I had a course in machine learning but I still have some questions about the RBF (Radial Basis Functions):
What is the difference between RBF in linear and non linear cases?
How does the RBF work in cases with only one hidden layer?
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An RBF-net is nonlinear when it has more than one layer (rare...) or when the basis function can change size (or move). Most of the times it is linear though and it works the following way: each hidden node is related to a center vector. The input is a vector $x$ which is sent to all the hidden nodes, the hidden node $i$ outputs $\phi_i(\|x-c_i\|)$. Then the output node receives a weighted sum of those values. The idea is actually quite close to PNN (probabilistic neural net).
Intuitively, each hidden node could be associated to one sample of the training set (or cluster centers) and hence each hidden neuron outputs a measure of how close the test sample is to the element corresponding in the training set (or the cluster center again). Then when you sum-weight all those hidden outputs and you get a real number that is a regression for your input.
