begin{algorithm}[h]
begin{algorithmic}[1]
caption{An Optimization Algorithm of our framework}
REQUIRE the observed user-movie rating data $textbf{R}$, learning rate $gamma$, regularization $lambda_1$,$lambda_2$, component weight $alpha$, $P_{v_j}$ for $v_j in P$
ENSURE the full rating matrix of user-movie\
STATE Initialize VGG16 by using pretrained weights on ImageNet
STATE Initialize $U,V,W$ with Normal distribution $N(0, 0.01)$
REPEAT
{
STATE
Update $U$ as $U leftarrow U + frac{partial F}{partial U}$
STATE
Update $V$ as $V leftarrow V + frac{partial F}{partial V}$
STATE
Update $W$ as $W leftarrow W + frac{partial F}{partial W}$
STATE
fine-tune $CNN$ using back propagation
}
UNTIL{convergence;}
RETURN the top-k movie list of each user based on $textbf{U}^Ttextbf{V}$
end{algorithmic}
end{algorithm}
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