An Improved K-Means Algorithm Based on Fuzzy Metrics

Abstract

The traditional K-means algorithm has been widely used in cluster analysis. However, the algorithm only involves the distance factor as the only constraint, so there is a problem of sensitivity to special data points. To address this problem, in the process of K-means clustering, ambiguity is introduced as a new constraint condition. Hence, a new membership Equation is proposed on this basis, and a method for solving the initial cluster center points is given, so as to reduce risks caused by random selection of initial points. Besides, an optimized clustering algorithm with Gaussian distribution is derived with the utilization of fuzzy entropy as the cost function constraint. Compared with the traditional clustering method, the new Equation's membership degree can reflect the relationship between a certain point and the set in a clearer way, and solve the problem of the traditional K-means algorithm that it is prone to be trapped in local convergence and easily influenced by noise. Experimental verification proves that the new method has fewer iterations and the clustering accuracy is better than other methods, thus having a better clustering effect.