, Volume 51, Issue 2, pp 209–240 | Cite as

Differential ordering of objects and attributes

  • J. P. Sutcliffe


By reference to nominated attributes, a genus, being a population of objects of one specified kind, may be partitioned into species, being subpopulations of different kinds. A prototype is an object representative of its species within the genus. Using this framework, the paper describes how objects can be relatively differentiated with respect to attributes, and how attributes can be relatively differentiating with respect to objects. Methods and rationale for such differential ordering of objects and attributes are presented by example, formal development, and application.

For a genus Θ comprisingn species of object there is a subsetP ofn distinct prototypes. With respect tom nominated attributes, each object in Θ has anm-element characterization. Together these determine ann ×m objects × attributes matrix, the rows of which are the characterizations of the prototypical objects. Over then species in Θ, an associated relative frequency vector gives the distribution of objects (and of their characterizations). The matrix and vector associate the objects in Θ with points in a metric space (P, δ); and it is with respect to various sums of distances in this attribute space that one can differentially order objects and attributes.

The definition of the distance functionδ is generalized across kinds of difference, types of characterization, scale-types of measurement, Minkowskiindex ≧ 1, and any form of distribution of objects over species. Explanatory and taxonomic applications in psychology and other fields are discussed, with focus on classification, identification, recognition, and search. The Braille code and the identification of its characters provide illustration.

