Alternating Minimization Concept Question
As in the video above, we now want to find U and V that minimize our new objective
(Yai - [UVT]) J = 2 (a,iED
U2 ak a,k
2
i,k
To simplify the problem, we fix U and solve for V, then fix V to be the result from the previous step and solve for U, and repeat this alternate process until we find the solution.
Consider the case k = 1. The matrices U and V reduce to vectors u and v, such that uaUal and v=Vi1
When v is fixed, minimizing J becomes equivalent to minimizing ...
(Yai 2
2
ua
(Yai - uav2 TI2 2 (a,iED
Yai - uav2 2 a,ieD
Yai - uav2 2 D() (aiED 2