Examples of artificial neural networks:
Now here as an example consider a ANN that has been trained to learn the following rule categorising the brightness of 2x2 black and white pixel images also as: if it contains 3 or 4 black pixels then it is dark; but if it contains 2, 3 or 4 white pixels then it is bright. So here we can model this with a perceptron through sa pixel then they output +1 if the pixel is white and if -1 then the pixel is black. But here also if the input example is to be categorised as bright when the output unit produces a 1and if the example is dark when the output unit produces a 1. In fact if we choose the weights as in the following diagram where the perceptron will perfectly categorise any image of four pixels by dark or light according to our rule: as there are 4 input units and one for each pixel then they output +1 if the pixel is white and for -1 if the pixel is black. Here also the output unit produces a 1 if the input example is to be categorised as bright and if the example is dark then -1. Whether we choose the weights as in the following diagram then the perceptron will perfectly categorise any image of four pixels through dark or light according to our rule:
Furthermore details we see that in this case there the output unit has a step function through the threshold set to -0.1. But note there the weights in this network are all the same that is not true in the practical case. So now here it is convenient to make the weights going in to a node add up to 1 also, means it is possible to compare them easily. Thus the reason this network perfectly captures our notion of darkness and lightness is it means that if three white pixels are input so then three of the input units produce +1 and one input unit produces -1. Hence this goes into the weighted sum that giving a value of S = 0.25*1 + 0.25*1 + 0.25*1 + 0.25*(-1) = 0.5. As we seen this is greater than the threshold of -0.1, the output node produces +1 that relates to our notion of a bright image. Furthermore details we see that four white pixels will produce a weighted sum of 1 that is greater than the threshold so then two white pixels will produce a sum of 0 and also greater than the threshold. In fact if there are three black pixels then S will be -0.5 that is below the threshold thus the output node will output -1 so the image will be categorised as dark. Actually an image with four black pixels will be categorised as dark.