Key words

numerical taxonomy information storage and retrieval classification identification recognition search genus species prototype object x attribute matrix datum Minkowski metric distance similarity differentiation distinguishing feature tree key Braille 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, A. J. B. (1971). Similarity measure for mixed attribute types.Nature, 232, 416–417.Google Scholar
  2. Attneave, F. (1950). Dimensions of similarity.American Journal of Psychology, 63, 516–556.Google Scholar
  3. Attneave, F. (1953). Psychological probability as a function of experienced frequency.Journal of Experimental Psychology, 46, 81–86.Google Scholar
  4. Buchanan, B. G. (1982). New research on expert systems. In J. E. Hays, D. Michie & Y-H. Pao (Eds.),Machine intelligence 10. Chichester: Ellis Horwood.Google Scholar
  5. Burr, E. J. (1968). Cluster sorting with mixed character types. I. Standardization of character values.Australian Computer Journal, 1, 97–99.Google Scholar
  6. Burt, C. (1937). Correlations between persons.British Journal of Psychology, 28, 59–96.Google Scholar
  7. Cain, A. J. (1956). The genus in evolutionary taxonomy.Systematic Zoology, 5, 97–109.Google Scholar
  8. Cattell, R. B. (1946).Description and measurement of personality. Yonkers: World Book.Google Scholar
  9. Clark, R. S. (1950).Books and reading for the blind (Library Association Pamphlet # 1). London: The Library Association.Google Scholar
  10. Coombs, C. H. (1964).A theory of data. New York: Wiley.Google Scholar
  11. Cox, D. R. (1958).Planning experiments. New York: Wiley.Google Scholar
  12. Daniels, H. E. (1944). The relation between measures of correlation in the universe of sample permutations.Biometrika, 33, 129–135.Google Scholar
  13. de Leeuw, J. (1973).Canonical analysis of categorical data. Leiden: Psychological Institute.Google Scholar
  14. de Saussure, F. (1949).Cours de linguistique générale (4th ed.) [Course in general linguistics]. Paris: Payot.Google Scholar
  15. de Saussure, F. (1959).Course in general linguistics (W. Baskin trans., edited by C. Bally, A. Sechehaye, & A. Reidlinger). New York: Philosophic Library.Google Scholar
  16. Dewey, G. (1923).Relative frequency of English speech sounds. Cambridge: Harvard University Press.Google Scholar
  17. Doyle, L. B. (1975).Information retrieval and processing. Los Angeles: Melville.Google Scholar
  18. Duda, R. O., & Hart, P. E. (1973).Pattern classification and scene analysis. New York: Wiley-Interscience.Google Scholar
  19. Estabrook, G. F. (1967). An information theory model for character analysis.Taxon, 16, 86–97.Google Scholar
  20. Feigenbaum, J. F., & Feldman, J. (Eds.). (1963).Computers and thought. New York: McGraw-Hill.Google Scholar
  21. Feller, W. (1957).An introduction to probability theory and its applications (Vol. 1, 2nd ed.). New York: Wiley.Google Scholar
  22. Ferguson, G. A. (1949). On the theory of test discrimination.Psychometrika, 14, 61–68.Google Scholar
  23. Fisher, R. A., Corbet, A. S., & Williams, S. C. B. (1943). The relation between the number of species and the number of individuals in a random sample of an animal population.Journal of Animal Ecology, 12, 42–58.Google Scholar
  24. Foulds, L. R., Penny, D., & Hendy, M. D. (1979). A general approach to proving the minimality of phylogenetic trees illustrated by an example with a set of 23 vertebrates.Journal of Molecular Evolution, 13, 151–166.Google Scholar
  25. Fréchet, M. Les probabilités associées à un système d'événements compatibles et dépendants [Probabilities associated with a system of concomitant dependent events].Actualités Scientifiques et Industrielles. Paris: Hermann, 1940, No. 859; 1943, No. 942.Google Scholar
  26. Fu, K. S. (Ed.). (1971). Special issue on feature extraction and selection in pattern recognition.IEEE Transactions on Computers, C-20, (Whole No. 9), 965–1117.Google Scholar
  27. Fu, K. S., & Mui, J. K. (1981). A survey of image segmentation.Pattern Recognition, 13, 3–16.Google Scholar
  28. Garner, W. R. (1966). To perceive is to know.American Psychologist, 21, 11–19.Google Scholar
  29. Garner, W. R. (1978). Aspects of a stimulus: Features, dimensions, and configurations. In E. Rosch & B. A. Lloyd (Eds.),Cognition and categorization. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  30. Gibson, E. J. (1969).Principles of perceptual learning and development. New York: Appleton-Century-Crofts.Google Scholar
  31. Gower, J. C. (1966). Some distance properties of latent root and vector methods used in multivariate analysis.Biometrika, 53, 315–328.Google Scholar
  32. Gower, J. C. (1971). A general coefficient of similarity and some of its properties.Biometrics, 27, 857–871.Google Scholar
  33. Gregson, R. A. M. (1975).Psychometrics of similarity. New York: Academic Press.Google Scholar
  34. Harmon, L. D. (1973). The recognition of faces.Scientific American, 229, 70–82.Google Scholar
  35. Hartigan, J. A. (1967). Representation of similarity matrices by trees.Journal of the American Statistical Association, 62, 1140–1158.Google Scholar
  36. Hill, M. O. (1974). Correspondence analysis: A neglected multivariate method.Applied Statistics, 23, 340–354.Google Scholar
