Analysis of convergence property of PSO and its application to nonlinear blind source separation

This article analyzes the convergence property of the particle swarm optimization and its application to the nonlinear blind source separation system. The inter-particle communication of the particle swarm optimization is realized by the past history of the neighbors and depends on the network structure of the swarm. We focus on an average path length of the network, and we clarify the relationship between the average path length and its searching performance. The result indicates that a long average path length is effective for multi-modal functions and multi-optima problems. Therefore, we apply the PSO with the long average path length to a nonlinear blind source separation system. Blind source separation is a technique for recovering an original source signal from mixing signals without the aid of information of the source signal. The system restores the original signal using the probability of the distribution of the original signal. In this study, we consider the case where the original signals are nonlinearly mixed. In general, the separation of the nonlinear mixture signals is quite difficult. In order to solve such problem, we apply a radial basis function network to the nonlinear blind source separation system. The radial basis function network can approximate the nonlinear mapping. Therefore, the inverse mapping of nonlinear mixture system is approximated by the RBF network. For the system to be able to approximate the inverse mapping, it is necessary to learn the parameter of the RBF network. PSO is used for a learning algorithm. Simulation results show that the proposed approach has good performance.