Clustering with a Weighted Sum Validity Function Using a Niching PSO Algorithm

In this paper, we will consider an objective function called the weighted sum validity function (WSVF), which is a weighted sum of several normalized cluster validity functions. In contrast to optimization techniques intended to find a single, global solution in a problem domain, niching techniques have the ability to locate multiple solutions in multimodal domains. Hence, a niching binary particle swarm optimization (NBPSO) approach is developed for automatically constructing the proper number of clusters as well as appropriate partitioning of the data set. We also hybridize the NBPSO method with the k-means algorithm to optimize the WSVF automatically. In experiments, we show the effectiveness of the WSVF and the validity of the NBPSO. In comparison with other related PSO, the NBPSO can consistently and efficiently converge to the optimum corresponding to the given data in concurrence with the convergence result. The WSVF is found generally able to improve the confidence of clustering solutions and achieve more accurate and robust results.