The main idea behind SVD$-$based Collaborative Filtering is to approximate the sparse user$-$game matrix with a rank$-$

matrix: $\backslash$Sigma $$

$.$

is also referred to as the number of "factors" which are represented by the columns of $$

or the rows of $$

$.$ Complete the function below that takes in a user$\_$game$\_$mat and a user$\_$idx as usual, and performs SVD$-$based Collaborative Filtering with num$\_$factors and random$\_$state. Likewise, it should return a np$.$ndarray $($or a np$.$matrix$)$ of shape $(1,$ user$\_$game$\_$mat.shape$[1])$ that represents the predicted playtime for each game for the user at user$\_$idx.The main idea behind SVD$-$based Collaborative Filtering is to approximate the sparse user$-$game matrix with a rank$-$k matrix: $R$~~$U_k{}_k{V}_k^T*k$ is also

referred to as the number of "factors" which are represented by the columns of $U_k$ or the rows of $V_k^T.$ Complete the function below that takes in a

user$\_$game$\_$mat and a user$\_$idx as usual, and performs SVD$-$based Collaborative Filtering with num$\_$factors and random$\_$state $.$ Likewise, it

should return a np$.$ndarray $($or a np$.$matrix$)$ of shape $(1,$ user$\_$game$\_$mat.shape $[1])$ that represents the predicted playtime for each game

for the user at user$\_$idx.

Hint: The idea of SVD$-$based Collaborative Filtering may look simple, but it may well take a while to figure out how to implement that with sklearn

$($unless you implement your own SVD$).$ It might be useful to think about what data you have available, what methods are associated with sklearn $\text{'}$s SVD

and what the shapes of your inputs to those methods should be$.$ The ideal solution uses just one line of code for making predictions.