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 mode1.

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