基于核的模糊c均值聚类算法的收敛性定理

摘要

利用Zangwill收敛性定理,证明了基于核的模糊c均值聚类算法(KFCM)的收敛性.结果表明,当核函数在给定数据集上诱导的距离矩阵满足一定条件时,KFCM算法产生的迭代序列收敛或至少存在一个子序列收敛于KFCM聚类模型目标函数的局部极小值点或鞍点.%The convergence of the kernel based fuzzy c-means clustering algorithm ( KFCM ) was established by applying the Zangwill' s convergence theorem. The result shows that when the distance matrix induced by kernel function satisfies the given conditions, the iteration sequence produced by the KFCM algorithm terminates at a local minimum or a saddle point, or at worst, contains a subsequence which terminates at a local minimum or saddle point of the objective function of the KFCM clustering model.