Comparison and Weighted Summation Type of Fuzzy Cluster Validity Indices

Finding the optimal cluster number and validating the partition resultsof 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 clusteringresults and determining the optimal number of clusters. In this paper, we present anextensive comparison of ten well-known CVIs for fuzzy clustering. Then we extendtraditional single CVIs by introducing the weighted method and propose a weightedsummation type of CVI (WSCVI). Experiments on nine synthetic data sets and fourreal-world UCI data sets demonstrate that no one CVI performs better on all datasets than others. Nevertheless, the proposed WSCVI is more effective by properlysetting the weights.