A generalized c-means clustering model using optimized via evolutionary computation

Abstract

Although all three conventional c-means clustering algorithms, namely hard c-means (HCM), fuzzy c-means (FCM), and possibilistic c-means (PCM), had their merits in the development of clustering theory, none of them are generally good solutions for unsupervised classification. Several hybrid solutions have been proposed to produce mixture algorithms. Possibilistic-fuzzy hybrids generally attempt to get rid of the FCM's sensitivity to outliers and PCM's coincident cluster prototypes, while hard-fuzzy mixtures usually aim at quicker convergence while preserving FCM's accurate partitions. This paper presents a unifying approach to c-means clustering: the novel clustering model is considered as a linear combination of the FCM, PCM, and HCM objective functions. The optimal solution is obtained via evolutionary computation. Our main goal is to reveal the properties of such mixtures and to formulate some rules that yield accurate partitions.