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An Agglomerative Method for Two-Mode Hierarchical Clustering

  • Thomas Eckes
  • Peter Orlik
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

A new agglomerative method is proposed for the simultaneous hierarchical clustering of row and column elements of a two-mode data matrix. The procedure yields a nested sequence of partitions of the union of two sets of entities (modes). A two-mode cluster (bi-cluster) is defined as the union of subsets of the respective modes. At each step of the agglomerative process, the algorithm merges two bi-clusters whose fusion results in the minimum increase in an internal heterogeneity measure. This measure takes into account both the variance within a bi-cluster and its elevation defined as the squared deviation of its mean from the maximum entry in the original matrix. Two applications concerning brand-switching data and gender subtype-situation matching data are discussed.

Keywords

Tree Representation Column Element Female Type Agglomerative Process Proximity Data 
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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Bibliography

  1. Bass, F.M., Pessemier, E.A. & Lehmann, D.R. (1972): An experimental study of relationships between attitudes, brand preference, ans choice. Behavioral Science, 17, 532–541.CrossRefGoogle Scholar
  2. Both, M. & Gaul, W. (1986): Ein Vergleich zweimodaler Clusteranalyseverfahren. Methods of Operations Research, 57, 593–605.Google Scholar
  3. Carroll, J.D. & Arabie, P. (1980): Multidimensional scaling. Annual Review of Psychology, 31, 607–649.CrossRefGoogle Scholar
  4. Desarbo, W.S. (1982): Gennclus: New models for general nonhierarchical clustering analysis. Psychometrika, 47, 449–475.zbMATHMathSciNetGoogle Scholar
  5. Desarbo, W.S. & De Soete, G. (1984): On the use of hierarchical clustering for the analysis of nonsymmetric proximities. Journal of Consumer Research, 11, 601–610.CrossRefGoogle Scholar
  6. De Soete, G. (1988): Tree representations of proximity data by least squares methods. In: H.H. BOCK (Ed.): Classification and related methods of data analysis (pp. 147-156). Amsterdam: North-Holland.Google Scholar
  7. De Soete, G., Desarbo, W.S., Furnas, G.W. & Carroll, J.D. (1984): The estimation of ultrametric and path lenght trees from rectangular proximity data. Psychometrika, 49, 289–310.Google Scholar
  8. Eckes, T. (1990): Strukturen der alltagssprachlichen Kategorisierung von Personen, Situationen und Person-Situations-Kombinationen. DFG-Abschlußbericht, Universität des Saarlandes, Saarbrücken.Google Scholar
  9. Espejo, E. & Gaul, W. (1986): Two-mode hierarchical clustering as an instrument for marketing research. In: W. GAUL & M. SCHADER (Eds.): Classification as a tool of research (pp. 121-128). Amsterdam: North-Holland.Google Scholar
  10. Furnas, G.W. (1980): Objects and their features: The metric representation of two-class data. Unpublished Doctoral Dissertation, Stanford-University.Google Scholar
  11. Hartigan, J.A. (1975): Clustering algorithms. New York: Wiley.zbMATHGoogle Scholar
  12. Hartigan, J.A. (1976): Modal blocks in definition of west coast mammals. Systematic Zoology, 25, 149–160.Google Scholar
  13. Mccormick, W.T., Schweitzer, P.J. & White, T.W. (1972): Problem decomposition and data reorganization by a clustering technique. Operations Research, 20, 993–1009.CrossRefzbMATHGoogle Scholar
  14. Milligan, G.W. & Cooper, M.C. (1985): An examination of procedures for determining the number of clusters in a data set. Psychometrika, 50, 159–179.Google Scholar
  15. Pruzansky, S., Tversky, A. & Carroll, J.D. (1982): Spatial versus tree representations of proximity data. Psychometrika, 47, 3–24.zbMATHGoogle Scholar
  16. Shepard, R.N. & Arabie, P. (1979): Additive clustering: Representation of similarities as combinations of discrete overlapping porperties. Psychological Review, 86, 87–123.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1991

Authors and Affiliations

  • Thomas Eckes
    • 1
  • Peter Orlik
    • 1
  1. 1.Fachrichtung PsychologieUniversität des SaarlandesSaarbrückenGermany

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