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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 TAAT | 2 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 ' e X'. Algorithm to find M PCAS = Let X be a set of m-dimensional vectors, i = 1 Repeat the following steps M times o Identify parameters A = [a], ...., am)" of F by A = aj,. maximizing Var({F(x) | XEXCR"}} For x E X, let F(x) be the i-th PC of x OX := {x xAAT | x X}, i :=i+1