A Noise-Resistant Fuzzy C Means Algorithm for Clustering - Fuzzy Systems Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE

Probabilistic clustering techniques use the concept of memberships to describe the degree by which a vector belongs to a cluster. The use of memberships provides probabilistic methods with more realistic clustering than “hard” techniques. However, fuzzy schemes (like the Fuzzy c Means algorithm, FCW are open sensitive to outliers. We review four existing algorithms, devised to reduce this sensitivity. These are: the noise cluster (NC) algorithm of Dave, the Possibilistic c Means (PCW scheme of KelIer and Krishnapuram, the Least Biased Fuzzy Clustering (LBFC) method of Beni and Liu, and the Fuzzy Possibilistic c Means algorithm of Pal et al. We then propose the new Credibilistic Fuzzy c Means (CFCM) algorithm to improve on these methods. It uses a new variable, credibility of a vector, which measures the typicality of the vector to the whole data set. By taking credibility into account, CFCMgenerates centroid which are less sensitive to outliers than other techniques, and closer to the centroidr generated when the outliers are artificially removed. 1. Existing “Robust” Clustering Techniques Clustering algorithms [l] partition a data set such as X = { X I , xZ,.. $,, I V i }, to reveal the underlying structure of X. The developing of clustering techniques is a mature art, and there exist families of “hard,” “fuzzy” and “possibilistic” algorithms, yielding different set partitions and drawing on different principles and objective functions. “Hard” or “crisp” models unequivocally assign each vector in the data set X into one of c subsets, where c is a natural number. Fuzzy and possibilistic clustering algorithms generate a membership matrix U, whose elements assume values in [O,l]. If uIk = a, we say that the membership of xk in cluster i is a. In this paper we denote the data set as X , its n vectors as (x,}:=, where xi E !Rp V i and the cluster centers (centroids) vi E CJip b’i=l,. . . ,c. We collect the centroids In the matrix V=[VI, VZ, ..., vJT The Fuzzy c Means Algorithm (FCM) [2] is the most popular fuzzy clustering algorithm. It assumes that the number of clusters c, is known apriori, and minimizes