2. (a) What is a linear scoring function? How can it be used for classifying test samples into positive and negative?[4 marks] (b) Consider the linear scoring function with parameters b = 2 and w = (2, −1, 1),where w are the weights. Calculate the predicted label for the test sample (c) What is the margin of a given separating hyperplane? (d) What is meant by the maximum margin hyperplane (also known as the optimal separating hyperplane)? (e) Define the notion of a support vector in the context of maximum margin classifiers.[3 marks] (f) Consider the following training set with two features: the positive samples are (0, 2) and (1, 2); ·the negative samples are (0,0), (0, 1), and (−1, 1). (g) Give an example of a training set for the problem of binary classification with only one feature where no separating hyperplane exists.[3 marks] (h) State an optimization problem whose solution is the maximum margin hyper-plane. Give the geometric interpretation of each formula in this optimization problem.[6 marks] (i) State the soft margin classifier as an optimization problem. Give the geometric interpretation of this problem.