A new efficient fuzzy cluster validity index: Application to images clustering

Finding the appropriate number of clusters in the absence of prior information is a hard and sensitive problem in clustering and data analysis. In this paper, we present a new cluster validity index (CV I) called HF able to find the optimal number of clusters present in a given data. The HF index is based on the membership partition. It can be seen as the generalisation of the Wu-and-Li (WL) and Tang (T) indices. Its particularity is the integration of a generalised ad-hoc punishing term, on the one hand, and the involving of median between centroids multiplied by the average of data per cluster for computing the separation, on the other hand. These contributions allow avoiding the monotony from which suffer the majority of CV Is and obtaining a precise evaluation. The optimal number of clusters C-op corresponds to the minimum of the HF index. In order to ensure the effective choice of the optimal number of clusters, we propose an algorithm based on the HF and WL indices. The performance of the proposed index and algorithm are demonstrated through different experimentations on images clustering using the algorithm Fuzzy-C-Means (FCM). The HF index's ability to appropriately determine the number of clusters is compared with those of WL, T and the Xi-Beni (XB) indices with different initialisations.