Balance-driven automatic clustering for probability density functions using metaheuristic optimization

For solving the clustering for probability density functions (CDF) problem with a given number of clusters, the metaheuristic optimization (MO) algorithms have been widely studied because of their advantages in searching for the global optimum. However, the existing approaches cannot be directly extended to the automatic CDF problem for determining the number of clusters k. Besides, balance-driven clustering, an essential research direction recently developed in the problem of discrete-element clustering, has not been considered in the field of CDF. This paper pioneers a technique to apply an MO algorithm for resolving the balance-driven automatic CDF. The proposed method not only can automatically determine the number of clusters but also can approximate the global optimal solution in which both the clustering compactness and the clusters’ size similarity are considered. The experiments on one-dimensional and multidimensional probability density functions demonstrate that the new method possesses higher quality clustering solutions than the other conventional techniques. The proposed method is also applied in analyzing the difficulty levels of entrance exam questions.