Classification Structures for Cognitive Maps

  • Stephen C. Hirtle
  • Guoray Cai
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


The ability to create and manipulate meaningful data structures of cognitive spaces remains a problem for designers of geographic information systems. Methods to represent the inherent hierarchical structure in cognitive spaces are discussed. Several alternative scaling techniques for developing hierarchical and overlapping representations, including ordered trees, ultrametric trees, and semi-lattices, are presented and discussed. To demonstrate the differences among these three representation schemes, each of three techniques is applied to two small datasets collected on the recall of capitals or countries in Europe. The methods discussed here were chosen to illustrate the limitations of a strict, hierarchical representation and because they have been used in the past to model cognitive spaces.


Geographic Information System Hierarchical Tree Hierarchical Representation Representational Structure Ultrametric Tree 
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.


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  1. Aho, A. V., et al. (1974): The design and analysis of computer programs, Addison-Wesley, Reading, MA.Google Scholar
  2. Alexander (1965): A city is not a tree, Design, 46–55.Google Scholar
  3. Barthelemy, J. P., et al. (1986): On the use of ordered sets in problems and consensus of classification, Journal of Classification, 3, 187–224.MathSciNetMATHCrossRefGoogle Scholar
  4. Carroll, J. D. and Corter, J. E. (1995): A graph-theoretic method for organizing overlap- ping clusters into trees, multiple trees, or extended trees, Journal of Classification,in press.Google Scholar
  5. Carroll, J. D. and Pruzansky, S. (1980): Discrete and hybrid scaling models. In: Si7nilarity and Choice, Lantermann, E. D. and Feger, H.. (eds.), Hans Huber, Bern.Google Scholar
  6. Couclelis, H., et al. (1987): Exploring the anchor-point hypothesis of spatial cognition, Journal of Environmental Psychology, 7, 99–122.CrossRefGoogle Scholar
  7. Diday, E. (1986): Orders and overlapping clusters in pyramids, In: Multidimensional data analysis de Leeuw, J., et al. (eds.), 201–234, DSWO Press, Leiden.Google Scholar
  8. Golledge, R. G. (1992): Place recognition and wayfinding: Making sense of space, Geoforum, 23, 199–214.CrossRefGoogle Scholar
  9. Hirtle, S. C. (1991): Knowledge representations of spatial relations. In: Mathematical psychology: Current developments, Doignon, J.-P. and Falmagne, J.-C. (eds.), 233–250, Springer-Verlag, New York.CrossRefGoogle Scholar
  10. Hirtle, S. C. (1995) Representational structures for cognitive space: Trees, ordered trees, and semi-lattices, In: Spatial information theory: A theoretical basis for GIS, Frank, A. V. and Kuhn, W. (eds.), Springer- Verlag, Berlin.Google Scholar
  11. Hirtle, S. C. and Heidorn, P. B. (1993): The structure of cognitive maps: Representations and processes. In:, Behavior and environment: Psychological and geographical approaches, Garling, T. and Golledge, R. G. (eds.), 170–192, North-Holland, Amsterdam.CrossRefGoogle Scholar
  12. Hirtle, S. C. and Jonides, J. (1985): Evidence of hierarchies in cognitive maps, Memory and Cognition, 3, 208–217.Google Scholar
  13. Kim, H., and Hirtle, S. C. (1995). Spatial metaphors and disorientation in hypertext browsing. Behaviour and Information Technology, 14, 239–250.CrossRefGoogle Scholar
  14. McNamara, T. P., et al. (1989): Subjective hierarchies in spatial memory, Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 211–227.Google Scholar
  15. Medyckyj-Scott, D. J. and Blades, M. (1992): Human spatial cognition, Geoforum, 2, 215226.Google Scholar
  16. Reitman, J. S. and Rueter, H. R. (1980): Organization revealed by recall orders and confirmed by pauses, Cognitive Psychology, 12, 554–581.CrossRefGoogle Scholar
  17. Sattath, S. and Tversky, A. (1977): Additive similarity trees. Psychometrika, 42, 319–345.CrossRefGoogle Scholar
  18. Shepard, R. N. and Arabie, P. (1979): Additive clustering: Representation of similarities as combinations of discrete overlapping properties, Psychological Review, 86, 87–123.CrossRefGoogle Scholar
  19. Stevens, A. and Coupe, P. (1978): Distortions in judged spatial relations, Cognitive Psychology, 10, 422–437.CrossRefGoogle Scholar
  20. Van Cutsem, B. (Ed.) (1994): Classification and dissimilarity analysis, Lecture Notes in Statistics, No. 93, Springer-Verlag, New York.CrossRefGoogle Scholar

Copyright information

© Springer Japan 1998

Authors and Affiliations

  • Stephen C. Hirtle
    • 1
  • Guoray Cai
    • 1
  1. 1.School of Information SciencesUniversity of PittsburghPittsburghUSA

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