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Spatial prediction needs to account for spatial information, which makes conventional radial basis function (RBF) networks inappropriate, for they assume independent and identical distribution. In this paper, we fuse spatial information at different layers of RBF. Experiments show fusion at hidden layer gives the best result and suggest that the optimal value is around one for the coefficient, which is used in the linear combination at the output layer.

This paper presents the pruning and model-selecting algorithms to the support vector learning for sample classification and function regression. When constructing RBF network by support vector learning we occasionally obtain redundant support vectors which do not significantly affect the final classification and function approximation results. The pruning algorithms primarily based on the sensitivity measure and the penalty term. The kernel function parameters and the position of each support vector are updated in order to have minimal increase in error, and this makes the structure of SVM network more flexible. We illustrate this approach with synthetic data simulation and face detection problem in order to demonstrate the pruning effectiveness.

In this work, several applications and the performances of the radial basis function (RBF) are briefly reviewed at first. After that, the binomial function combined with three different RBFs including the multiquadric (MQ), inverse quadric (IQ) and inverse multiquadric (IMQ) distributions are adopted to model the tourism data of Huangshan in China. Simulation results showed that all the models match very well with the sample data. It is found that among the three models, the IMQ-RBF model is more suitable for forecasting the tourist flow.

We extend the traditional RBF network to be a more powerful tool in terms of considering dependence among explanatory variables. For this purpose, we propose two kernel functions of RBF network, i.e., FGM-Gauss kernel and ρ-Gauss kernel based on a copula. A copula is another expression of a joint probability distribution function. After proposing the new models, we compare the regression performances between RBF network with the traditional Gauss kernel, FGM-Gauss kernel, ρ-Gauss kernel, and the multiple linear regression analysis by numerical experimentations. We show that new models have better regression performances than RBF network with Gauss kernel and multiple regression analysis if the explanatory variables depend on each other.

In this paper, we propose a genetic algorithm based design procedure for a radial-basis function neural network. A Hierarchical Rank Density Genetic Algorithm (HRDGA) is used to evolve the neural network's topology and parameters simultaneously. Compared with traditional genetic algorithm based designs for neural networks, the hierarchical approach addresses several deficiencies highlighted in literature. In addition, the rank-density based fitness assignment technique is used to optimize the performance and topology of the evolved neural network to deal with the confliction between the training performance and network complexity. Instead of producing a single optimal solution, HRDGA provides a set of near-optimal neural networks to the designers so that they can have more flexibility for the final decision-making based on certain preferences. In terms of searching for a near-complete set of candidate networks with high performances, the networks designed by the proposed algorithm prove to be competitive, or even superior, to three other traditional radial-basis function networks for predicting Mackey–Glass chaotic time series.

Structural safety monitoring system uses an array of sensors to continuously monitor a structure to provide an early indication of problems such as damage to the structure from fatigue, corrosion or impact. The system is a large sensor network containing about two hundred nodes, each of which contains multiple sensors. So the sensor fault diagnosis is getting more and more important. A fuzzy-neural method is suggested in this paper. Based on the function equivalence between T-S fuzzy inference and RBF network, a kind of fuzzy neural controller based on RBF network with full-net structure is put forward. This paper proposes a real code GA to optimize all factors including scaling factors, membership functions and fuzzy rules. The RBF network with two inputs-one output model is used as fuzzy controller, the result of the simulation illustrates that the controller has good dynamic performance and strong robust.