Journal of Classification

, Volume 4, Issue 2, pp 227–242 | Cite as

On the classification of recall strings using lattice-theoretic measures

  • Stephen C. Hirtle
Authors Of Articles

Abstract

Lattice theory is used to develop techniques for classifying groups of subjects on the basis of their recall strategies or multiple recall strategies within individual subjects. Using the ordered tree algorithm to represent sets of recall orders, it is shown how both trees and single recall strings can be represented as points within a nonsemimodular, graded lattice. Distances within the lattice structure are used to construct a dissimilarity measure,S, which can then be used to partition the individual recall strings. The measureS between strings is compared to Kendall's tau in three empirical tests, examining differences between individual subjects, differences between groups of subjects, and differences within a subject. It was shown that onlyS could recover the original differences. Differences between comparing chunks versus comparing orders are discussed.

Keywords

Lattice theory Memory Cluster analysis 

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References

  1. BARTHELEMY, J. P., LECLERC, B., and MONJARDET, B. (1986), “On the Use of Ordered Sets in Problems of Comparison and Consensus in Classification,”Journal of Classification, 3, 187–224.Google Scholar
  2. BIRKHOFF, G. (1967),Lattice Theory (3rd edition), Providence, RI: American Mathematical Society.Google Scholar
  3. BOOTH, K. S., and LUEKER, G. S. (1976), “Testing for the Connective Ones Property, Interval Graphs, and Graph Planarity Using PQ-tree Algorithms,”Journal of Computer and System Sciences, 13, 335–379.Google Scholar
  4. BROADBENT, D. E., COOPER, P. J., and BROADBENT, M. H. P. (1978), “A Comparison of Hierarchical and Matrix Retrieval Schemes in Recall,”Journal of Experimental Psychology: Human Learning and Memory, 4, 486–497.Google Scholar
  5. CUNNINGHAM, J.P. (1980), “Trees as Memory Representations for Simple Visual Patterns,”Memory and Cognition, 8, 593–605.Google Scholar
  6. DERSHOWITZ, N., and ZAKS, S. (1980), “Enumeration of Ordered Trees,”Discrete Mathematics, 31, 9–28.Google Scholar
  7. GORDON, A. D. (1979), “A Measure of the Agreement Between Rankings,”Biometrika, 66, 7–15.Google Scholar
  8. HAYS, W. L., and WINKLER, R. L. (1971),Statistics: Probability, Inference, and Decision. New York: Holt, Rinehart, & Winston.Google Scholar
  9. HIRTLE, S. C. (1982), “Lattice-based Similarity Measures Between Ordered Trees,”Journal of Mathematical Psychology, 25, 206–223.Google Scholar
  10. HIRTLE, S. C., and JONIDES, J. (1985), “Evidence of Hierarchics in Cognitive Maps,”Memory and Cognition, 13, 208–217.Google Scholar
  11. KENDALL, M. G. (1955),Rank Correlation Methods, 2nd Ed., London: Charles Griffin.Google Scholar
  12. KNUTH, D. E. (1968),The Art of Computer Programming, Vol. 1: Fundamental Algorithms, Reading, MA: Addison-Wesley.Google Scholar
  13. MCKEITHEN, K. B., REITMAN, J.S., RUETER, H. R., and HIRTLE, S.C. (1981), “Knowledge Organization and Skill Differences in Computer Programmers,”Cognitive Psychology, 13, 307–325.CrossRefGoogle Scholar
  14. MONJARDET, B. (1985), “Concordance et consensus d'ordres totaux: Les coefficients K et W,”Revue de Statistique Appliquée, 33, 55–87.Google Scholar
  15. REITMAN, J. S., and RUETER, H. R. (1980), “Organization Revealed by Recall Orders and Confirmed by Pauses,”Cognitive Psychology, 12, 554–581.Google Scholar
  16. RUETER, H.R. (1985), “Identifying Memory Structure from Free Recall,”, Unpublished doctoral dissertation, University of Michigan, Ann Arbor.Google Scholar
  17. 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

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Stephen C. Hirtle
    • 1
  1. 1.Department of Information ScienceUniversity of PittsburghPittsburghUSA

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