Given a dataset of N data points x, Rd which are labelled by y, {-1,+1}, i=1,...,N, support vector machine (SVM) aims to find a separating hyperplane (H): w'x+b=0 with werd and ber that separates x, into two classes defined by y;, i=1,..., N. Ideally, one would like to make sure that if y;=+1, w x +b1 and if y =-1, wx, + b -1 for all i = 1,..., N. 1. (25%) One of the SVM models can be written as the following optimisation problem: N || w || +C. u, i=1 min where | w w,b,u y;(wx; +b)1u;, \i=1,...,N, u, 0, Vi=1,..., N, -norm and C> 0 is a parameter. Explain why this optimisation problem can be used to find a suitable separating hyperplane to separate the given data into two classes. Explain the additional decision variables u, the constraints, and the two components of the objective function. s.t. d =w; \, the j=1