On the Fuzziness Index of the FCM Algorithms

The fuzzy c-means algorithm (FCM) is a widely used clustering algorithm. It is well known that the fuzziness index m has a significant impact on the performance of the FCM. However, it is an open problem how to select an appropriate fuzziness index m in theory when implementing the FCM. In this paper, we point out that each subset is often expected to have a different prototype (or cluster center) than others when the data set is clustered into c (c1) subsets in general cases. But the FCM has a trivial solution--the mass center of the data set. According to the above assumption, the mass center of the data set is not expected to be stable. We get a simpler criterion to judge whether the trivial solution of the FCM is stable or not. As such criterion is related to the fuzziness index m,we also prove that the optimal choice of the fuzziness index m depends on the data set itself. Therefore, a theoretical approach to choose the appropriate fuzziness index m is obtained. Finally, we carry out numerical experiments in order to verify if our method is effective or not.The experimental results show that these rules are effective.