User-based Nearest-neighbuor Collaborative Filtering (Recommendation)

Definition

User-based Nearest-neighbour Collaborative Filtering (Recommendation)

User-based nearest-neighbour collaborative filtering is a collaborative filtering method that predicts an active user $u$‘s rating of an unseen item $i$ from the ratings given by users whose past ratings resemble those of $u$.

Let $N_k(u;i)$ be the $k$ users most similar to $u$ among those who have rated $i$. The basic unweighted estimate is

$${\hat{r}}_{ui}=\frac{1}{|N_k(u;i)|}\sum _{v\in N_k(u;i)}{r}_{vi}.$$

The method finds peers using items rated by both users, transfers those peers’ ratings of $i$ to $u$, and repeats this estimate for every item unseen by $u$. The items with the largest predicted ratings are recommended. Variants weight each peer by user similarity or correct for differences in users’ typical rating levels.