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Classification of Binary Vectors by Stochastic Complexity

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  • Gyllenberg, Mats
  • Koski, Timo
  • Verlaan, Martin
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    Abstract

    Stochastic complexity is treated as a tool of classification, i.e., of inferring the number of classes, the class descriptions, and the class memberships for a given data set of binary vectors. The stochastic complexity is evaluated with respect to the family of statistical models defined by finite mixtures of multivariate Bernoulli distributions obtained by the principle of maximum entropy. It is shown that stochastic complexity is asymptotically related to the classification maximum likelihood estimate. The formulae for stochastic complexity have an interpretation as minimum code lengths for certain universal source codes for storing the binary data vectors and their assignments into the classes in a classification. There is also a decomposition of the classification uncertainty in a sum of an intraclass uncertainty, an interclass uncertainty, and a special parsimony term. It is shown that minimizing the stochastic complexity amounts to maximizing the information content of the classification. An algorithm of alternating minimization of stochastic complexity is given. We discuss the relation of the method to the AUTOCLASS system of Bayesian classification. The application of classification by stochastic complexity to an extensive data base of strains ofEnterobacteriaceaeis described.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 63 (1997)
    Issue (Month): 1 (October)
    Pages: 47-72

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    Handle: RePEc:eee:jmvana:v:63:y:1997:i:1:p:47-72

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    Related research

    Keywords: bacterial identification classification maximum likelihood estimate information content maximal predictive classification mixture of multivariate Bernouli distributions principle of maximum entropy universal source codes AUTOCLASS;

    References

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    1. Michael Windham, 1987. "Parameter modification for clustering criteria," Journal of Classification, Springer, vol. 4(2), pages 191-214, September.
    2. Gilles Celeux & GĂ©rard Govaert, 1991. "Clustering criteria for discrete data and latent class models," Journal of Classification, Springer, vol. 8(2), pages 157-176, December.
    3. Mats Gyllenberg & Timo Koski, 1996. "Numerical taxonomy and the principle of maximum entropy," Journal of Classification, Springer, vol. 13(2), pages 213-229, September.
    4. Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer, vol. 50(2), pages 159-179, June.
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    Cited by:
    1. Bouguila, Nizar, 2010. "On multivariate binary data clustering and feature weighting," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 120-134, January.
    2. Jukka Corander & Mats Gyllenberg & Timo Koski, 2009. "Bayesian unsupervised classification framework based on stochastic partitions of data and a parallel search strategy," Advances in Data Analysis and Classification, Springer, vol. 3(1), pages 3-24, June.

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