Fuzzy Robust Clustering and C Spherical Shells Algorithms

Abstract

Clustering algorithms play an important role in the field of pattern recognition. Most of the traditional clustering algorithms are hard clustering. Some algorithms based on fuzzy set theorem have been proposed recently. Some algorithms based on the fuzzy clustering theory have been proposed recently. They modify not only the winner but also other prototypes for each input. Many fuzzy clustering algorithms including GLVQ-F use the membership from fuzzy c-means (FCM). Since the objective function in FCM is constrained by a probability premise, the total sum of the membership shared by all classes for an input data must be one. If the number of classes is large, the fuzzy membership may be minute. It has been shown that if the number of classes is large, the traditional clustering algorithms may be better than the fuzzy ones. Moreover, the outliers that may appear are not considered in FCM. We propose a new family of clustering algorithms called fuzzy robust clustering (FRC) without the above disadvantages. The size of updating prototype is independent of the number of prototypes and the influence of outliers is reduced. We modify the objective function and propose a robust algorithm for the extraction of spherical shells. Artificially generated data are used to test FRC.