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What Clusters Are Generated by Normal Mixtures?

  • Christian Hennig
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Model based cluster analysis is often carried out by estimation of the parameters of a normal mixture. But mixture components do not necessarily reflect the idea of a “cluster”. I discuss how to formalize the concept of “clusters” w.r.t. probability distributions on the real line by means of fixed point clusters, i.e., sets that do not contain any outlier and with respect to which the rest of the real line consists of outliers. The concept is applied to some normal mixtures

Keywords

Real Line Outlier Region Mixture Component Reference Distribution Normal Mixture 
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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References

  1. BOCK, H.H.(1996): Probability Models and Hypotheses Testing in Partitioning Cluster Analysis. In: P. Arabie, L. J. Hubert, G. De Soete (Eds.): Clustering and Classification. World Scientific Publishers, New Jersey, 377–453Google Scholar
  2. DAVIES, P.L. and GATHER, U.(1993): The identification of multiple outliers. Journal of the American Statistical Association, 88, 782–801CrossRefGoogle Scholar
  3. HENNIG, C.(1998): Clustering and Outlier Identification: Fixed Point Cluster Analysis. In: A. Rizzi, M. Vichi, H.-H. Bock (Eds.): Advances in Data Science and Classification. Springer, Berlin, 37–42Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2000

Authors and Affiliations

  • Christian Hennig
    • 1
  1. 1.Institut für Mathematische StochastikHamburgGermany

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