Improved Clustering Algorithm Based on Calculus of Variation

A major problem in data clustering is the degradation in performance due to outliers. We have developed a robust method to solve this problem using the l_2m-FCM algorithm. However, this method has to solve a non-linear equation and can converge to a local optimum. In this paper, we introduce a regularized version of the l_2m-FCM algorithm. The essential idea is to constrain the descent direction in the optimization procedure. We employ a novel method to correct the direction using the calculus of variations. Experimental results show that the proposed method has a better performance than seven other clustering algorithms for both synthetic and real world data sets