Multi-dimensional Particle Swarm Optimization for dynamic clustering

This paper addresses dynamic data clustering as an optimization problem and propose techniques for finding optimal (number of) clusters in a multi-dimensional data or feature space. In order to accomplish this objective we first propose two novel techniques, which successfully address several major problems in the field of particle swarm optimization (PSO) and promise a significant breakthrough over complex, multi-modal optimization problems at high dimensions. The first one, so-called multi-dimensional (MD) PSO, re-forms the native structure of swarm particles in such a way that they can make inter-dimensional passes with a dedicated dimensional PSO process. Therefore, in a multidimensional search space where the optimum dimension is unknown, swarm particles can seek both positional and dimensional optima. This eventually removes the necessity of setting a fixed dimension a priori, which is a common drawback for the family of swarm optimizers. Nevertheless, MD PSO is still susceptible to premature convergences due to lack of divergence. To address this problem we propose fractional global best formation (FGBF) technique, which basically collects all promising dimensional components and fractionally creates an artificial global-best particle (aGB) that has the potential to be a better ldquoguiderdquo than the PSO's native gbest particle. We investigated both individual and mutual applications of the proposed techniques and demonstrated that the best clustering performance can be achieved by their mutual operation. In order to test and evaluate their clustering performance in terms of accuracy, robustness and scalability, a synthetic data-set, which contains ground-truth clusters and offers a broad range of complexity levels is used. An extensive set of experiments demonstrate that the proposed dynamic clustering technique based on MD PSO with FGBF can extract the optimal (number of) clusters by converging to the global optimum of the validity index function at the true dimension.