The Projective Clustering Ensemble Problem for Advanced Data Clustering

After more than five decades, a huge number of models and algorithms have been developed for data clustering. While most attention has been devoted to data types, algorithmic features, and application targets, in the last years there has also been an increasing interest in developing advanced dataclustering tools. In this respect, projective clustering and clustering ensembles represent two of the most important directions: the former is concerned with the discovery of subsets of the input data having different, possibly overlapping subsets of features associated with them, while the latter allows for the induction of a prototype consensus clustering from an available ensemble of clustering solutions. In this paper we discuss the current state-of-the-art research in which the problems of projective clustering and clustering ensembles have been revisited and integrated in a unified framework, called Projective Clustering Ensemble (PCE). We discuss how PCE has originally been formalized as either a two-objective or a single-objective optimization problem, and how the limitations of such early approaches have been overcome by a metacluster-based formulation. We also summarize main empirical results, and provide pointers for future research.