By Christopher MacLeod

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**Extra info for An Introduction to Practical Neural Networks and Genetic Algorithms For Engineers and Scientists**

**Example text**

Likewise, the same can be said of neurons 5, 6 and 7 and they are combined to give region a. Finally regions a and b or combined by neuron i (an OR function in this case) so that an input in either region will give an output of 1. 4, a three layer network. 1 2 A 3 1 A 3 b 5 a 4 6 a i 4 2 b 7 B B 5 6 7 39 Out If we were to increase the number of neurons in the first layer we could increase the separators in the system, increasing the number layer two neurons increases the number of separate regions.

714 Now let’s calculate the length of the new weight vector (the training formula doesn’t preserve length). 79 57 Worked example (continued). Finally then let’s plot a graph showing what’s happened: Old weight vector New vector We can see that the weight vector has moved towards the input. Obviously then, this network requires a little more thought to set up compared to some of the others. The weights and inputs need to be processed so that they are all vectors of length one. The network will also work better if the weights are equally distributed around the unit circle.

Since the network is performing a mapping function, it can also be trained to process the waveforms and implement mathematical transforms on them to form Digital Signal Processing (DSP) functions3. This example also illustrates a problem which we will return to in the next chapterthat of the presentation of data to the network. The network will only recognise the waveform if it is the same size as the data the network was trained form. If it has speeded up or slowed down then the network won’t “see” it as the same pattern.