Fuzzy C-means with non-extensive entropy regularization

A new fuzzy c-means clustering with non-extensive entropy regularization is proposed in this paper. The purpose of entropy regularization is to form approximate solutions of singular problems in the maximum entropy framework. The non-extensive entropy with Gaussian gain is generally used for identifying non-uniform probability densities as in regular texture patterns. It is thus well suited for regularizing the FCM problem due to the presence of extremal points in real world datasets which translate to uneven probability graphs. The new objective function is formulated and the update equations are derived subject to the constraint which is same as that of fuzzy c-means clustering. The result is a highly improved clustering accuracy superior to state-of-the-art methods when tested on benchmark UCI datasets.