I question 6 of 2018's exam, the fact "In PCA, the first principale direction is the eigenvector of the data matrix X with largest associated eigenvalue" is not marked as correct. How come it is wrong ? Isn't it the reason why we only keep the largest eigenvalues of the SVD decomposition when we want to compress information using SVD ?
This question was not that clear according to me either, the fact is that here we consider that X is a data matrix with means that it is of size N*D (not squared matrix thus no PCA). That's why, the solution is not correct if the question was of XX^T or XX^T the solution would have been correct. Don't mess up everything, PCA is a particular case of SVD where the matrix is squared. For a SVD decomposition, we do not talk about eigenvalues but singular values. The rest you said is correct.
first eigenvalue of SVD Decomposition
Good evening,
I question 6 of 2018's exam, the fact "In PCA, the first principale direction is the eigenvector of the data matrix X with largest associated eigenvalue" is not marked as correct. How come it is wrong ? Isn't it the reason why we only keep the largest eigenvalues of the SVD decomposition when we want to compress information using SVD ?
Thanks for your help
1
This question was not that clear according to me either, the fact is that here we consider that X is a data matrix with means that it is of size N*D (not squared matrix thus no PCA). That's why, the solution is not correct if the question was of XX^T or XX^T the solution would have been correct. Don't mess up everything, PCA is a particular case of SVD where the matrix is squared. For a SVD decomposition, we do not talk about eigenvalues but singular values. The rest you said is correct.
3
Yes, definitely, I was confused and answered too fast to the question, thanks a lot for your help.
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