pattern recognition

Consider the criterion function Jw) required for the Fisher linear discriminant function (a) (4 marks) Fill in the steps leading from Eqs. 96, 98, and 102 to Eq. 103, i.e., from ini -mal? J(w) (96) Sw = S + S2 SB = (m-m2)(m - m2) (98) (102) to W'Sgw J(w) = (103) w'Sww (b) (13 marks) Use matrix method to show that the solution to Eq. 103 is indeed given by Eq. 104, i.e., SBw = ASww (104) (c) (13 marks) At the extreme of J(w), a small change in w must leave J(w) unchanged. Consider a small perturbation away from the optimal, w + Aw, and derive the solution condition of Eq. 104 Consider the criterion function Jw) required for the Fisher linear discriminant function (a) (4 marks) Fill in the steps leading from Eqs. 96, 98, and 102 to Eq. 103, i.e., from ini -mal? J(w) (96) Sw = S + S2 SB = (m-m2)(m - m2) (98) (102) to W'Sgw J(w) = (103) w'Sww (b) (13 marks) Use matrix method to show that the solution to Eq. 103 is indeed given by Eq. 104, i.e., SBw = ASww (104) (c) (13 marks) At the extreme of J(w), a small change in w must leave J(w) unchanged. Consider a small perturbation away from the optimal, w + Aw, and derive the solution condition of Eq. 104