Representation of structure in similarity data: Problems and prospects (original) (raw)
References
Abelson, R. P., and Tukey, J. W. Efficient conversion of nonmetric information into metric information.Proceedings of the American Statistical Association Meetings, Social Statistics Section, 1959, 226–230.
Anderson, J. R., and Bower, G. H. Human associative memory. Washington, D. C.: V. H. Winston & Sons, 1973. Google Scholar
Arabie, P. Concerning Monte Carlo evaluations of nonmetric multidimensional scaling algorithms.Psychometrika, 1973,38, 607–608. Google Scholar
Arabie, P. and Boorman, S. A. Multidimensional scaling of measures of distance between partitions.Journal of Mathematical Psychology, 1973,10, 148–203. Google Scholar
Arabie, P. and Shepard, R. N. Representation of similarities as additive combinations of discrete overlapping properties. Presented at the Mathematical Psychology Meeting in Montreal, August, 1973.
Arnold, J. B. A multidimensional scaling study of semantic distance.Journal of Experimental Psychology Monograph, 1971,90, 349–372. Google Scholar
Attneave, F. Dimensions of similarity.American Journal of Psychology, 1950,63, 516–556. Google Scholar
Beals, R., Krantz, D. H., and Tversky, A. Foundations of multidimensional scaling.Psychological Review, 1968,75, 127–142. PubMed Google Scholar
Bennett, R. S. The intrinsic dimensionality of signal collections. Doctoral dissertation, The Johns Hopkins University, 1965. University Microfilms, Inc., Ann Arbor, Michigan.
Bennett, R. S. The intrinsic dimensionality of signal collections.IEEE Transactions on Information Theory, 1969, Vol. IT-15, No. 5, 517–525. Google Scholar
Blank, A. A. Axiomatics of binocular vision: The foundations of metric geometry in relation to space perception.Journal of the Optical Society of America, 1958,48, 328–334. PubMed Google Scholar
Blank, A. A. The Luneburg theory of binocular space perception. In S. Koch (Ed.),Psychology: A study of a science. New York: McGraw-Hill, 1959. Pp. 395–426. Google Scholar
Blumenthal, L. M.Theory and applications of distance geometry. Oxford: Clarendon Press, 1953. Google Scholar
Boyd, J. P. Information distance for discrete structures. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.),Multidimensional scaling: Theory and applications in the behavioral sciences, Vol. I. New York: Seminar Press, 1972. Pp. 213–223. Google Scholar
Busemann, H.The geometry of geodesics. New York: Academic Press, 1955. Google Scholar
Carroll, J. D. Individual differences and multidimensional scaling. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.),Multidimensional scaling: Theory and applications in the behavioral sciences, Vol. I. New York: Seminar Press, 1972. (a) Pp. 105–155. Google Scholar
Carroll, J. D. Algorithms for rotation and interpretation of dimensions and for configuration matching. Bell Telephone Laboratories, 1972. (b) (Multilithed handout prepared for the workshop on multidimensional scaling, held at the University of Pennsylvania in June, 1972.)
Carroll, J. D., and Chang, J.-J. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition.Psychometrika, 1970,35, 283–319. Google Scholar
Chang, J.-J., and Shepard, R. N. Exponential fitting in the proximity analysis of confusion matrices. Presented at the annual meeting of the Eastern Psychological Association, New York, April 14, 1966.
Clark, H. H. Linguistic processes in deductive reasoning.Psychological Review, 1969,76, 387–404. Google Scholar
Clark, H. H. Word associations and linguistic theory. In J. Lyons (Ed.),New horizons in linguistics. Baltimore, Maryland: Penguin Books, 1970. Pp. 271–286. Google Scholar
Coombs, C.A theory of data. New York: Wiley, 1964. Google Scholar
Cross, D. V. Metric properties of multidimensional stimulus generalization. In D. I. Mostofsky (Ed.),Stimulus generalization. Stanford, Calif.: Stanford University Press, 1965. Pp. 72–93. Google Scholar
Cunningham, J. P. On finding an optimal tree realization of a proximity matrix. Presented at the mathematical psychology meeting, Ann Arbor, Michigan, August 29, 1974.
