A novel combinatorial merge-split approach for automatic clustering using imperialist competitive algorithm

Cluster analysis has a wide application in many areas, including pattern recognition, information retrieval, and image processing. In most real-world clustering problems, the number of clusters must be predetermined. Automatic clustering is a promising solution for this challenge which automatically determines the number and structure of clusters in data. In recent years, the evolutionary algorithm due to their search mechanisms has been popular in solving automatic clustering problems. Imperialist Competitive Algorithm (ICA) is a successful evolutionary algorithm. In this paper, for the first time, Imperialist Competitive Algorithm (ICA) is used for solving automatic clustering problems, called “the automatic clustering using ICA (AC-ICA)”. In the proposed algorithm, in order to increase the exploration ability, the movement of colonies toward the imperialist was changed at the assimilation step. A new method has been provided for changing the number of clusters by combining random and homogeneity based merge-split approach. Furthermore, an efficient method based on density has been proposed for reinitializing empty cluster centers. To use AC-ICA in automatic clustering, the initialization and imperialist competition steps were changed. Based on changes in these two steps, a framework was provided for changing different types of ICA to solve automatic clustering problems. Then, the basic ICA and its three recently developed types, were changed by this framework and their performances in automatic clustering were compared to AC-ICA. The examinations were done on six synthetic and ten real word data sets. The comparison of the proposed algorithm's results with basic ICA, its three recently developed types and several state-of-art automatic clustering methods, shows AC-ICA's superiority in terms of the speed of convergence to the optimal solution and quality of the obtained solution. We also applied our algorithm to a real world application (i.e., face recognition) and the achieved results were acceptable.