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By Kroese B., van der Smagt P.

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Top left: The original learning samples; Top right: The approximation with the network; Bottom left: The function which generated the learning samples; Bottom right: The error in the approximation. programmed with two inputs, 10 hidden units with sigmoid activation function and an output unit with a linear activation function. 20) should be adapted for the linear instead of sigmoid activation function. The network weights are initialized to small values and the network is trained for 5,000 learning iterations with the back-propagation training rule, described in the previous section.

4 An example A feed-forward network can be used to approximate a function from examples. Suppose we have a system (for example a chemical process or a financial market) of which we want to know 38 CHAPTER 4. BACK-PROPAGATION the characteristics. The input of the system is given by the two-dimensional vector x and the output is given by the one-dimensional vector d. 3 (top left). 3: Example of function approximation with a feedforward network. Top left: The original learning samples; Top right: The approximation with the network; Bottom left: The function which generated the learning samples; Bottom right: The error in the approximation.

RECURRENT NETWORKS 6 Self-Organising Networks In the previous chapters we discussed a number of networks which were trained to perform a mapping F : ℜn → ℜm by presenting the network ‘examples’ (x p , dp ) with dp = F (xp ) of this mapping. However, problems exist where such training data, consisting of input and desired output pairs are not available, but where the only information is provided by a set of input patterns xp . In these cases the relevant information has to be found within the (redundant) training samples x p .

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An Introduction to Neural Networks by Kroese B., van der Smagt P.


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