Performance evaluation of the silhouette index

Abstract

This article provides the performance evaluation of the Silhouette index, which is based on the so called silhouette width. However, the index can be calculated in two ways, and so, the first approach uses the mean of the mean silhouettes through all the clusters. On the other hand, the second one is realized by averaging the silhouettes over the whole data set. These various approaches of the index have significant influence on indicating the proper number of clusters in a data set. To study the performance of the index, as the underlying clustering algorithms, two popular hierarchical methods were applied, that is, the complete-linkage and the single-linkage algorithm. These methods have been used for artificial and real-life data sets, and the results confirm very good performances of the index and they also allow to choose the best approach.