Neural Network Toolbox

Demonstrations

The demonstration script demorb1 shows how a radial basis network is used to fit a function. Here the problem is solved with only five neurons.

Demonstration scripts demorb3 and demorb4 examine how the spread constant affects the design process for radial basis networks.

In demorb3, a radial basis network is designed to solve the same problem as in demorb1. However, this time the spread constant used is 0.01. Thus, each radial basis neuron returns 0.5 or lower, for any input vectors with a distance of 0.01 or more from its weight vector.

Because the training inputs occur at intervals of 0.1, no two radial basis neurons have a strong output for any given input.

In demorb3, it was demonstrated that having too small a spread constant can result in a solution that does not generalize from the input/target vectors used in the design. This demonstration, demorb4, shows the opposite problem. If the spread constant is large enough, the radial basis neurons will output large values (near 1.0) for all the inputs used to design the network.

If all the radial basis neurons always output 1, any information presented to the network becomes lost. No matter what the input, the second layer outputs 1's. The function newrb will attempt to find a network, but will not be able to do so because to numerical problems that arise in this situation.

The moral of the story is, choose a spread constant larger than the distance between adjacent input vectors, so as to get good generalization, but smaller than the distance across the whole input space.

For this problem that would mean picking a spread constant greater than 0.1, the interval between inputs, and less than 2, the distance between the left-most and right-most inputs.

More Efficient Design (newrb)

Generalized Regression Networks

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