Suppose the mean corrected data matrix is XC. Decompose it with SVD as XC=UA*V. Use (n-1)U...

 

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Suppose the mean corrected data matrix is XC. Decompose it with SVD as XC=UA*V. Use (n-1)U as the coordinates for the n observations and A*V/n-1 as the coordinates for the p- variables. Prove that the correlation of two variables is reflected by the angle between the two corresponding vectors of the two variables. Suppose the mean corrected data matrix is XC. Decompose it with SVD as XC=UA*V. Use (n-1)U as the coordinates for the n observations and A*V/n-1 as the coordinates for the p- variables. Prove that the correlation of two variables is reflected by the angle between the two corresponding vectors of the two variables.

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Let XC be the mean corrected data matrix with dimensions n x p and let XC UA V be the singular value decomposition of XC First we can define the coord... View the full answer