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5 y 4 V Men 3 Boys 2 1 O o O o 1 2 o 3 4 5 o O O x O o O O Figure 1: The data sets 'men' and 'boys' with decision boundaries. Question 1 (a) In some two dimensional space points can be represented by a coordinate pair (x.y). In Figure 1 you see a data set where some points in this space have been classified as 'boys', others as 'men'. You have to write a classifier that separates 'boys' from 'men'.(i) Explain why no single perceptron can learn the classification of boys and men. Use the definition of a perceptron in your explanation. [3 marks] (ii) Determine three perceptrons which correspond to three straight lines surrounding the 'men' points. If a 'men' point is presented to one of the perceptrons, then it should be classified as a '1'. [6 marks] (iii) Combine the three individual perceptrons into a single network that performs the classification correctly. [3 marks] A A A OP A o O O

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a) i. A perceptron is a learning algorithm used for linear classification; it can be interpreted geometrically as an intersecting hyperplane, or algebraically as a classification function over a dot product.

So, in essence, perceptrons can only solve linearly separable problems. A;gebraically, a non linearly separable problem would require from a perceptron to learn conflicting weights (say, the line -0.2x-y<0 is to be classified as Men, though not for all...

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