Given data fame X that consists of 6 data objects, each with 2 attributes: | | X1 | X2 | |---|---|---| | 1 | 19 | 12 | | 2 | 22 | 6 | | 3 | 6 | 9 | | 4 | 3 | 15 | | 5 | 2 | 13 | | 6 | 20 | 5 | 1. [1pt] Convert data frame into centered matrix 2. [1pt] Compute covariance matrix CX (with estimated sample mean version) 3. [1pt] Compute characteristic polynomial of CX and eigenvalues of CX 4. [1pt] find principal components/rotation matrix P (such that YT = PXT) 5. [1pt] how much variance (%) is explained by new first principal component p1? 6. [1pt] Compute PCA transformation (rotation) of X (without centering) to obtain Y = XPT.
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Let's denote the original attributes as X1 and X2. The mean of X1, μX1, and the mean of X2, μX2, are calculated as follows: - μX1 = (19 + 22 + 6 + 3 + 2 + 20) / 6 - μX2 = (12 + 6 + 9 + 15 + 13 + 5) / 6 Calculating the means: - μX1 = 72 / 6 = 12 - μX2 = 60 / 6 = Show more…
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