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Spatial processes and Galois/concept lattices

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  • John Martin

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    Abstract

    There is a fair amount of interest in the use of Galois or Concept Lattices in the social sciences as a way of representing complex data structures; it does not seem to be widely appreciated that these structures are homologous to those arising from a discrete noncompensatory multidimensional response process, as originally outlined by Coombs. Here I formalize the spatial intuition underlying Coombs’s proposal, and show how, for any set of data, we may recreate the set of all possible minimal spatial representations. Copyright Springer Science+Business Media Dordrecht 2014

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    File URL: http://hdl.handle.net/10.1007/s11135-012-9818-9
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    Bibliographic Info

    Article provided by Springer in its journal Quality & Quantity.

    Volume (Year): 48 (2014)
    Issue (Month): 2 (March)
    Pages: 961-981

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    Handle: RePEc:spr:qualqt:v:48:y:2014:i:2:p:961-981

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    Web page: http://www.springer.com/economics/journal/11135

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    Related research

    Keywords: Galois lattices; Concept lattices; Coombs; Noncompensatory factor analysis;

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    1. Doignon, Jean-Paul & Falmagne, Jean-Claude, 1984. "Matching relations and the dimensional structure of social choices," Mathematical Social Sciences, Elsevier, vol. 7(3), pages 211-229, June.
    2. Michael Greenacre, 1988. "Clustering the rows and columns of a contingency table," Journal of Classification, Springer, vol. 5(1), pages 39-51, March.
    3. Susan Whitely, 1980. "Multicomponent latent trait models for ability tests," Psychometrika, Springer, vol. 45(4), pages 479-494, December.
    4. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
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