I have some problems in understanding the solutions to the last question for the 2016 Examination.
Subquestion 1: Since \(u\) also appears in \(||v_u||^2\), why this term is not considered in the derivative? And for the first part of the objective, shouldn't it be like \(\sum_{u~m}{(f_{um}-r_{um})}f_{um}^{'}r_{um}^{'}\)?
Subquestion 2: How to get the function \(f(v,w) = 0.5(vw+c-r)^2\) given the condition that there is only 1 user, 1 moive and the assumption of D = 1?
I am also curious about some general conclusions regarding the knowledge in Matrix Factorization (I failed to find the answer online):
What's the relationship between Hessian and PSD/SD? In other words, what kind of conclusion could we draw if a Hessian is a PSD/SD?
What's the difference between element-wise convex and jointly convex. (I am sorry that these English terminologies is new for me, and it will be great if a specific example can be provided)
2016 Q5 Matrix Factorization
Hi,
I have some problems in understanding the solutions to the last question for the 2016 Examination.
Subquestion 1: Since \(u\) also appears in \(||v_u||^2\), why this term is not considered in the derivative? And for the first part of the objective, shouldn't it be like \(\sum_{u~m}{(f_{um}-r_{um})}f_{um}^{'}r_{um}^{'}\)?
Subquestion 2: How to get the function \(f(v,w) = 0.5(vw+c-r)^2\) given the condition that there is only 1 user, 1 moive and the assumption of D = 1?
I am also curious about some general conclusions regarding the knowledge in Matrix Factorization (I failed to find the answer online):
Thanks!
1
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