## Recommender System: Recommendation Algorithms

- Non-Personalized Summary Statistics
- Mean-based:
- Background: In a 5-star scale rating system
- Symbols:
- $U_i$ for users who rated item $i$
- $r_{ui}$ for rating by user $u$ to item $i$
- $|U_i|$ for number of user who rated item $i$
- $\alpha$ for damping factor, larger would cause the rating floats more smooth
- $\mu$ for global rating across all items and users
- $s(i)$ for score of item $i$

- Mean: $s(i) = \dfrac{\sum_{u \in U_i}^n r_{ui}}{|U_i|}$
- Damped Mean: $s(i) = \dfrac{\sum_{u \in U_i}^n r_{ui} + \alpha\mu}{|U_i| + \alpha}$

- Association-based:
- Background: typically in a shop that customs buying products
- Symbols:
- $P(i|j)$: probability of buying i when already buying j

- Basic Association, measuring probability by counting:
- Story: How many percentage of people who buying i also buying j among the whole people who buying i?
- Formula: $P(i|j) = \dfrac{P(i \land j)}{P(j)} = \dfrac{|U_i \cap U_j| / |U|}{|U_j| / |U|}$
- Bad case: if j is popular, then the result is bad

- Bayes's Law: $P(i|j) = \dfrac{P(j|i) P(i)}{P(j)}$
- Lift Association, measuring score by counting:
- Story: people who bought i and j together more often means i and j are more associative
- Formula: $s(i|j) = \dfrac{P(j \land i)}{P(i) P(j)}$

- Content-Based Filtering
- Information Filtering
- Knowledge-Based

- Collaborative Filtering
- User-User
- Item-Item
- Dimensionality Reduction

- Others
- Critique / Interview Based Recommendations
- Hybrid Techniques