Clustering Validity Based on the Improved Hubert \Gamma Statistic and the Separation of Clusters

Abstract

The validity of clustering is one important research field in clustering analysis, and many clustering validity functions have been proposed, especially those based on the geometrical structure of data set, such as Dunn's index and Xie-Beni index. In this way, the compactness and the separation of clusters are usually taken into account. Xie-Beni index decreases with the number of partitions increasing. It is difficult to choose the optimal number of clusters when there are lots of clusters in data. In this paper, a novel clustering validity function is proposed, which is based on the improved Huber \Gamma statistic combined with the separation of clusters. Unlike other clustering validity, the function has the only maximum with the clustering number increasing. The experiments indicate that the function can be used as the optimal index for the choice of the clustering numbers.