Introduction Given a dataset of A data points x, ER" which are labelled by y, e {-1,+1}, /=1,.... N, support vector machine (SVM) aims to find a separating hyperplane (1) : w x+b=0 with we R" and belk 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, +b21 and if y, =-1, w x, +bs-1 for all i =1,....N . Questions 1. (25%) One of the SVM models can be written as the following optimisation problem: minwbu I| wh + c. Eu, S.t. NI=1A "n-12 (9+'x M)'d 1, 20, Vi = 1. .... N, where I will,= [| w, I, the f,-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. 2. (20%) Reformulate the above problem as a linear optimisation problem. Explain in detail how you can solve the resulting optimisation problem in Excel using Open Solver (https://opensolver.org/). 3. (25%) You are given a dataset Data.x/sx of Australian credit approval data generated from https://www.csie.ntu.edu.tw/~cilin/libsvmtools/datasets/binary.html. The first column is the classification and the remaining 14 columns are attributes. There are four binary attributes (1, 8, 9, 11) and four categorical attributes (4, 5, 6, 12) while others are continuous. Explain any data preparation process that one should apply on