Fuzzy Supervised Clustering Algorithm with the Particle Swarm Optimization

Abstract

In GK-algorithm, fuzzy clustering algorithm with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. A Fuzzy C-Means algorithm based on Mahalanobis distance (FCM-HM) was proposed to improve those limitations of GG and GK algorithms, but it is not stable enough when some of its covariance matrices are not equal. The singular problem and the selecting initial values problem are improved. We pointed out that the initial memberships of fuzzy c-mean algorithm which was based on Mahalanobis distance algorithm and the traditional Fuzzy c-means algorithm (FCM) Algorithm can’t 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-HM)”, 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.