OPTIMALITY TESTS FOR THE FUZZY C-MENAS ALGORITHM

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 Recognition 21, 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.