On tolerant entropy regularized fuzzy c-means

This paper presents a new type of clustering algorithm by using tolerance vector. The tolerance vector is considered from a new viewpoint that the vector shows a correlation between each data and cluster centers in proposed algorithm. First, a new concept of tolerance is introduced into optimization problem. This optimization problem is based on entropy regularized fuzzy c-means. Second, the optimization problem with the tolerance is solved by using the Karush-Kuhn-Tucker conditions. Next, new clustering algorithm is constructed based on the unique and explicit optimal solutions of the optimization problem. Finally, the effectiveness of the proposed algorithm is verified through some numerical examples.