Issue No. 02 - February (1986 vol. 8)
Shokri Z. Selim , Department of Systems Engineering, University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
M. A. Ismail , School of Computer Science, University of Windsor, Windsor, Ont., Canada N9B 3P4.
The convergence of the fuzzy ISODATA clustering algorithm was proved by Bezdek . 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.
M. A. Ismail and S. Z. Selim, "On the Local Optimality of the Fuzzy Isodata Clustering Algorithm," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 8, no. , pp. 284-288, 1986.