Consensus Multiobjective Differential Crisp Clustering for Categorical Data Analysis

In this article, an evolutionary crisp clustering technique is described that uses a new consensus multiobjective differential evolution. The algorithm is therefore able to optimize two conflicting cluster validity measures simultaneously and provides resultant Pareto optimal set of nondominated solutions. Thereafter the problem of choosing the best solution from resultant Pareto optimal set is resolved by creation of consensus clusters using voting procedure. The proposed method is used for analyzing the categorical data where no such natural ordering can be found among the elements in categorical domain. Hence no inherent distance measure, like the Euclidean distance, would work to compute the distance between two categorical objects. Index-coded encoding of the cluster medoids (centres) is used for this purpose. The effectiveness of the proposed technique is provided for artificial and real life categorical data sets. Also statistical significance test has been carried out to establish the statistical significance of the clustering results. Matlab version of the software is available at http://bio.icm.edu.pl/~darman/CMODECC.