I don't understand why there is an exact solution to the matrix factorization problem... Didn't we see in class that the problem is not identifiable, hence there are multiple solutions ?
I think that :
If you assume that \(X \in |R^{NxD}\) and if you take \(K = D\) then you have : \(X = WZ^T\)
With \(W \in |R^{NxD}\) and \(Z \in |R^{DxD}\). If you set \(Z = I_{D} \) and \(W = X \) then you have an exact solution
problem 15, exam 2018
Hello,
I don't understand why there is an exact solution to the matrix factorization problem... Didn't we see in class that the problem is not identifiable, hence there are multiple solutions ?
Thanks for your help
I think that :
If you assume that \(X \in |R^{NxD}\) and if you take \(K = D\) then you have :
\(X = WZ^T\)
With \(W \in |R^{NxD}\) and \(Z \in |R^{DxD}\). If you set \(Z = I_{D} \) and \(W = X \) then you have an exact solution
4
Oh, I see, thanks a lot, I understand now, I misread the answer as "there is exactly one solution"
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