Support Vector Machines topic

Consider the following linearly separable training data set:

D = { ((3, 4), 1),

((2, 3), 1),

((2, 1), 1),

((1, 2), 1),

((1, 3), 1),

((4, 4), 1) }

a) Formulate the optimization function as well as the constraints for the corresponding linear max- imum margin optimization problem without a regularization term. Also show the corresponding Lagrangian as well as the Lagrangian Dual for this problem.

b) Manually perform 2 iterations of the SMO algorithm on this data. You do not have to use any specific heuristic to pick the two parameters in each iteration.

c) Use a SVM solver (e.g. MatLab's fitcsvm function) to learn the linear SVM parameters for this problem. Show the resulting decision boundary and identify the support vectors in this problem.

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Instructions

1You only need to implement it for this specific network, not for general networks.

2You need to assign each weight randomly to make sure that the weights of the units are not identical.