Question: PCA by SVD (30 points) Consider 3 data points in a 3D space: p1: (1, 2, 0) p2: (2, 1, 0) p3: (0, 0, 0)

PCA by SVD (30 points) Consider 3 data points in a 3D space: p1: (1, 2, 0) p2: (2, 1, 0) p3: (0, 0, 0) (1) What is the mean point? (4 points) (2) Centering the 3 3 data matrix X into Xc (4 points) (3) Compute Xc T Xc (4 points) (4) Find the eigenvalues of Xc T Xc (5 points) Hint: (5) Find the first principal component of X (4 points). Hint: Xc T Xc vi = i 2 vi (6) Find the second principal component of X (4 points) (7) The first two principal components account for how much of the total variance? (5 points

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