Abstract:

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, conta
ins a subsequence which terminates at a local minimum or saddle point of the objective function of the KFCM clustering model.

Key words: cluster analysis, fuzzy cmeans, kernel function, convergence