Multi-objective gene expression programming for clustering

Abstract

This paper proposes a multi-objective gene expression programming for clustering (MGEPC), which could automatically determine the number of clusters and the appropriate partitioning from the data set. The clustering algebraic operations of gene expression programming are extended first. Then based on the framework of the Nondominated Sorting Genetic Algorithm-II, two enhancements are proposed in MGEPC. First, a multi-objective k-means clustering is proposed for local search, where the total symmetrical compactness and the cluster connectivity are used as two complementary objectives and the point symmetry based distance is adopted as the distance metric. Second, the power-law distribution based selection strategy is proposed for the parent population generation. In addition, the external archive and the archive truncation are used to keep a historical record of the non-dominated solutions found along the search process. Experiments are performed on five artificial and three real-life data sets. Results show that the proposed algorithm outperforms the PESA-II based clustering method (MOCK), the archived multiobjective simulated annealing based clustering technique with point symmetry based distance (VAMOSA) and the singleobjective version of gene expression programming based clustering technique (GEP-Cluster).