Comparison and Weighted Summation Type of Fuzzy Cluster Validity Indices

Abstract

Finding the optimal cluster number and validating the partition results of a data set are difficult tasks since clustering is an unsupervised learning process. Cluster validity index (CVI) is a kind of criterion function for evaluating the clustering results and determining the optimal number of clusters. In this paper, we present an extensive comparison of ten well-known CVIs for fuzzy clustering. Then we extend traditional single CVIs by introducing the weighted method and propose a weighted summation type of CVI (WSCVI). Experiments on nine synthetic data sets and four real-world UCI data sets demonstrate that no one CVI performs better on all data sets than others. Nevertheless, the proposed WSCVI is more effective by properly setting the weights.