newrbe (Neural Network Toolbox)

Design an exact radial basis network

net = newrbe(P,T,spread)

Radial basis networks can be used to approximate functions. newrbe very quickly designs a radial basis network with zero error on the design vectors.

newrbe(P,T,spread) takes two or three arguments,

P - R x Q matrix of Q input vectors.

T - S x Q matrix of Q target class vectors.

spread - Spread of radial basis functions, default = 1.0.

and returns a new exact radial basis network.

The larger the spread is, the smoother the function approximation will be. Too large a spread can cause numerical problems.

Examples

Here we design a radial basis network given inputs P and targets T.

P = [1 2 3];
T = [2.0 4.1 5.9];
net = newrbe(P,T);

Here the network is simulated for a new input.

P = 1.5;
Y = sim(net,P)

Algorithm

newrbe creates a two layer network. The first layer has radbas neurons, and calculates its weighted inputs with dist, and its net input with netprod. The second layer has purelin neurons, and calculates its weighted input with dotprod and its net inputs with netsum. Both layers have biases.

newrbe sets the first layer weights to P', and the first layer biases are all set to 0.8326/spread, resulting in radial basis functions that cross 0.5 at weighted inputs of +/- spread.

The second layer weights IW{2,1} and biases b{2} are found by simulating the first layer outputs A{1}, and then solving the following linear expression:

[W{2,1} b{2}] * [A{1}; ones] = T