Hi, I have a few questions regarding the lecture notes of ALS:
First of all, what is the cost of ALS with no missing observations ? When calculating it on my own I arrived to the following result:
For the optimal Z , cost = \(\(K^2\) D ) + \(K^3 \) + \(K* D * N \)
For the optimal W , cost = \(\(K^2\) N ) + \(K^3 \) + \(K* D * N \)
--> The first term is obtained by multiplying \(W^T\) and W for optimal Z, and multiplying \(Z^T\) and Z for optimal W. The second term is from taking the inverse of a KxK matrix. And the last term from multiplying a KxD matrix with the DxN matrix X.
Is this the correct answer ?
Also, at the end of the lecture notes it's also asked: how can you reduce the cost if D and N are large ? I actually have no idea how to do this..
And my last question is regarding the solution from ALS: since our the objective function is not jointly convex in W and Z this solution is not the global optimum, right ? So should we perform multiple steps of ALS to verify whether the optimum obtained is indeed any good or does it not matter much in practice ?
Cost of ALS
Hi, I have a few questions regarding the lecture notes of ALS:
First of all, what is the cost of ALS with no missing observations ? When calculating it on my own I arrived to the following result:
--> The first term is obtained by multiplying \(W^T\) and W for optimal Z, and multiplying \(Z^T\) and Z for optimal W. The second term is from taking the inverse of a KxK matrix. And the last term from multiplying a KxD matrix with the DxN matrix X.
Is this the correct answer ?
Also, at the end of the lecture notes it's also asked: how can you reduce the cost if D and N are large ? I actually have no idea how to do this..
And my last question is regarding the solution from ALS: since our the objective function is not jointly convex in W and Z this solution is not the global optimum, right ? So should we perform multiple steps of ALS to verify whether the optimum obtained is indeed any good or does it not matter much in practice ?
Best regards and thank you in advance.
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