Radial Basis Function Network (RBF Network)

Question

According to the link below, i didn't understand what is the "center vector for neuron i", in other words "center of the RBF units called also prototype ".

read the Network architecture in this link

Please i need your appreciated help.

Answer 1

If you read on to the Training section in your link, it explains what the centre vectors are:

Reading the above, it seems to me that you have your set of samples, the x's, and from these you choose a number of centre vectors - one for each neuron in the hidden layer . The centre vectors, broadly speaking are centres of clusters in your sample data.

As the remarks say, you can use an unsupervised clustering algorithm, such as k-means, to find n cluster centres in your data, where n is the number of neurons in the hidden layer that you are dealing with. Different layers may have more or less neurons and so will have correspondingly more or less centre vectors.

Then the RBF relates each individual sample, x, to each centre vector by some function of the Euclidean distance between them.

Answer 2

The center vector of the neuron are the centers of the RBF. RBF is just a function the distance of a point (called x in the article) to a center (called ci in the article). Each neuron has its own center.