Question: 18. (3 pts.) PCA. The plot below shows a sample drawn from a two dimensional multivariate Normal (Gaussian) distribution. Define vectors v1 and v2 as

18. (3 pts.) PCA. The plot below shows a sample drawn from a two dimensional multivariate Normal (Gaussian) distribution. Define vectors v1 and v2 as the directions of the first and second principal components, after applying PCA to the dataset, where | v, | = |v2| |=1. Data 10 . . . . . 9 .. . A . : . . : . . . .X . . .X 8 XX : B . . . . X. . . .. X XXX . . . . .. . . K . 6 . . . XX 5 .. . X X. . " . X MX xxX . : . . " . X . . . X ' . .. . . ... N XOX X2 . . . . X : X X O 6 7 8 9 10 0 1 2 3 4 5 (i) Sketch and label v1 and v2 in the figure above. The arrows should originate from the mean of the distribution. You do not need to compute the actual PCA procedure, instead simply visually estimate the directions of the arrows.(ii) Which point (A or B) would have the higher reconstruction error after projecting onto the first principal component direction v1? Circle one: Point A Point B

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