Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

RBF Neural Networks

Radius basis function networks (RBF networks) form a special type of neural networks, which are closely related to density estimation methods. Some workers in the field do not regard this type as neural networks at all. A thorough mathematical description of RBF networks is given by Broomhead , a short introduction is also given by Lohninger . RBF networks fall in between regression models and nearest neighbor classification schemes, which can be looked upon as content-addressable memories. Furthermore the behavior of a RBF network can be controlled by a single parameter which determines if the network behaves more like a multiple linear regression or a content-addressable memory.

RBF networks have a special architecture in that they have only three layers (input, hidden, output) and there is only one layer where the neurons show a nonlinear response. In addition, other authors have suggested including some extra neurons which serve to calculate the reliability of the output signals (extrapolation flag).


The input layer has, as in many other network models, no calculating power and serves only to distribute the input data among the hidden neurons. The hidden neurons show a non-linear transfer function which is derived from Gaussian bell curves. The output neurons in turn have a linear transfer function which makes it possible to simply calculate the optimum weights associated with these neurons.