$7.$ Unrated items for the target user

# Select all unrated items for the target user

unrated$\_$target $=$ r$\_$matrix$[$r$\_$matrix$[$userX$].$isna$()][$topn$]$

# rename the axis of the unrated item matrix

unrated$\_$target $=$ unrated$\_$target.rename$\_$axis$(\text{'}$movie$\_$id$\text{'},$ axis$=1).$rename$\_$axis$($None$,$ axis$=0)$

# Remove items that are not rated by all top n neighbors

unrated$\_$target.dropna$($axis $=0,$ how $=$ 'all', inplace $=$ True$)$

unrated$\_$target.head$()$

$8.$ Predict the rating

# Randomly select the item to be rated

itemX $=7$

# Predict the rating value for the unrated item

predicted$\_$value $=$ rXmean $+(($neighbors$\_$sim.T$.$dot$($averaged$\_$neighbors$\_$ratings.loc$[$itemX$].$T$).$values$[0])/$ neighbors$\_$sim.sum$())$

$9.$ Write a function that predicts a rating using Cosine Similarity:

def predict$\_$rating$\_$cosine$\_$similarity$($user$\_$id$,$ item$\_$id$,$ user$\_$item$\_$matrix, user$\_$similarity$)$:

$"""$

Predicts the rating for a given user and item using Cosine Similarity.

Parameters:

$-$ user$\_$id $($int$)$: ID of the target user.

$-$ item$\_$id $($int$)$: ID of the target item.

$-$ user$\_$item$\_$matrix $($pd$.$DataFrame$)$: User$-$item matrix with ratings.

$-$ user$\_$similarity $($np$.$ndarray$)$: Cosine similarity matrix between users.

Returns:

$-$ float: Predicted rating for the user on the specified item.

$"""$

# Function implementation will go here

$10.$ Predicts rating using Cosine Similarity for User $5$ and item $7$:

# Example usage

user$\_$id$\_$example $=5$

item$\_$id$\_$example $=7$

$11.$ Handle Cold Start Problems for User and Item:

To enhance the robustness of the recommender system, address the cold start problem for both users and items. In the case of a new user, return the mean rating of the specified item. If the item is new, recommend the highest$-$rated item based on existing data.