I would like to implement a Radial Basis Function (Neural) Network.

Specifically, I would like to implement the network as described in this paper: http://www.ncbi.nlm.nih.gov/pubmed/15732389. The name of the network is GGAP-RBF. A variant which is related is M-RAN. I have also studied that paper. However, I encounter the same problem. The problem is that I have difficulty with interpreting the description of the algorithms. Because in both descriptions the author states that the network starts with no hidden neurons. According to a growing criterion the neuron is added.

Page 62. describes the algorithm. First I need to start with computing the overall network output: \begin{align} f(x_{n}) = \sum_{k = 1}^{K} \alpha_{k} \exp \left(- \frac{1}{\sigma_{k}^{2}} || x_{n} - \mu_{k} ||^{2} \right) \end{align}

However, how could I do this when no neurons are available?

If we assume that was intended we skip step 2 and move to step 3. Here we need to apply the growing criterion for neurons. I will only describe the relevant part. That is: \begin{align} ||x_{n} - \mu_{nr} || > \epsilon_{n} \end{align}

If no neurons are available how could I compute this part of the growing criterion? Should it be a zero vector because no information is available?

I assume that I am missing some information. Would someone be so kind and explain that information?

A generalized growing and pruning RBF (GGAP-RBF) neural network for function approximation appears to start by comparing the output neuron with the $k=1$, i.e., first hidden neuron. That is, the radial basis function is evaluated for statistical validity even for the first neuron.