A simple and effective algorithm for implementing particle swarm optimization in RBF network's design using input-output fuzzy clustering

In this paper we investigate the implementation of particle swarm optimization in the design of radial basis function neural networks under the framework of input–output fuzzy clustering. The problem being studied concerns the optimal estimation of the basis function centers, provided that the learning process is guided by the information of the output space. The proposed method encompasses a cost function, which is defined by a reformulated version of the fuzzy c-means applied in the product (i.e. input–output) space. The minimization of this function is accomplished by using the particle swarm optimization, where each particle encodes a set of cluster centers associated to a single fuzzy partition. The algorithm is simple and easy to implement, yet very effective. The performance of the resulting network is tested and verified through a number of experimental cases in terms of a 10-fold cross validation analysis.