Part 1 In the case of normally distributed classes, discriminant functions are linear (straight lines, planes, and hyperplanes for two-, three-, and n-dimensional feature vectors, respectively) when the covariances matrices of corresponding classes are equal. Confirm this by deriving discriminant functions for a binary classification problem. Given: 1 P(x[ ) q) = (27) "/2 21/2 exp (-7 (X - H, ) E-' (x - H)); q=1,2 Prove that linear discriminant functions gq ( X ) = U. E x - ZHE Hq+ In P(yq); q = 1, 2 And decision boundary g(x) = gi(x) - gz(x) = 0 is given by g ( x) = w xtwo=0 wx + wo = ( H , - H? ) E -' x - } ( HI E - ' H, - HZ E- H2) + In P(VI) P(v2) (Hint: Use equations 3.61-3.62 in the textbook) Part 2 Perform two iterations of the gradient algorithm to find the minima of E(w) = 2w1 +2w1w2 +5wz The starting point is w = [2 -2]