Quantum behaved particle swarm optimization for data clustering with multiple objectives

Clustering is an important tool in many fields such as exploratory data mining and pattern recognition. It consists in organizing a large data set into groups of objects that are more similar to each other than to those in other groups. Despite its use for over three decades, it is still subject to a lot of controversy. In this paper, we cast clustering as a Pareto based multi-objective optimization problem which is handled using a quantum behaved particle swarm optimization algorithm. The search process is carried out over the space of cluster centroids with the aim to find partitions that optimize two objectives simultaneously, namely compactness and connectivity. Global best leader selection is performed using a hybrid method based on sigma values and crowding distance. The proposed algorithm has been tested using synthetic and real data sets and compared to the state of the art methods. The results obtained are very competitive and display good performance both in terms of the cluster validity measure and in terms of the ability to find trade-off partitions especially in the case of close clusters.