Two principles for partitioning a set into groups are revisited in the paper. In addition to the well-known cluster analysis principle, two other set partition, principles are considered: the similarity principle and the anticluster principle. In similarity principle the initial set is partitioned into groups, so that each group possesses property similar to the property of the initial set. In anticluster principle, the initial set is partitioned into groups in such a way, that elements belonging to each group are dissimilar but the groups are similar. If a criterial function for quality of partitioning is defined on the set of all possible partitions, then the set partitioning problem is to construct such a partition, for which the criterial function is extremal. Optimization procedures are suggested for both partitioning principles.

Key words

Set Partition Principles Cluster Analysis Principle Similarity Principle Anticluster Principle Discrete Optimization Procedures 


  1. [1]
    Duran, B., Odell, P.: Cluster analysis: A survey. New York: Springer-Verlag, (1974)Google Scholar
  2. [2]
    Valev, V.: Set partition principles. Transactions of the Ninth Prague Conference on Information Theory, Statistical Decision Functions, and Random Processes. Ninth Prague Conference on Information Theory, Statistical Decision Functions, and Random Processes, Prague, 1982, Publishing House of the Czechoslovak Academy of Sciences: Academia, Prague (1983) 251–256Google Scholar
  3. [3]
    Späth, H.: Anticlustering: Maximizing the variance criterion. Control and Cybernetics. 15 (1986) 213–218Google Scholar
  4. [4]
    Späth, H.: Homogeneous and heterogeneous clusters for distance matrices. In: Classification and related methods of data analysis. Bock, H.H. (Editor) North Holland (1986) 157–164Google Scholar
  5. [5]
    Arabie, P., Hubert, L.J.: An overview of combinatorial data analysis. In: Clustering and classification. P.Arabie, P., Hubert, L.J., De Soete, G. (Editors) World Scientific (1996) 5–63Google Scholar
  6. [6]
    Zagoruiko, N.G., Zaslavskaja, T.I.: Pattern Recognition Methods in Sociological Research. In: Quantitative sociology. Blalok, H.M. at al. (Editors), Academic Press (1975) 429–440Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Ventzeslav Valev
    • 1
  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

Personalised recommendations