Department of Systems Engineering, University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
IEEE Trans Pattern Anal Mach Intell. 1986 Feb;8(2):284-8. doi: 10.1109/tpami.1986.4767783.
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.
贝兹德克[3]证明了模糊 ISODATA 聚类算法的收敛性。他推导出了两组条件，并推测这些条件是局部极小点的充分必要条件。本文针对这一猜想展开讨论，并研究了基础优化问题的性质。文中使用简化目标函数、改进和可行方向的概念来检验这一猜想。最后，基于所推导的问题性质，提出了一种新的模糊 ISODATA 算法停止准则。
