    • 1
  • David M. Green
    • 1
  1. 1.Bolt Beranek and Newman Inc.Cambridge

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