13.1.2 RBF Network

First, investigate the storage format of the network. RBF networks are stored in objects with head RBFNet. The first component contains the parameters and the second component is a list of rules, as discussed in Section 3.2, Package Conventions.

Load the Neural Networks package.

In[1]:=<<NeuralNetworks`

Initialize an RBF network with three inputs, two outputs, and five neurons. This is done by initializing a network with matrices of the appropriate size without any data.

Initialize an RBF network with five neurons.

In[2]:=

Out[2]=

The variables w1, , w2, and contain the parameters. Compare this to Figure 2.7 in Section 2.5.2, Radial Basis Function Networks.

The RBF network can be described using the following matrix form that is comparable to the description in Section 2.5.2, Radial Basis Function Networks. Here, G is the basis function.

Parameter storage is explained by the following rules:

is a matrix with a center of a basis function in each column.

is a vector with one component describing the width of the basis function for each neuron.

w is a matrix with one column for each output of the network. The last row contains the bias parameters.

is a matrix with one column for each output of the network and one row for each network input.

Retrieve some information about the RBF network.

In[3]:=

Out[3]=

The values of the parameters can be changed by modifying the corresponding element in the network object. To do this safely, follow the idea described in Section 13.1.1, Feedforward Network.