Exercise 1 Consider the following two datasets. Dataset 1 0.0 1.3 3.4 5.0 7.4 Dataset 2 -1.0 2.0 2.4 2.8 9.1 where each entry stands for a feature. You are required to calculate the mean and variance for each dataset and discuss which dataset consists of data points spreading out much more. Exercise 2 The algorithm to produce several principal components (shown at the last page of the slide) depends on the update of dataset X to X' as follows: X':= {r rAA" | 1 X} where X is an M x N-matrix for the number M of data points and the number N of features, and A is a parameter (weight) column vector of the size N for computing principal components on X. Confirm A is no informative on X' by proving x'A equivalent to 0 for each a' X