Artificial Neural Network: Radial Basis Networks

1. Artificial Neural Network:Radial Basis Networks @ Dr. J. Razjouyan By: Dr. J. Razjouyan

2. Introduction • Radial basis networks can require more neurons than standard feedforwardbackpropagation networks, but often they can be designed in a fraction of the time it takes to train standard feedforward networks. • They work best when many training vectors are available. @ Dr. J. Razjouyan

3. Radial Basis FunctionsNeuron Model • Notice that the expression for the net input of a radbas neuron is different from that of other neurons. Here the net input to the radbas transfer function is the vector distance between its weight vector w and the input vector p, multiplied by the bias b. (The || dist || box in this figure accepts the input vector p and the single row input weight matrix, and produces the dot product of the two.) @ Dr. J. Razjouyan

4. The transfer function for a radial basis neuron is • Here is a plot of the radbas transfer function. • The radial basis function has a maximum of 1 when its input is 0. As the distance between w and p decreases, the output increases. Thus, a radial basis neuron acts as a detector that produces 1 whenever the input p is identical to its weight vector w @ Dr. J. Razjouyan

5. Network Architecture • Radial basis networks consist of two layers: a hidden radial basis layer of S1 neurons, and an output linear layer ofS2 neurons. @ Dr. J. Razjouyan

6. You can understand how this network behaves by following an input vector p through the network to the output a2. If you present an input vector to such a network, each neuron in the radial basis layer will output a value according to how close the input vector is to each neuron's weight vector. • Thus, radial basis neurons with weight vectors quite different from the input vector p have outputs near zero. These small outputs have only a negligible effect on the linear output neurons. • In contrast, a radial basis neuron with a weight vector close to the input vector p produces a value near 1. If a neuron has an output of 1, its output weights in the second layer pass their values to the linear neurons in the second layer. • In fact, if only one radial basis neuron had an output of 1, and all others had outputs of 0s (or very close to 0), the output of the linear layer would be the active neuron's output weights. This would, however, be an extreme case. Typically several neurons are always firing, to varying degrees. @ Dr. J. Razjouyan