Fuzzy c-means (FCM) is a simple but powerful clustering method using the concept of fuzzy sets that has been proved to be useful in many areas. There are, however, several well known problems with FCM, such as sensitivity to initialization, sensitivity to outliers, and limitation to convex clusters. In this paper, global fuzzy c-means (G-FCM) and kernel fuzzy c-means (K-FCM) are combined and extended to form a non-linear variant of G-FCM, called kernelized global fuzzy c-means (KG-FCM). G-FCM is a variant of FCM that uses an incremental seed selection method and is effective in alleviating sensitivity to initialization. There are several approaches to reduce the influence of noise and properly partition non-convex clusters, and K-FCM is one. K-FCM is used in this paper because it can easily be extended with different kernels, which provide sufficient flexibility to allow for resolution of the shortcomings of FCM. By combining G-FCM and K-FCM, KG-FCM can resolve the shortcomings mentioned above. The usefulness of the proposed method is demonstrated by experiments using artificial and real world data sets.
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