The Particle Swarm Optimization Based on Mahalanobis Distance

Abstract

An improved new fuzzy clustering algorithm is developed to obtain better quality of fuzzy clustering results. The objective function includes the regulating terms about the covariance matrices. The cluster centers and the covariance matrices are directly derived from the Lagrange’s method. The fuzzy c-mean algorithm is different from the GK and GG algorithms. The singular problem and the selecting initial values problem are improved by the Eigenvalue method and the Ratio method. We proposed a proposition which pointed out that the initial memberships of fuzzy c-mean algorithm which was based on Mahalanobis distance Algorithm and the traditional FCM Algorithm can not be all equal. The other important issue is how to approach the global minimum value that can improve the cluster accuracy. The methods to detect the local extreme value were developed by this paper. Focusing attention to these two faults, an improved new algorithm, “Fuzzy C-Means based on Particle Swarm Optimization with Mahalanobis distance (PSO-FCM-M)”, is proposed. We have two aims and goals of our research summary. One is to compare the classification accuracies of fuzzy clustering algorithms based on mahalanobis distances and euclidean distances. The other is to choose the initial membership to promote the classification accuracies.