Weighting exponent m in fuzzy C-means (FCM) clustering algorithm

The weighting exponent m is an important parameter in fuzzy c-means (FCM) algorithm. In this paper, three basic problems about m in FCM algorithm: clustering validity method based on optimal m (or whether does optimal m exist), how does m effect on the performance of fuzzy clustering, and which is the proper range of m in general applications, are studied with the knee of objective function Jm, and fuzzy decision-making methods. Numerical experimental results show that the optimal m* for specific data set does exist. Moreover, a group of numerical experimental results indicate that, within the range of m (epsilon) (1.5, 3.5), the optimal m* monotone increase linearly against the separability (rho) of data set. So in practical applications, one can choose the value of m within the range of [1.5, 3.5].