Are cluster validity measures (in) valid?

Internal cluster validity measures (such as the Calinski-Harabasz, Dunn, or Davies-Bouldin indices) are frequently used for selecting appropriate number of partitions a dataset should be split into. In this paper we consider what happens if treat such indices objective functions in unsupervised learning activities. Is optimal grouping with regards to, say, Silhouette index really meaningful? It turns out that many (in)validity promote clusterings match expert knowledge quite poorly. We also introduce new, well-performing variant Dunn is built upon OWA operators and near-neighbour graph so subspaces higher density, regardless their shapes, can separated from each other better.