Weighted By Taste, Not By Genre

A neighbourhood recommender predicts user uu's rating for item ii as the similarity-weighted average of ratings from users who already rated it:

r^ui=∑vsuv rvi∑vsuv\hat{r}{ui} = \frac{\sum{v} s_{uv} , r_{vi}}{\sum_{v} s_{uv}}

Three neighbours have rated the film Dune:

neighbour similarity to uu rating of Dune
A 0.8 5
B 0.4 2
C 0.2 1

What does the model predict on the 1 to 5 scale?

A

≈1.67\approx 1.67

B

≈3.57\approx 3.57

C

≈2.67\approx 2.67

D

5.05.0