  37. Hu, T. C., & Tucker, A. C. Optimal computer search trees and variable length alphabetical codes.SIAM Journal of Applied Mathematics, 21, 514–532.Google Scholar
  38. Hubert, L. (1974). Problems of seriation using a subject by item response matrix.Psychological Bulletin, 81, 976–983.Google Scholar
  39. Hubert, L. J., & Baker, F. B. (1977). Analyzing distinctive features.Journal of Educational Statistics, 2, 79–98.Google Scholar
  40. Huffman, D. A. (1952). A method for the construction of minimum redundancy codes.Proceedings of the Institute of Radio Engineers, 50, 1098–1101.Google Scholar
  41. Hull, C. L. (1939). The problem of stimulus equivalence in behavior theory.Psychological Review, 46, 9–30.Google Scholar
  42. Jakobson, R., Fant, C. G. M., & Halle, M. (1963).Preliminaries to speech analysis: The distinctive features and their correlates. Cambridge: MIT Press.Google Scholar
  43. Jardine, N., & Sibson, R. (1971).Mathematical taxonomy. London: Wiley.Google Scholar
  44. Jevons, W. S. (1958).The principles of science (2nd ed.). New York: Dover.Google Scholar
  45. Jičin, R. (1972). Some problems of description of sets of objects.Journal of Theoretical Biology, 34, 295–311.Google Scholar
  46. Jičin, R., & Vašiček, Z. (1969). The problem of similarity of objects in numerical taxonomy.Journal of General Microbiology, 58, 135–139.Google Scholar
  47. Johnson, S. C. (1967). Hierarchical clustering schemes.Psychometrika, 32, 241–254.Google Scholar
  48. Kendall, M. G. (1970).Rank correlation methods (4th ed.). London: Griffin.Google Scholar
  49. Kolmogorov, A. N., & Fomin, S. V. (1957).Elements of the theory of functions and functional analysis: Volume I.Metric and normed spaces (L. F. Boron trans.). Rochester, NY: Graylock Press. (Original work published 1954)Google Scholar
  50. Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971).Foundations of measurement (Vol. I). New York: Academic Press.Google Scholar
  51. Lockhart, W. R., & Hartman, P. A. (1963). The formation of monothetic groups in quantitative bacterial taxonomy.Journal of Bacteriology, 85, 68–77.Google Scholar
  52. Lord, F. M., & Novick, M. R. (1968).Statistical theories of mental test scores. Reading, MA: Addison-Wesley.Google Scholar
  53. Marr, D. (1976). Early processing of visual information.Philosophical Transactions of the Royal Society, 275 (Series B), 483–524.Google Scholar
  54. McNeill, J. (1972). The hierarchical ordering of characters as a solution to the dependent character problem in numerical taxonomy.Taxon, 21, 71–82.Google Scholar
  55. Minkowski, H. (1896). Geometrie der zahlen [Geometry of numbers]. Leipzig: Teubner.Google Scholar
  56. Morse, L. E. (1971). Specimen identification and key construction with time sharing computers.Taxon, 20, 269–282.Google Scholar
  57. Morse, L. E. (1974). Computer assisted storage and retrieval of the data of taxonomy and systematics.Taxon, 23, 29–43.Google Scholar
  58. Morton, J. (1969). Interaction of information in word recognition.Psychological Review, 76, 165–178.Google Scholar
  59. Murdock, B. B. (1960). The distinctiveness of stimuli.Psychological Review, 67, 16–31.Google Scholar
  60. Neisser, U. (1964). Visual search.Scientific American, 210, 94–202.Google Scholar
  61. Neisser, U. (1966).Cognitive psychology. New York: Appleton-Century-Crofts.Google Scholar
  62. Nishisato, S. (1980).Analysis of categorical data: Dual scaling and its applications. Toronto: University of Toronto Press.Google Scholar
  63. Nowakowska, M. (1975). Takie same, różne, pobodne—psychologiczne podstawy pomiaru [Same, different, similar—psychological foundations of measurement].Przeglad Psychologiczny, 18, 297–309.Google Scholar
  64. Orloci, L. (1969). Information theory models for hierarchic and nonhierarchic classifications. In A. J. Cole (Ed.),Numerical Taxonomy. London: Academic Press.Google Scholar
  65. Pankhurst, R. J. (1970). A computer program for generating diagnostic keys.The computer Journal, 13, 145–151.Google Scholar
  66. Pankhurst, R. J. (Ed.). (1975).Biological identification with computers. London: Academic Press.Google Scholar
  67. Pankhurst, R. J. (1978).Biological identification. London: Arnold.Google Scholar
  68. Picard, C. (1965).Théorie des questionnaires [Theory of Keys]. Paris: Gauthiers-Villars.Google Scholar
  69. Pitts, W., & McCulloch, W. S. (1947). How we know universals: The perception of auditory and visual forms.Bulletin of Mathematical Biophysics, 9, 127–147.Google Scholar
  70. Ramsay, J. O. (1980). The joint analysis of direct ratings, pairwise preferences, and dissimilarities.Psychometrika, 45, 149–165.Google Scholar
  71. Rasch, G. (1977). On specific objectivity: An attempt at formalizing the request for generality and validity of scientific statements.Danish Yearbook of Philosophy, 14, 58–94.Google Scholar
  72. Rescher, N., & Oppenheim, P. (1955). Logical analysis of Gestalt concepts.British Journal of the Philosophy of Science, 6, 89–106.Google Scholar
  73. Rescigno, A., & Maccacaro, G. A. (1960, September). The information content of biological classifications, In C. Cherry (Ed.),Information theory. London: Butterworth. (A symposium held at the Royal Institution, London, August 29–September 2, 1960)Google Scholar
