Comparison of Cluster Validity Measures Based x-Means

Abstract

The x-means determines the suitable number of clusters automatically by executing k-means recursively. The Bayesian Information Criterion is applied to evaluate a cluster partition in the x-means. A novel type of x-means clustering is proposed by introducing cluster validity measures that are used to evaluate the cluster partition and determine the number of clusters instead of the information criterion. The proposed x-means uses cluster validity measures in the evaluation step, and an estimation of the particular probabilistic model is therefore not required. The performances of a conventional x-means and the proposed method are compared for crisp and fuzzy partitions using eight datasets. The comparison shows that the proposed method obtains better results than the conventional method, and that the cluster validity measures for a fuzzy partition are effective in the proposed method.