A noise-resistant fuzzy c means algorithm for clustering

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, FCM) are often sensitive to outliers. We review four existing algorithms, devised to reduce this sensitivity. These are: the noise cluster (NC) algorithm of Dave (1991), the possibilistic c means (PCM) scheme of Krishnapuram and Keller (1996), the least biased fuzzy clustering (LBFC) method of Beni and Liu (1994), and the fuzzy possibilistic c means algorithm of Pal et al. (1997). 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 CFCM generates centroids which are less sensitive to outliers than other techniques, and closer to the centroids generated when the outliers are artificially removed.