General fuzzy C-means clustering algorithm using Minkowski metric

As one of the most commonly used clustering methods, fuzzy clustering technique such as the Fuzzy C-means (FCM) has undergone a rapid development. In this paper, a general FCM clustering algorithm based on contraction mapping (cGFCM) is proposed for more general cases of using Minkowski metric (L_p-norm distance) as the similarity measure, and the analytical method for calculating the parameters of the proposed algorithm is given. The core of the proposed cGFCM algorithm lies on constructing a contraction mapping to update the prototypes when an arbitrary Minkowski metric is used to measure the closeness of data points. Subsequently, mainly guided by the Banach contraction mapping principle, the algorithm and implementation approaches are discussed in detail, and the correctness and feasibility of the proposed method are proved. Moreover, the convergence of the proposed algorithm is also discussed. Experimental studies carried out on both synthetic data sets and real-world data sets show that the proposed cGFCM algorithm extends FCM to more general cases without extra time and space costs. Compared with another generalized FCM clustering strategy and other five state-of-the-art clustering methods, the proposed algorithm can not only reach better performance in both clustering accuracy and stability, but reduce the running time several-fold.