Recommender System Study Notes - Nomination(1/6)

• Item CF
• Swing
• User CF

Item CF

Intuition

• If user likes i1 and i1 is similar with i2 -> Then user is likely to like i2

Formula

• $score = \sum_j \text{like}(\text{user}, \text{item}\_j) \times \text{sim}(\text{item}\_j, \text{item})$, to compute Item CF score
• $\text{sim}(i_1, i_2) = \frac{|\mathbf{v}|}{\sqrt{|\mathbf{w}_1| \cdot |\mathbf{w}_2|}}$, to compute similarity, w1 as the user who likes i1, w2 as the set, v as the intersection between i1 and i2.
• $\text{sim}(i*1, i_2) = \frac{\sum*{v \in v} \text{like}(v, i*1) \cdot \text{like}(v, i_2)}{\sqrt{\sum*{u*1 \in w_1} \text{like}^2(u_1, i_1)} \cdot \sqrt{\sum*{u_2 \in w_2} \text{like}^2(u_2, i_2)}}$, to take like score into consideration).

Implementation

Offline:

• User -> Item Indexing
  • return the last-n items with interaction that this user interacts with.
• Item -> Item Indexing
  • compute sim (i, j) maybe maintaining User->Item
  • for each item, find the cloest k items

Online Inference: (user id -> 100 items)

• user id -> last-n items
• for each item in last-n, use item-item to find k items
• Use score formula to compute n * k items’ score
• pick top 100, and output top 100 items as the nomination result in this Item CF Channel

Swing

Intuition

• If two items are not that relavant, but it got forwarded into a same small group, we want to lower the similarity score.

Formula

• u1 -> j1, u2 -> j2
  • $\text{overlap}(u_1, u_2) = |\mathcal{J}_1 \cap \mathcal{J}_2|$
• i1 -> w1, i2 -> w2, v = w1 ∩ w2
  • $\text{sim}(i_1, i_2) = \sum_{u_1 \in V} \sum_{u_2 \in V} \frac{1}{\alpha + \text{overlap}(u_1, u_2)}$, to compute similarity, a is a hyper-parameter
• if overlap is big, then the contribution to similarity becomes low

User CF

Intuition

• I will like the notes which liked by someone who is similar to me.

Formula

• Method1: like, collect, click notes are similar
• Method2: Subscribed authors are similar
• u1 -> j1, u2 -> j2, I = j1 ∩ j2, nl: the number of users who likes l
  • $sim = \text{sim}(u_1, u_2) = \frac{|I|}{\sqrt{|\mathcal{J}_1| \cdot |\mathcal{J}_2|}}$
  • $sim = \text{sim}(u_1, u_2) = \frac{\sum_{I \in I} \frac{1}{\log(1 + n_I)}}{\sqrt{|\mathcal{J}_1| \cdot |\mathcal{J}_2|}}$
• $score = \sum_j \text{sim(user, user}_j\text{)} \times \text{like(user}_j, \text{item)}$

Implementation

Offline:

• User -> Item Indexing
  • return the last-n items with interaction that this user interacts with.
• User -> User Indexing
  • compute sim (i, j)
  • for each user, find the cloest k users

Online:

• user-user indexing: id -> k cloest users
• user-item indexing: for each user, find his/her last-n, use user-item to find n items
• compute score: Use the formula to compute n * k items’ score
• rank: pick top 100, and output top 100 items as the nomination result in this User CF Channel