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Abstract

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 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

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

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