Given a training set Dwith a separation margin 0, the original perceptron algorithm predicts a mistake when ywn|x < 0. As we have discussed in

Given a training set Dwith a separation margin 0, the original perceptron algorithm predicts a mistake when yw¹nº|x < 0. As we have discussed in Section 6.1, this algorithm converges to a linear classifier that can perfectly separate Dbut does not necessarily achieve the maximum margin. The margin perceptron algorithm extends Algorithm 6.4 to approximately maximize the margin in the perceptron algorithm, where it is considered to be a mistake when y w¹nº|x kw¹nº k

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2 , where > 0 is a parameter. Prove that the number of mistakes made by the margin perceptron algorithm is at most 8 2 0 if  0.