On the local optimality of the fuzzy isodata clustering algorithm

S Z Selim; M A Ismail

doi:10.1109/tpami.1986.4767783

On the local optimality of the fuzzy isodata clustering algorithm

IEEE Trans Pattern Anal Mach Intell. 1986 Feb;8(2):284-8. doi: 10.1109/tpami.1986.4767783.

Authors

S Z Selim¹, M A Ismail

Affiliation

¹ Department of Systems Engineering, University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.

PMID: 21869348
DOI: 10.1109/tpami.1986.4767783

Abstract

The convergence of the fuzzy ISODATA clustering algorithm was proved by Bezdek [3]. Two sets of conditions were derived and it was conjectured that they are necessary and sufficient for a local minimum point. In this paper, we address this conjecture and explore the properties of the underlying optimization problem. The notions of reduced objective function and improving and feasible directions are used to examine this conjecture. Finally, based on the derived properties of the problem, a new stopping criterion for the fuzzy ISODATA algorithm is proposed.