A Prototype based Hybrid Approach to speed-up Kernel FCM-K

Kernel versions of FCM have been proved to be better than FCM in identifying overlapping and linearly inseparable clusters in the input space. Kernel FCM-F (KFCM-F) and Kernel FCM-K (KFCM-K) are the two kernel versions of FCM. In KFCM-F the cluster centers are considered in the feature space, where as in KFCM-K the cluster centers are identified in the kernel space. KFCM-K is superior than KFCM-F w.r.t the clustering quality, but it is not applicable on large data sets because of its quadratic time complexity i.e., $O(n^{2})$ where $n$ is the size of the data set. This paper propose a new prototype based hybrid technique to speed-up KFCM-K for large data sets. The proposed method initially identifies some representative data items from the given data, say $l$ where $l < < n$, in linear time. The conventional kernel FCM-K is then applied over these representatives. As $l < < n$ the clustering time is reduced to $O(n+l^{2})$ from $O(n^{2})$. Experimental study on several benchmark data sets shows that the proposed method converges in less time when compare to conventional KFCM-K, but with a negligible deviation in the clustering quality.