Algorithms for L1 and Lp Fuzzy c-Means and Their Convergence

  • Sadaaki Miyamoto
  • Yudi Agusta
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Algorithms for L 1 and L p based fuzzy c-means are proposed. These algorithms calculate cluster centers in the general alternating algorithm of the fuzzy c-means. The algorithm for the L 1 space is based on a simple linear search on nodes of step functions derived from derivatives of components of the objective function for the fuzzy c-means, whereas the algorithm for the L p spaces use binary search on the nodes and then the interval to which the cluster center belong. Termination of the algorithms based on different criteria for the convergence is discussed. The algorithm for the L 1 space is proved to be convergent after a finite number of iterations. A numerical example is shown.


Cluster Center Fuzzy Cluster Binary Search Fuzzy Partition Monotone Nonincreasing 
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Copyright information

© Springer Japan 1998

Authors and Affiliations

  • Sadaaki Miyamoto
    • 1
  • Yudi Agusta
    • 2
  1. 1.Institute of Information SciencesElectronics University of TsukubaIbaraki 305Japan
  2. 2.Development and Documentation Division Central Bureau of StatiticsProgram ResearchIndonesia

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