Cunningham, J. P., and Shepard, R. N. Monotone mapping of similarities into a general metric space.Journal of Mathematical Psychology, 1974,11, (in press).
Degerman, R. L. Multidimensional analysis of complex structure: Mixtures of class and quantitative variation.Psychometrika, 1970,35, 475–491. Google Scholar
Ekman, G. Dimensions of color vision.Journal of Psychology, 1954,38, 467–474. Google Scholar
Fillenbaum, S., and Rapoport, A.Structures in the subjective lexicon, New York: Academic Press, 1971. Google Scholar
Foley, J. M. The size-distance relation and the intrinsic geometry of visual space.Vision Research, 1972,12, 323–332. PubMed Google Scholar
Greenberg, J. H.Language universals. The Hague: Mouton, 1966. Google Scholar
Guttman, L. A new approach to factor analysis: The radex. In P. F. Lazarsfeld (Ed.),Mathematical thinking in the social sciences. Glencoe, Illinois: Free Press, 1954. Pp. 258–348. Google Scholar
Guttman, L. A generalized simplex for factor analysis.Psychometrika, 1955,20, 173–192. Google Scholar
Guttman, N., and Kalish, H. I. Discriminability and stimulus generalization.Journal of Experimental Psychology, 1956,51, 79–88. PubMed Google Scholar
Halle, M. On the bases of phonology. In J. A. Fodor and J. J. Katz (Eds.),The structure of language. Englewood Cliffs, N. J.: Prentice-Hall, 1964. Pp. 324–333. Google Scholar
Harshman, R. A. Foundations of the parafac procedure: Models and conditions for an explanatory multi-modal factor analysis. Unpublished doctoral dissertation, University of California at Los Angeles, 1970.
Haviland, S. E., and Clark, E. V. ‘This man's father is my father's son’: A study of the acquisition of English kin terms.Journal of Child Language, 1974,1, 23–47. Google Scholar
Helm, C. E. Multidimensional ratio scaling analysis of perceived color relations.Journal of the Optical Society of America, 1964,54, 256–262. PubMed Google Scholar
Hyman, R., and Well, A. Judgments of similarity and spatial models.Perception and Psychophysics, 1967,2, 233–248. Google Scholar
Hyman, R., and Well, A. Perceptual separability and spatial models.Perception and Psychophysics, 1968,3, 161–165. Google Scholar
Indow, T. Applications of multidimensional scaling in perception. In E. C. Carterette and M. P. Friedman (Eds.),Handbook of perception, Vol. 2. New York: Academic Press, in press.
Jardine, N., and Sibson, R.Mathematical taxonomy. New York: Wiley, 1971. Google Scholar
Johnson, S. C. Hierarchical clustering schemes.Psychometrika, 1967,32, 241–254. PubMed Google Scholar
Klahr, D. A Monte Carlo investigation of the statistical significance of Kruskal's nonmetric scaling procedure.Psychometrika, 1969,34, 319–330. Google Scholar
Koopman, R. F., and Cooper, M. Some problems with Minkowski distance models in multidimensional scaling. Presented at the annual meeting of the Psychometric Society, Stanford University, March 28, 1974.
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964,29, 1–27. (a) Google Scholar
Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method.Psychometrika, 1964,29, 28–42. (b) Google Scholar
Kruskal, J. B. Linear transformation of multivariate data to reveal clustering. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.),Multidimensional scaling: Theory and applications in the behavioral sciences. Vol I. New York: Seminar Press, 1972. Pp. 179–191. Google Scholar
Kruskal, J. B. Multidimensional scaling and other methods for discovering structure. In A. J. Ralston, H. S. Wilf, and K. Enslein, (Eds.),Statistical methods for digital computers. New York: Wiley, in press.
