Self generating radial basis function as neuro-fuzzy model and its application to nonlinear prediction of chaotic time series

The authors propose a self-generating algorithm for radial basis functions to automatically determine the minimal number of basis functions to achieve the specified model error. This model is also regarded as a multilayered neural network or fuzzy model of class C^∞. The self-generating algorithm consists of two processes: model parameter tuning by the gradient method for a fixed number of rules, and a basis function generation procedure by which a new basis function is generated in such a way that the center is located at the point where maximal inference error takes place in the input space, when the effect of parameter tuning is diminished. A numerical example shows that the algorithm can achieve the specified model error with fewer basis functions than other methods by which only coefficients of the basis functions are tuned. The method is applied to the nonlinear prediction of optical chaotic time series