Pareto Optimality of Cluster Objective and Validity Functions

Clustering is often done by minimizing an objective function of a clustering model. Several runs with different initializations or parameters yield multiple solutions. The best of these solutions is often selected by cluster validity measures. We analyze cluster objective and validity functions and show that they can be contradictory and therefore should be considered jointly in an integrated clustering approach. For this reason we define a Pareto fuzzy c-means clustering model that produces the Pareto optimal set of both objective and validity functions. In our experiments with the single outlier and the lung cancer data sets Pareto clustering considerably outperforms conventional clustering.