Enhancing Single-Objective Projective Clustering Ensembles

Projective Clustering Ensembles (PCE) has recently been formulated to solve the problem of deriving a robust projective consensus clustering from an ensemble of projective clustering solutions. In [1], PCE is formalized as an optimization problem with either a two-objective or a singleobjective function, depending on whether the object-based and the feature-based representations of the ensemble clusters are treated separately. A major result in [1] is that single-objective PCE outperforms two-objective PCE in terms of efficiency, at the expense of lower accuracy in consensus clustering. In this paper, we enhance the single-objective PCE formulation, with the ultimate goal of providing more effective formulations capable of reducing the accuracy gap with its two-objective counterpart, while maintaining its efficiency advantages. Specifically, we provide theoretical insights into the single-objective function, and introduce two heuristics that overcome the major limitations of the previous single-objective PCE formulation. Experimental evidence has demonstrated the significance of our proposed heuristics. The results, in fact, have confirmed a far better efficiency with respect to two-objective PCE and, at the same time, have shown the claimed improvements in accuracy of the consensus clustering. These results make enhanced single-objective PCE a very promising approach in the context of projective clustering ensembles.