Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Stochastic simulations of web search engines: RBF versus second-order regression models
Information Sciences—Informatics and Computer Science: An International Journal
Fast learning in networks of locally-tuned processing units
Neural Computation
Visual RBF network design based on Star Coordinates
Advances in Engineering Software
On training radial basis function neural networks using optimal fuzzy clustering
MED '09 Proceedings of the 2009 17th Mediterranean Conference on Control and Automation
IEEE Transactions on Neural Networks
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
RBF neural network based on particle swarm optimization
ISNN'10 Proceedings of the 7th international conference on Advances in Neural Networks - Volume Part I
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
On cluster validity for the fuzzy c-means model
IEEE Transactions on Fuzzy Systems
Conditional fuzzy clustering in the design of radial basis function neural networks
IEEE Transactions on Neural Networks
Analysis of input-output clustering for determining centers of RBFN
IEEE Transactions on Neural Networks
A new clustering technique for function approximation
IEEE Transactions on Neural Networks
Robust and adaptive backstepping control for nonlinear systems using RBF neural networks
IEEE Transactions on Neural Networks
High-speed face recognition based on discrete cosine transform and RBF neural networks
IEEE Transactions on Neural Networks
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This paper elaborates on the use of particle swarm optimization in training Gaussian type radial basis function neural networks under the umbrella of input-output fuzzy clustering. The problem being investigated concerns the selection of basis function centers that contribute most in network's performance, given that the clustering process in the input space is guided by the clustering in the output space. To accomplish this task, we quantify the effect of the input space fuzzy partition upon network's square error in terms of an objective function that describes the ability of the partition to accurately reconstruct the input training samples. We, then, theoretically prove that the minimization of the above function acts to minimize an upper bound of the network's square error. Therefore, the resulting solution corresponds to a minimal square error, while at the same time it maintains the structure of the input data. Due to the peculiarity of the aforementioned objective function, we treat it as the fitness function used by the particle swarm optimizer. The proposed methodology encompasses three design steps. The first step implements an independent fuzzy clustering in the output space to obtain a set of cluster centers. In the second step, unlike other approaches, the above centers are directly involved in the estimation of the membership degrees in the input-output space. In the third step, these membership degrees are used by the particle swarm optimizer in order to obtain optimal values for the centers. To summarize, the novelty of our contribution lies in: (a) the way we handle the information flow from output to input space, and (b) the way we handle the effect of the input space partition upon network's performance. The experiments indicate that the fitness function decreases as the number of hidden node increases. Finally, a comparison between the proposed method and other sophisticated approaches shows its statistically significant superiority.