The area under the ROC curve as a measure of clustering quality

The Area Under the Receiver Operating Characteristics (ROC) Curve, referred to as AUC, is a well-known performance measure in supervised learning domain. Due its compelling features, it has been employed number of studies evaluate and compare different classifiers. In this work, we explore AUC unsupervised domain, more specifically, context cluster analysis. particular, elaborate on use an internal/relative clustering quality, which refer Curve for Clustering (AUCC). We show that AUCC given candidate solution expected value under null model random solutions, regardless size dataset and, importantly, or (im)balance clusters evaluation. addition, fact that, validation consider, actually linear transformation Gamma criterion from Baker Hubert (1975), also formally derive theoretical chance clusterings. discuss computational complexity these criteria while ordinary implementation can be computationally prohibitive impractical most real applications analysis, equivalence with unveils much efficient algorithmic procedure. Our findings are supported by experimental results. These results addition effective robust quantitative evaluation provided AUCC, visual inspection ROC curves themselves useful further assess broader, qualitative perspective well.