A robust cluster validity index for fuzzy c-means clustering

Fuzzy c-means clustering algorithm (FCM) is one of the mostly used clustering algorithms. Although several cluster validity have been proposed to execute FCM as unsupervised clustering algorithm, the performance of FCM and its validity index is deeply influenced by the noises and outliers. To solve such problem, a robust cluster validity for FCM is proposed in this paper. The proposed index consists of two terms, i.e., compactness and separation measure. The compactness measure is determined by the fuzzy membership matrix and the cluster number, which indicates the compactness within a cluster. The separation measure is defined as the distance of the different fuzzy sets, which indicates the separability of different clusters. The proposed validity is compared with typical cluster validity indices on six data sets, including two real and four artificial data sets. The experimental results show the effectiveness of the proposed index.