Are Cluster Validity Measures (In)valid?
This work addresses the reliability of cluster validity measures for practitioners in data analysis, highlighting limitations and proposing an incremental improvement.
The paper investigates whether using internal cluster validity measures as objective functions leads to meaningful clusterings, finding that many indices produce results poorly aligned with expert knowledge. It also introduces a new variant of the Dunn index that improves separation of dense subspaces regardless of shape.
Internal cluster validity measures (such as the Calinski-Harabasz, Dunn, or Davies-Bouldin indices) are frequently used for selecting the appropriate number of partitions a dataset should be split into. In this paper we consider what happens if we treat such indices as objective functions in unsupervised learning activities. Is the optimal grouping with regards to, say, the Silhouette index really meaningful? It turns out that many cluster (in)validity indices promote clusterings that match expert knowledge quite poorly. We also introduce a new, well-performing variant of the Dunn index that is built upon OWA operators and the near-neighbour graph so that subspaces of higher density, regardless of their shapes, can be separated from each other better.