NK Hybrid Genetic Algorithm for Clustering

The NK hybrid genetic algorithm (GA) for clustering is proposed in this paper. In order to evaluate the solutions, the hybrid algorithm uses the NK clustering validation criterion 2 (NKCV2). NKCV2 uses information about the disposition of <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> small groups of objects. Each group is composed of <inline-formula> <tex-math notation="LaTeX">${K+1}$ </tex-math></inline-formula> objects of the dataset. Experimental results show that density-based regions can be identified by using NKCV2 with fixed small <inline-formula> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula>. In NKCV2, the relationship between decision variables is known, which in turn allows us to apply gray box optimization. Mutation operators, a partition crossover (PX), and a local search strategy are proposed, all using information about the relationship between decision variables. In PX, the evaluation function is decomposed into <inline-formula> <tex-math notation="LaTeX">${q}$ </tex-math></inline-formula> independent components; PX then deterministically returns the best among <inline-formula> <tex-math notation="LaTeX">${2^{q}}$ </tex-math></inline-formula> possible offspring with computational complexity <inline-formula> <tex-math notation="LaTeX">${O(N)}$ </tex-math></inline-formula>. The NK hybrid GA allows the detection of clusters with arbitrary shapes and the automatic estimation of the number of clusters. In the experiments, the NK hybrid GA produced very good results when compared to another GA approach and to state-of-art clustering algorithms.