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Show that maximization of the class separation criterion given by (4.23) with respect to w, using a Lagrange multiplier to enforce the constraint w?w =

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Show that maximization of the class separation criterion given by (4.23) with respect to w, using a Lagrange multiplier to enforce the constraint w?w = 1, leads to the result that | W X (m2 m). hint: Lagrange multipliers provides a strategy for finding the maxima and minima of a function subject to constraints. For example, maximize f(x, y) subject to g(x, y) = c. We introduce a new variable (^) called a Lagrange multiplier, and define the Lagrange function A(x, y, 1) = f(x, y) + 1. (g(x,y) c). The extrema can be found by solving the equation array A a = 0 Show that maximization of the class separation criterion given by (4.23) with respect to w, using a Lagrange multiplier to enforce the constraint w?w = 1, leads to the result that | W X (m2 m). hint: Lagrange multipliers provides a strategy for finding the maxima and minima of a function subject to constraints. For example, maximize f(x, y) subject to g(x, y) = c. We introduce a new variable (^) called a Lagrange multiplier, and define the Lagrange function A(x, y, 1) = f(x, y) + 1. (g(x,y) c). The extrema can be found by solving the equation array A a = 0

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