Fuzzy c-varieties/elliptotypes clustering in reproducing kernel Hilbert space

Fuzzy clustering algorithms are successfully applied to a wide variety of problems, such as: pattern recognition, image analysis, modeling and so on. The Fuzzy C-Means (FCM) method is one of the most popular clustering methods based on the minimization of a criterion function. However, the performance of the FCM method is good only when a data set contains clusters that are approximately the same size and shape. In this paper, a simple idea will be used, to overcome this problem. The original input (data) space will be mapped into the high (possibly infinite)-dimensional feature space F through some nonlinear mapping. In this space the data structures will be modeled by the linear varieties or elliptotypes. This method is called Kernel Fuzzy C-Varieties /Elliptotypes clustering algorithm. Performance of the new clustering algorithm is experimentally compared with FCM and fuzzy c-varieties /elliptotypes methods using synthetic datasets and real-life datasets.