  74. Restle, F. (1959). A metric and an ordering on sets.Psychometrika, 24, 207–220.Google Scholar
  75. Rider, P. R. (1951). The distribution of the range in samples from a discrete rectangular population.Journal of the American Statistical Association, 46, 375–378.Google Scholar
  76. Riesz, F., & Szökefalvi-Nagy, B. (1955).Functional analysis (2nd French ed., L. F. Boron trans.) New York: Frederick Ungar.Google Scholar
  77. Roblin, J. (1955).The reading fingers: Life of Louis Braille 1809–1952 (R. G. Mandalian trans.). New York: American Foundation for the Blind.Google Scholar
  78. Rosch, E., & Lloyd, B. B. (Eds.). (1978).Cognition and categorization. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  79. Rosenfeld, A. (1969).Picture processing by computer. New York: Academic Press.Google Scholar
  80. Rothkopf, E. Z. (1957). A measure of stimulus similarity and errors in some paired-associate learning tasks.Journal of Experimental Psychology, 53, 94–101.Google Scholar
  81. Rubin, E. J. (1921). Visuell wahrgenommene figuren [Visually perceived figures—studies in psychological analysis].Studien in Psychologischer Analyse. I. Copenhagen: Glydendal.Google Scholar
  82. Salton, G., Yang, C. S., & Yu, C. T. (1975). A vector space model for automatic indexing.Communications of the Association for Computing Machinery, 18, 613–620.Google Scholar
  83. Sattath, S., & Tversky, A. (1977). Additive similarity trees.Psychometrika, 42, 319–345.Google Scholar
  84. Shepard, R. N. (1962). The analysis of proximities: Multidimensional scaling with an unknown distance function.Psychometrika, 27, 125–140.Google Scholar
  85. Shepard, R. N., Romney, A. K., & Nerlove, S. B. (Eds.). (1972).Multidimensional scaling: Theory and applications in the social sciences. New York: Seminar Press.Google Scholar
  86. Simpson, G. G. (1961).Principles of animal taxonomy. New York: Columbia University Press.Google Scholar
  87. Sneath, P. H. A., & Sokal, R. R. (1973).Numerical taxonomy. San Francisco: W. H. Freeman.Google Scholar
  88. Sokal, R. R. (1961). Distance as a measure of taxonomic similarity.Systematic Zoology, 10, 70–79.Google Scholar
  89. Sokal, R. R., & Sneath, P. H. A. (1963).Principles of numerical taxonomy. San Francisco: W. H. Freeman.Google Scholar
  90. Solomon, R. L., & Howes, D. H. (1951). Word frequency, personal values and visual duration thresholds.Psychological Review, 58, 256–270.Google Scholar
  91. Sternberg, S. (1969). Memory scanning: Mental processes revealed by reaction time experiments.American Scientist, 57, 421–457.Google Scholar
  92. Suppes, P., & Zinnes, J. L. (1963). Basic measurement theory. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.),Handbook of mathematical psychology (Vol. I). New York: Wiley.Google Scholar
  93. Sutcliffe, J. P. (1972). An application of a pattern recognition scheme based on differential concept formation to the problems of perceptual organization and shape. In J. F. O'Callaghan (Ed.),Pictorial organization and shape. Canberra: CSIRO Division of Computing Research.Google Scholar
  94. Sutcliffe, J. P. (1973, June). Differential ordering of objects and attributes. Paper presented at the meeting of the Psychometric Society Chicago, IL.Google Scholar
  95. Sutcliffe, J. P. (1985).SYDNEY: A computer program for the simulation of recognition and search processes. FORTRAN V Listing and User Manual. Sydney: University of Sydney Computing Centre.Google Scholar
  96. Sutcliffe, J. P., & Bristow, R. A. (1966). Do rank order and scale properties remain invariant under changes in the set of scaled stimuli.Australian Journal of Psychology, 18, 26–40.Google Scholar
  97. Talkington, L. (1967). A method of scaling for a mixed set of discrete and continuous variables.Systematic Zoology, 16, 149–152.Google Scholar
  98. Thurstone, L. L. (1947).Multiple factor analysis. Chicago: University of Chicago Press.Google Scholar
  99. Tippett, L. H. C. (1925). On the extreme individuals and the range of samples taken from a normal population.Biometrika, 17, 364–387.Google Scholar
  100. Torgerson, W. S. (1958).Theory and methods of scaling. New York: Wiley.Google Scholar
  101. Torgerson, W. S. (1965). Multidimensional scaling of similarity.Psychometrika, 30, 379–393.Google Scholar
  102. Tversky, A. (1977). Features of similarity.Psychological Review, 84, 327–352.Google Scholar
  103. Tversky, A., & Krantz, D. H. (1970). The dimensional representation and the metric structure of similarity data.Journal of Mathematical Psychology, 7, 572–596.Google Scholar
  104. Underwood, B. J. (1953). Studies of distributed practice. VIII. Learning and retention of paired nonsense syllables as a function of intra-list similarity.Journal of Experimental Psychology, 45, 133–142.Google Scholar
  105. Underwood, B. J. (1972). Word recognition memory and frequency information.Journal of Experimental Psychology, 94, 276–283.Google Scholar

Copyright information

© The Psychometric Society 1986

Authors and Affiliations

  • J. P. Sutcliffe
    • 1
  1. 1.Department of PsychologyUniversity of SydneySydneyAustralia

Personalised recommendations