Are Cluster Validity Measures (In)valid?

TL;DR

This paper critically examines the effectiveness of internal cluster validity measures when used as objective functions, revealing their limitations and proposing a new variant of the Dunn index that improves clustering quality in certain scenarios.

Contribution

It demonstrates the poor correlation of many validity indices with expert knowledge and introduces a novel Dunn index variant based on OWA operators and near-neighbour graphs.

Findings

Many validity indices poorly match expert clustering judgments.

The new Dunn index variant better separates high-density subspaces.

Using validity indices as objective functions can lead to less meaningful clusterings.

Abstract

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.