On the evaluation of clustering results: measures, ensembles, and gene expression data analysis - Jaskowiak, Pablo Andretta (2015)
Clustering plays an important role in the exploratory analysis of data. Its goal is to organize objects into a finite set of categories, i.e., clusters, in the hope that meaningful and previously unknown relationships will emerge from the process. Not every clustering result is meaningful, though. In fact, virtually all clustering algorithms will yield a result, even if the data under analysis has no true clusters. If clusters do exist, one still has to determine the best configuration of parameters for the clustering algorithm in hand, in order to avoid poor outcomes. This selection is usually performed with the aid of clustering validity criteria, which evaluate clustering results in a quantitative fashion. In this thesis we study the evaluation/validation of clustering results, proposing, in a broad context, measures and relative validity criteria ensembles. Regarding measures, we propose the use of the Area Under the Curve (AUC) of the Receiver Operating Characteristics (ROC) curve as a relative validity criterion for clustering. Besides providing an empirical evaluation of AUC, we theoretically explore some of its properties and its relation to another measure, known as Gamma. A relative criterion for the validation of density based clustering results, proposed with the participation of the author of this thesis, is also reviewed. In the case of ensembles, we propose their use as means to avoid the evaluation of clustering results based on a single, ad-hoc selected, measure. In this particular scope, we: (i) show that ensembles built on the basis of arbitrarily selected members have limited practical applicability; and (ii) devise a simple, yet effective heuristic approach to select ensemble members, based on their effectiveness and complementarity. Finally, we consider clustering evaluation in the specific context of gene expression data. In this particular case we evaluate the use of external information from the Geno Ontology for the evaluation of distance measures and clustering results