Fuzziness parameter selection in fuzzy c-means: The perspective of cluster validation

Fuzzy c-means (FCM) algorithm is an important clustering method in pattern recognition, while the fuzziness parameter, m, in FCM algorithm is a key parameter that can significantly affect the result of clustering. Cluster validity index (CVI) is a kind of criterion function to validate the clustering results, thereby determining the optimal cluster number of a data set. From the perspective of cluster validation, we propose a novel method to select the optimal value of m in FCM, and four well-known CVIs, namely XB, VK, VT, and SC, for fuzzy clustering are used. In this method, the optimal value of m is determined when CVIs reach their minimum values. Experimental results on four synthetic data sets and four real data sets have demonstrated that the range of m is [2, 3.5] and the optimal interval is [2.5, 3].