Levelt, W. J. M., Van de Geer, J. P., and Plomp, R. Triadic comparisons of musical intervals.British Journal of Mathematical and Statistical Psychology, 1966,19, 163–179. Google Scholar
Lévi-Strauss, C.The savage mind. Chicago: University of Chicago Press, 1967. Google Scholar
Liberman, A. M., Cooper, F. S., Shankweiler, D. P., and Studdert-Kennedy, M. Perception of the speech code.Psychological Review, 1967,74, 431–461. PubMed Google Scholar
Lingoes, J. C. A general survey of the Guttman-Lingoes nonmetric program series. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.),Multidimensional scaling: Theory and applications in the behavioral sciences. Vol. I. New York: Seminar Press, 1972. Google Scholar
Luneburg, R. K.Mathematical analysis of binocular vision. Princeton, N. J.: Princeton University Press, 1947. Google Scholar
Luneburg, R. K. The metric of binocular visual space.Journal of Optical Society of America, 1950,40, 637–642. Google Scholar
Miller, G., and Nicely, P. E. An analysis of perceptual confusions among some English consonants.Journal of the Acoustical Society of America, 1955,27, 338–352. Google Scholar
Osgood, C. E., Suci, G. J., and Tannenbaum, P. H.The measurement of meaning. Urbana, Ill.: University of Illinois Press, 1957. Google Scholar
Peters, R. W. Dimensions of perception of consonants.Journal of the Acoustical Society of America, 1963,35, 1985–1989. Google Scholar
Quillian, M. R. Semantic memory. In M. Minsky (Ed.),Semantic information processing. Cambridge, Mass.: M.I.T. Press, 1968. Google Scholar
Rips, L. J., Shoben, E. J., and Smith, E. E. Semantic distance and the verification of semantic relations.Journal of Verbal Learning and Verbal Behavior, 1973,12, 1–20. Google Scholar
Romney, A. K., and D'Andrade, R. G. Cognitive aspects of English kinship terms.American Anthropologist, 1964,66, 146–170. Google Scholar
Rumelhart, D. E., and Abrahamson, A. A. A model for analogical reasoning.Cognitive Psychology, 1973,5, 1–28. Google Scholar
Rumelhart, D. E., Lindsay, P. H., and Norman, D. A. A process model for long-term memory. In E. Tulving and W. Donaldson (Eds.),Organization of memory. New York: Academic Press, 1972. Google Scholar
Rund, H.The differential geometry of Finsler space. Berlin: Springer-Verlag, 1959. Google Scholar
Shepard, R. N. Multidimensional scaling of concepts based upon sequences of restricted associative responses.American Psychologist, 1957,12, 440–441. (abstract) (a) Google Scholar
Shepard, R. N. Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space.Psychometrika, 1957,22, 325–345. (b) Google Scholar
Shepard, R. N. Stimulus and response generalization: Deduction of the generalization gradient from a trace model.Psychological Review, 1958,65, 242–256. (a) PubMed Google Scholar
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) PubMed Google Scholar
Shepard, R. N. Similarity of stimuli and metric properties of behavioral data. In H. Gulliksen and S. Messick (Eds.),Psychological scaling: Theory and applications. New York: Wiley, 1960. Pp. 33–43. Google Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. I.Psychometrika, 1962,27, 125–140. (a) Google Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. II.Psychometrika, 1962,27, 219–246. (b) Google Scholar
Shepard, R. N. Analysis of proximities as a technique for the study of information processing in man.Human Factors, 1963,5, 33–48. (a) PubMed Google Scholar
Shepard, R. N. Comments on Professor Underwood's paper “Stimulus selection in verbal learning.” In C. N. Cofer and B. S. Musgrave (Eds.),Verbal behavior and learning: Problems and processes. New York: McGraw-Hill, 1963. Pp. 48–70. (b) Google Scholar
Shepard, R. N. Attention and the metric structure of the stimulus space.Journal of Mathematical Psychology, 1964,1, 54–87. (a) Google Scholar
Shepard, R. N. Polynomial fitting in the analysis of proximities.Proceedings of the XVIIth international congress of psychology. Amsterdam: North-Holland Publisher, 1964, 345–346. (abstract) (b) Google Scholar
Shepard, R. N. Approximation to uniform gradients of generalization by monotone transformations of scale. In D. I. Mostofsky (Ed.),Stimulus Generalization. Stanford, Calif.: Stanford University Press, 1965. Pp. 94–110. Google Scholar
Shepard, R. N. Computer explorations of psychological space. Invited research address presented at the annual meeting of the American Psychological Association, New York, September 3, 1966. (a)
Shepard, R. N. Metric structures in ordinal data.Journal of Mathematical Psychology, 1966,3, 287–315. (b) Google Scholar
Shepard, R. N. Continuity versus the triangle inequality as a central principle for the spatial analysis of similarity data. Presented in a symposium on alternative models for the geometric representation of psychological data, at the mathematical psychology meetings, Stanford University, August 28, 1968.
