Internal Evaluation of Density-Based Clusterings with Noise

Being able to evaluate the quality of a clustering result even in the absence of ground truth cluster labels is fundamental for research in data mining. However, most cluster validation indices (CVIs) do not capture noise assignments by density-based clustering methods like DBSCAN or HDBSCAN, even though the ability to correctly determine noise is crucial for successful clustering. In this paper, we propose DISCO, a Density-based Internal Score for Clusterings with nOise, the first CVI to explicitly assess the quality of noise assignments rather than merely counting them. DISCO is based on the established idea of the Silhouette Coefficient, but adopts density-connectivity to evaluate clusters of arbitrary shapes, and proposes explicit noise evaluation: it rewards correctly assigned noise labels and penalizes noise labels where a cluster label would have been more appropriate. The pointwise definition of DISCO allows for the seamless integration of noise evaluation into the final clustering evaluation, while also enabling explainable evaluations of the clustered data. In contrast to most state-of-the-art, DISCO is well-defined and also covers edge cases that regularly appear as output from clustering algorithms, such as singleton clusters or a single cluster plus noise.