Optimality tests for the fuzzy c-means algorithm

摘要

Because of lack of convexity of the fuzzy c-means (FCM) objective functionals, the FCM algorithm may converge to a local minimizer or a saddle point. In this paper, we present a new scheme for testing the optimality of the fixed points of the FCM algorithm, one which needs much less computation than Kim et al.'s scheme (Pattern Recognition21, 651–663, 1988). We also point out that Kim et al.'s scheme is partly incorrect, and propose a repair of it. Numerical experiments are presented for several sets of data; they compare Kim et al.'s scheme, the repaired scheme, and our scheme.