S8 illustrates some of the difficulties inherent with cluster analysis; its aim is to alert investigators to the fact that various algorithms can suggest radically different substructures in the same data set. The balance of Chapter 3 concerns objective functional methods based on fuzzy c-partitions of finite data. The nucleus for all these methods is optimization of nonlinear objectives involving the weights u ik ; functionals using these weights will be differentiable over M fc —but not over M c —a decided advantage for the fuzzy embedding of hard c-partition space. Classical first- and second-order conditions yield iterative algorithms for finding the optimal fuzzy c-partitions defined by various clustering criteria.


Feature Selection Hiatal Hernia Cluster Center Fuzzy Cluster Cluster Criterion 


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Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • James C. Bezdek
    • 1
  1. 1.Utah State UniversityLoganUSA

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