Shepard, R. N. Introduction to Volume I. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.),Multidimensional scaling: Theory and applications in the behavioral sciences, Vol. I. New York: Seminar Press, 1972. Pp. 1–20. (a) Google Scholar
Shepard, R. N. A taxonomy of some principal types of data and of multidimensional methods for their analysis. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.),Multidimensional scaling: Theory and applications in the behavioral sciences, Vol. I. New York: Seminar Press, 1972. Pp. 21–47. (b) Google Scholar
Shepard, R. N. Psychological representation of speech sounds. In E. E. David & P. B. Denes (Eds.),Human communication: A unified view. New York: McGraw-Hill, 1972. Pp. 67–113. (c) Google Scholar
Shepard, R. N., and Carroll, J. D. Parametric representation of nonlinear data structures. In P. R. Krishnaiah (Ed.),Multivariate analysis: Proceedings of an international symposium. New York: Academic Press, 1966. Pp. 561–592. Google Scholar
Shepard, R. N., and Cermak, G. W. Perceptual-cognitive explorations of a toroidal set of free-form stimuli.Cognitive Psychology, 1973,4, 351–377. Google Scholar
Shepard, R. N., Hovland, C. I. and Jenkins, H. M. Learning and memorization of classifications.Psychological Monographs, 1961,75, (13, whole no. 517).
Shepard, R. N., Kilpatric, D. W., and Cunningham, J. P. The internal representation of numbers.Cognitive Psychology, in press.
Silberstein, L. Investigations of the intrinsic properties of the color domain.Journal of the Optical Society of America, 1938,28, 63–85. Google Scholar
Silberstein, L., and MacAdam, D. L. The distribution of color matchings around a color center.Journal of the Optical Society of America, 1945,35, 32–39. Google Scholar
Sokal, R. R., and Sneath, P. H. A.Principles of numerical taxonomy. San Francisco: W. H. Freeman, 1963. Google Scholar
Stenson, H. H., and Knoll, R. L. Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure.Psychological Bulletin, 1969,71, 122–126. Google Scholar
Thomas, H. Spatial models and multidimensional scaling of random shapes.American Journal of Psychology, 1968,81, 551–558. Google Scholar
Torgerson, W. S. Multidimensional scaling: I. theory and method.Psychometrika, 1952,17, 401–419. Google Scholar
Torgerson, W. S.Theory and methods of scaling. New York: Wiley, 1958. Google Scholar
Torgerson, W. S. Multidimensional scaling of similarity.Psychometrika, 1965,30, 379–393. PubMed Google Scholar
Tucker, L. R. Relations between multidimensional scaling and three-mode factor analysis.Psychometrika, 1972,37, 3–27. Google Scholar
Wish, M., and Carroll, J. D. Applications of “INDSCAL” to studies of human perception and judgment. In E. C. Carterette and M. P. Friedman (Eds.),Handbook of perception, Vol. 2. New York: Academic Press, in press.
Young, F. W. Nonmetric multidimensional scaling: Recovery of metric information.Psychometrika, 1970,35, 455–473. Google Scholar
Young, F. W., and Torgerson, W. S. TORSCA, A FORTRAN IV program for Shepard-Kruskal multidimensional scaling analysis.Behavioral Science, 1967,12, 498. Google Scholar