6.2 ( ) In this exercise, we develop a dual formulation of the perceptron learning algorithm. Using the perceptron learning rule (4.55), show that the learned weight vector w can be written as a linear combination of the vectors tnφ(xn) where tn ∈

{−1, +1}. Denote the coefficients of this linear combination by αn and derive a formulation of the perceptron learning algorithm, and the predictive function for the perceptron, in terms of the αn. Show that the feature vector φ(x) enters only in the form of the kernel function k(x, x) = φ(x)Tφ(x).