1 Soft-Margin SVM Dual Derivation [12 pts] Consider the primal formulation of a soft-margin SVM with regularization and offset, where C 0 is a regularization hyperparameter. minimize ||+C +0 &i 0,6, subject to From this, we can obtain the dual formulation. maximize subject to n n Xi i=1 n i=1 y() (. (i) + b) 1 i, i 0, Vi = 1, ..., n. n n ;a;y(i)y()(i) . (1) i=1 j=1 | ry(i) = 0, 0 x(i) [-1.5, -2.1 ]T [-1.9, 0]T [-3.7, -2.5 ]T [0.5, 0.75 ]T [2,3.3]T 2 1 2 3 4 5 6 [ 1.6, -2.5 ]T y (i) Xi 1 1 -1 -1 0 0.322 0 0.497 0 0.175 (b) (2 pt) Based on the above dataset, state which points are support vectors. (c) (3 pt) Use the same dataset and your results from part a ii to find the optimal value of 6 and 7 and use them to classify the following points: [4, 1] and [2, 5]T.