Interval Type-2 Approach to Kernel Possibilistic C-Means Clustering

Kernel based fuzzy clustering has been extensively used for pattern sets that have clusters that overlap and clusters of different volume. The kernel approach adds additional degree of freedom by implicitly mapping input patterns into higher dimensional space known as kernel space. Kernel based fuzzy clustering has shown to produce improved results over conventional fuzzy clustering algorithms such as fuzzy C-means (FCM), possibilistic c-means (PCM) and possibilistic fuzzy C-means (PFCM) not only for spherical data sets but also non spherical data sets. However, in the case of kernel possibilistic C-means (KPCM) as well as PCM, the cluster coincidence drawback still exist which results in poor locations of the prototypes. In this paper, we propose an interval type-2 (IT2) approach to KPCM to overcome the cluster coincidence problem in PCM and KPCM. Although the choice of kernel function can be data dependent, we use the Gaussian kernel for our experiments. Using the same value of variance for the Gaussian kernel our proposed method outperforms KPCM. Experimental results show the validity of our proposed method.