Quantitative evaluation of internal cluster validation indices using binary data sets

Abstract

Aims: Different clustering methods often classify the same data set differently. Selecting the “best” clustering solution from alternatives is possible with cluster validation indices. Because of the large variety of cluster validation indices (CVIs), choosing the most suitable index concerning the data set and clustering algorithms is challenging. We aim to assess different internal clustering validation indices. Methods: Artificial binary data sets with equal- and unequal-sized well-separated a priori clusters were simulated and three levels of noise were then added. Twenty replications of each of the six types of data sets (two group sizes × three levels of noise) were created and analyzed by three clustering algorithms with Jaccard dissimilarity. Twenty-seven clustering validation indices are evaluated including both geometric and non-geometric indices. Results: Although, in theory, all CVIs could differentiate between good and wrong classifications, only a few perform as expected with noisy data. Tau and silhouette widths proved to be the best geometric CVIs both for equal and unequal cluster sizes. Among non-geometric indices, crispness and OptimClass performed best. Conclusion: We recommend using these best-performing CVIs. We suggest plotting the CVI value against the number of clusters because the lack of a sharp peak means that the position of the maximum is uncertain.