Support Vector Machines problem

1. Consider the following training set of 16 points. The eight purple squares are positive examples, and the eight green circles are negative examples. (5,10) (7,10) (1,8) (3,8) (5,8) (7,8) (1,6) (3,6) (5,6) ((7,6) (1,4) (3,4) (5,4) ((7,4)) (1,2) (3,2) We propose to use the diagonal line with slope +1 and intercept +2 as a decision boundary, with positive examples above and negative examples below. However, like any linear boundary for this training set, some examples are misclassified. We can measure the goodness of the boundary by computing all the slack variables that exceed 0, and then using them in one of several objective functions. In this problem, we shall only concern ourselves with computing the slack variables, not an objective function. To be specific, suppose the boundary is written in the form w.x+b=0, where w=(-1.1) and b =-2. Note that we can scale the three numbers involved as we wish, and so doing changes the margin around the boundary. However, we want to consider this specific boundary and margin. Determine the slack for each of the 16 points. Then, identify the correct statement in the list below. a) The slack for (5.6) is 0. Ob) The slack for (3.4) is 0. Oc) The slack for (7,8) is 0. Od) The slack for (1,4) is 0. 1. Consider the following training set of 16 points. The eight purple squares are positive examples, and the eight green circles are negative examples. (5,10) (7,10) (1,8) (3,8) (5,8) (7,8) (1,6) (3,6) (5,6) ((7,6) (1,4) (3,4) (5,4) ((7,4)) (1,2) (3,2) We propose to use the diagonal line with slope +1 and intercept +2 as a decision boundary, with positive examples above and negative examples below. However, like any linear boundary for this training set, some examples are misclassified. We can measure the goodness of the boundary by computing all the slack variables that exceed 0, and then using them in one of several objective functions. In this problem, we shall only concern ourselves with computing the slack variables, not an objective function. To be specific, suppose the boundary is written in the form w.x+b=0, where w=(-1.1) and b =-2. Note that we can scale the three numbers involved as we wish, and so doing changes the margin around the boundary. However, we want to consider this specific boundary and margin. Determine the slack for each of the 16 points. Then, identify the correct statement in the list below. a) The slack for (5.6) is 0. Ob) The slack for (3.4) is 0. Oc) The slack for (7,8) is 0. Od) The slack for (1,4) is 0