Prove that the perceptron training algorithm given in Eqs. (12.2-34) through (12.2-36) con...

Prove that the perceptron training algorithm given in Eqs. (12.2-34) through (12.2-36) converges in a finite number of steps if the training pattern sets are linearly separable. [Hint: Multiply the patterns of class ω2 by − 1 and consider a nonnegative threshold, T, so that the perceptron training algorithm (with c = 1) is expressed as w(k + 1) = w(k),if wT(k)y(k) > T, and w(k + 1) = w(k) + y(k) otherwise. You may need to use the Cauchy-Schwartz inequality: ||a||2||b||2 ≥ (aTb)2.]

(12.2-34)

(12.2-35)

(12.2-36)