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Fuzzy Optimization and Decision Making

, Volume 12, Issue 4, pp 415–432 | Cite as

On the convergence of some possibilistic clustering algorithms

  • Jian Zhou
  • Longbing Cao
  • Nan YangEmail author
Article

Abstract

In this paper, an analysis of the convergence performance is conducted for a class of possibilistic clustering algorithms (PCAs) utilizing the Zangwill convergence theorem. It is shown that under certain conditions the iterative sequence generated by a PCA converges, at least along a subsequence, to either a local minimizer or a saddle point of the objective function of the algorithm. The convergence performance of more general PCAs is also discussed.

Keywords

Fuzzy clustering Possibilistic clustering Convergence 

Notes

Acknowledgments

This work was supported in part by the Shanghai Philosophy and Social Science Planning Project grant (2012BGL006), Australian Research Council Discovery Grants (DP1096218 and DP130102691) and Linkage Grants (LP100200774 and LP120100566).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of ManagementShanghai UniversityShanghaiChina
  2. 2.Faculty of Engineering and Information TechnologyUniversity of TechnologySydneyAustralia
  3. 3.School of Statistics and ManagementShanghai University of Finance and EconomicsShanghaiChina

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