Automatic Determination of the Number of Fuzzy Clusters Using Simulated Annealing with Variable Representation

Abstract

In this article a simulated annealing based approach for automatically clustering a data set into a number of fuzzy partitions is proposed. This is in contrast to the widely used fuzzy clustering scheme, the fuzzy C-Means (FCM) algorithm, which requires the a priori knowledge of the number of clusters. The said approach uses a real-coded variable representation of the cluster centers encoded as a state of the simulated annealing, while optimizing the Xie-Beni cluster validity index. In order to automatically determine the number of clusters, the perturbation operator is defined appropriately so that it can alter the cluster centers, and increase as well as decrease the encoded number of cluster centers. The operators are designed using some domain specific information. The effectiveness of the proposed technique in determining the appropriate number of clusters is demonstrated for both artificial and real-life data sets.