On the 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 J m , 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∈ [1.5, 3.5], the optimal m * monotone increase linearly against the separability ρ of data set. So in practical applications, one can choose the value of m within the range of [1.5, 3.5].