Bias-correction fuzzy clustering algorithms

Keywords: Cluster analysis Fuzzy clustering Fuzzy c-means (FCM) Initialization Bias correction Probability weight a b s t r a c t Fuzzy clustering is generally an extension of hard clustering and it is based on fuzzy membership partitions. In fuzzy clustering, the fuzzy c-means (FCM) algorithm is the most commonly used clustering method. Numerous studies have presented various generalizations of the FCM algorithm. However, the FCM algorithm and its generalizations are usually affected by initializations. In this paper, we propose a bias-correction term with an updating equation to adjust the effects of initializations on fuzzy clustering algorithms. We first propose the so-called bias-correction fuzzy clustering of the generalized FCM algorithm. We then construct the bias-correction FCM, bias-correction Gustafson and Kessel clustering and bias-correction inter-cluster separation algorithms. We compared the proposed bias-correction fuzzy clustering algorithms with other fuzzy clustering algorithms by using numerical examples. We also applied the bias-correction fuzzy clustering algorithms to real data sets. The results indicated the superiority and effectiveness of the proposed bias-correction fuzzy clustering methods. Clustering is a method for determining the cluster structure of a data set such that objects within the same cluster demonstrate maximum similarity and objects within different clusters demonstrate maximum dissimilarity. Numerous clustering theories and methods have been evaluated in the literature (see Jain and Dubes [10] and Kaufman and Rousseeuw [11]). In general, the most well-known approaches are partitional clustering methods based on an objective function of similarity or dissimilarity measures. In partitional clustering methods, the k-means (see MacQueen [14] and Pollard [20]), fuzzy c-means (FCM) (see Bezdek [2] and Yang [23]), and possibilistic c-means (PCM) algorithms (see Krishnapuram and Keller [12], Honda et al. [8], and Yang and Lai [24]) are the most commonly used approaches. Fuzzy clustering has received considerable attention in the clustering literature. In fuzzy clustering, the FCM algorithm is the most well-known clustering algorithm. Previous studies have proposed numerous extensions of FCM clustering (see Gath Regarding the generalization of FCM clustering, Yu and Yang [26] proposed a generalized FCM (GFCM) model to unify numerous variations of FCM. However, initializations affect FCM clustering and its generalizations. In this paper, we evaluated a bias-correction approach by using an updating equation to adjust the effects of initial values and then propose the bias-correction fuzzy clustering methods.