5. 5. (16 marks) (a) What are the four main objectives of Principal Components Analysis (PCA)? (4 marks) (b) Consider 3 data points in the 2-d space: (-4, -2), (0,0), (2,1). (8 marks) i. What is the first principal component (write down the actual vector)? Note that the principal component should be normalised to have unit length. ii. If we project the original data points into the 1-d subspace by the principal com- ponent you choose, what are their coordinates in the 1-d subspace? And what is the biased standard deviation of the projected data? Show all your working out. (c) Which model is often more accurate, SVM or logistic regression? Why? (4 marks)