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General Formulation of Rough C-Means Clustering


Seiki Ubukata, Akira Notsu, and Katsuhiro Honda


Vol. 17  No. 9  pp. 29-38


Hard C-means (HCM) clustering and fuzzy C-means (FCM) clustering, a fuzzy extension of HCM, are widely used non-hierarchical clustering techniques. Rough C-means (RCM), on the other hand, is a rough set-based extension of HCM that introduces the lower and upper areas of clusters representing the positive and possible memberships of objects to the clusters, respectively. In the context of RCM clustering, the problem exists of selecting one out of two counterbalancing methods, namely, Lingras and West’s RCM (LRCM) and Peters’ RCM (PRCM). In this paper, we propose generalized rough C-means (GRCM) clustering by re-organizing notations of RCM and unifying LRCM and PRCM. GRCM is formulated as a hybrid model based on LRCM and PRCM. Therefore, GRCM can represent not only the conventional LRCM and PRCM, but also their intermediate mixed states by adjusting some parameters. We performed numerical experiments to compare the performances of the proposed method using various parameters. We observed the trade-off between the classification accuracy in the lower areas and the fraction of objects classified as the lower areas. Through this research, we experimentally conclude that GRCM enables to observe advantages and disadvantages of LRCM and PRCM. Furthermore, it provides good results by combining them.


Clustering, Rough Clustering, Hard C-Means, Rough C-Means, Rough Set Theory