Improving KFCM-F Algorithm Using Prototypes

Abstract

FCM algorithm is considered as the basis for all algorithms in fuzzy clustering. Due to its limitations in clustering the linearly inseparable and overlapping data, kernel-based fuzzy c-means was introduced. In literature, there are two kernel-based fuzzy clustering approaches, viz., KFCM-F and KFCM-K. In both kernel-based methods, the data items are implicitly mapped into a high-dimensional feature space, where the linearly inseparable clusters get well separable. In KFCM-F, the cluster centers are computed in the given input space, whereas in KFCM-K the cluster centers are present in the feature space and inverse mapping is used to compute these centers in the input space [3]. The time complexity of KFCM-F is O(N), where N is the size of the dataset. KFCM-F becomes infeasible to work for large values of N. The objective of the present work is to reduce the time complexity of KFCM-F by selecting few prototypes say, M from the given data, where $$M\ll N$$. The key contribution of this work is that the memberships of a group of data items say S can be easily approximated using a single membership computation. Hence, our method requires only MC membership computations instead of NC, where C denotes the number of clusters. Experimentally, we proved that our proposed improvement over KFCM-F results in a great reduction in its running time.