Recommender-System Algorithms #1

Collaborative Filtering

  • CF
  • User-Based CF
  • Item-Based CF
  • KNN CF

Best for: User-item recommendations Aliases: CF, User-Based CF, Item-Based CF, KNN CF

How it works

$$\hat{r}_{ui}=\bar{r}_u+\frac{\sum_{v\in N(u)}\mathrm{sim}(u,v)(r_{vi}-\bar{r}_v)}{\sum_{v\in N(u)}|\mathrm{sim}(u,v)|}$$

User-based CF predicts a rating as a mean-centred weighted average over neighbour users $N(u)$, using similarity $\mathrm{sim}(u,v)$ such as cosine $\frac{r_u\cdot r_v}{\|r_u\|\|r_v\|}$ or Pearson correlation on co-rated items. Item-based CF reverses the roles and aggregates over items most similar to the target. Memory-based KNN variants are simple and interpretable but scale poorly, and similarities shrink towards zero when few ratings are shared, motivating shrinkage or regularised estimates.

When to use

Recommending from user-item interaction matrices when you have enough ratings/interactions per user.

Watch out

Cold-start for new users and items; sparse data hurts; naive KNN scales poorly to large catalogs.

Common fields

E-commerce · streaming · news feeds