# Documentation

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# newrb

## Description

Radial basis networks can be used to approximate functions. newrb adds neurons to the hidden layer of a radial basis network until it meets the specified mean squared error goal.

net = newrb(P,T,goal,spread,MN,DF) takes two of these arguments,

 P R-by-Q matrix of Q input vectors T S-by-Q matrix of Q target class vectors goal Mean squared error goal (default = 0.0) spread Spread of radial basis functions (default = 1.0) MN Maximum number of neurons (default is Q) DF Number of neurons to add between displays (default = 25)

and returns a new radial basis network.

The larger spread is, the smoother the function approximation. Too large a spread means a lot of neurons are required to fit a fast-changing function. Too small a spread means many neurons are required to fit a smooth function, and the network might not generalize well. Call newrb with different spreads to find the best value for a given problem.

## Examples

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

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

The network is simulated for a new input.

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

## Algorithms

newrb 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.

Initially the radbas layer has no neurons. The following steps are repeated until the network’s mean squared error falls below goal.

1. The network is simulated.

2. The input vector with the greatest error is found.

3. A radbas neuron is added with weights equal to that vector.

4. The purelin layer weights are redesigned to minimize error.