2. In this problem, you will compute a maximum margin classifier by hand. Consider the following...

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2. In this problem, you will compute a maximum margin classifier by hand. Consider the following data set: Obs. x1 x2 Y 1 0.4 0.5 1 2 0.5 0.6 -1 3 1.0 0.4 -1 4 0.8 0.9 -1 5 0.2 0.6 1 6 0.4 0.4 1 7 0.9 0.8 -1 8 0.2 0.1 1 (a) Plot the data and sketch the optimal (maximum margin) separating hyperplane. Using basic geometric principles (as we did in class) write the equation for this hyperplane in the form Bo + x = 0. (b) What is the normal vector to the maximum margin hyperplane? What is the magnitude of the maximal margin? (c) Identify all support vectors for the maximum margin hyperplane. (d) Solve the dual to this "hard margin classifier" problem, proving that your solution in (a) is correct. That is, i. Compute the Lagrange multipliers a; for the dual problem. ii. Show that in (c). iii. Compute Bo. ies vixi, where i = ay; and S is the set of support vectors you identified 2. In this problem, you will compute a maximum margin classifier by hand. Consider the following data set: Obs. x1 x2 Y 1 0.4 0.5 1 2 0.5 0.6 -1 3 1.0 0.4 -1 4 0.8 0.9 -1 5 0.2 0.6 1 6 0.4 0.4 1 7 0.9 0.8 -1 8 0.2 0.1 1 (a) Plot the data and sketch the optimal (maximum margin) separating hyperplane. Using basic geometric principles (as we did in class) write the equation for this hyperplane in the form Bo + x = 0. (b) What is the normal vector to the maximum margin hyperplane? What is the magnitude of the maximal margin? (c) Identify all support vectors for the maximum margin hyperplane. (d) Solve the dual to this "hard margin classifier" problem, proving that your solution in (a) is correct. That is, i. Compute the Lagrange multipliers a; for the dual problem. ii. Show that in (c). iii. Compute Bo. ies vixi, where i = ay; and S is the set of support vectors you identified