Q25: (10 pоints) Item-Item Cоllаbоrаtive FilteringBelow is user-movie rаting matrix with partial ratings available. Please use the item-item collaborative filtering method to estimate the rating of the user #5 for the movie #1. Hints: first use Pearson correlation as similarity by: subtracting mean rating from each movie, then calculating cosine similarities (Sij) between rows. Later, we predict the rating by taking weighted average using the equation: rix=∑j∈N(i;x)Sij⋅rjx∑Sijr_{ix} = frac{sum_{j in N(i;x)} S_{ij} cdot r_{jx}}{sum S_{ij}} where i is the index of an item, x is the index of a user, rjxr_{jx} is the rating of the user x for the item j, N(i;x)N(i;x) is the selected neighbor set of the item i given the user x, and the number of the neighbor set (∣N(i;x)∣|N(i;x)|) is 2.
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