By Christopher MacLeod
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Additional resources for An Introduction to Practical Neural Networks and Genetic Algorithms For Engineers and Scientists
If the inputs corresponding to output “1s” and “0s” are mixed and distributed randomly through the graph, then the network would have a hard time picking all of these up (and generalising them). 7 (and that would be a lot of neurons). On the other hand that’s the sort of problem that a human would also have difficulty with as what we’re effectively saying is that there’s no real pattern to see. 4. 2 A C O O 3D case, Inputs A, B, C X O Data Space X O X Separator B Three input are the most which can be reliably shown on a simple graph.
1 w1,1 = 0 w1,2 = -3 w1,3 = 1. w2,2 = 0 w2,1 = -3 w2,3 = -1 w3,3 = 0 w3,1 = 1 w3,2 = -1 50 8. 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.
Next, we train only the weights of the winning neuron, so that if the same pattern returns, it will give an even higher output. 2 below. Input 1 Input 2 1 2 3 Output 1 Output 2 Output 3 51 The formula for doing this is very simple, it’s: W + = W + η (input − W ) W+ is the new (trained) weight. W is the initial weight and η is the learning rate (a number between 0 and 1, which controls the speed of training). Of course, if another, different, pattern came along, then another neuron would fire and it would be trained – hence the network self-organises itself to recognise different patterns (each neuron fires for a different pattern).