1. (20 points) Maximum Margin Classifier and Support Vector Machine. You are given four training samples. where xi1 and xi2 are the features and yi is the label of the two classes. (a) (10 points) Is it possible to use a linear function xi1+xi2+b=0 to perfectly separate the two classes for some parameter b ? If it is possible, what is the value of b that maximize the margin? What is the maximum margin? (b) (10 points) Consider an SVM classifier, y={11ifz>0,ifz0,z=i=1NiyiK(x,xi)+b for the kernel function, K(x,xi):={10ifxxi2r2,ifxxi2>r2 where r>0 is some parameter and w2 denotes the squared norm w2=w12+w22. Find parameters r,i and b such that the SVM classifier makes no errors on the training data. Use at most two non-zero values of i. (Hint: You should be able to find the parameters directly, instead of solving an optimization.)