By Christopher MacLeod
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Extra info for An Introduction to Practical Neural Networks and Genetic Algorithms For Engineers and Scientists
Working with such waveforms can by difficult because as mentioned briefly in the section above, they can be of different length (imagine someone speaking; they might say the word quickly or slowly). Because of difficulties like this, audio and similar waveforms are often transformed out of the time domain and into the frequency domain using a mathematical transform. The transform used is usually a Fourier Transform4. The frequency domain representation is a graph of amplitude verses frequency. The point is that patterns which aren’t obvious in the normal time domain representation of the wave, are sometimes much more obvious in the frequency domain and are therefore easier for a network to handle.
Competitive networks In this chapter we’ll look at a different type of network called the Competitive Network. This and its relations are sometimes also called Kohonen, Winner Takes All or Self Organising networks. They are used to identify patterns in data, even when the programmer may not know the nature of the pattern. Their operation is best illustrated by example. 1. 1, a network of three neurons. Input 1 Input 2 1 2 3 Output 1 Output 2 Output 3 We’ll not worry too much about the set up of the weights at the moment except to say that they are all essentially random.
Adjacent neurons partially trained. Other, further-out, layers of neurons can also be trained by reducing η further. 8. 8, an alternative layout. “winning” neuron, fully trained. Adjacent neurons partially trained. 59 The result of this is that when the network is fully trained it classifies the patterns which are most similar, closer together on the grid, producing an ordered “map” of the inputs. It’s worth mentioning at this point that instead of making all the vectors one unit in length (and there may be times which this is not practical) there is an alternative measure of their similarity which is to measure their Euclidian distance apart: Activation = X − W This is measured by subtracting each input from its weight.