9. Suppose that we are given a training set X₁, X₂, , X_n, with corresponding classifications z₁, z₂, , z_n, where z_i {1, +1} for all i, and we train a linear SVM on this data.

a) For a linear SVM, the scoring function is given in (5.21). For this case, explicitly determine the weight associated with each component of a scored vector.

b) Explain how we could use the SVM weights to reduce the dimensionality of the training data.

c) If we want to reduce the dimensionality, what are the advantages and disadvantages of SVM, as compared to PCA.