Collaborative Filtering Based on Star Users

Qiang Liu with Bingfei Cheng and Congfu Xu

College of Computer Science and Technology

Zhejiang University Hangzhou, Zhejiang 310027, China

2012dtd@gmail.com

ICTAI 2011, Boca Raton November 7, 2011

Outline

Introduction Star-user-based Collaborative Filtering Experimental Results Conclusion

INTRODUCTION

Collaborative Filtering

Neighborhood-based

Model-based

Collaborative Filtering(CF)

User-based Item-based

Bayesian Model Factorization Model Maximum Entropy Classification or Clustering ……

Motivation To improve the most widely used

technology in real-life recommender systems.

Neighborhood Model Similarity between users：

◦ Pearson：cov(𝑎,𝑏)𝜎𝑎𝜎𝑏

◦ Cosine: 𝑎∙𝑏𝑎 𝑏

◦ Other similarity measures

Weighted sum of neighbors’ ratings:

◦ 𝒑𝒂,𝒊 = 𝒓𝒂 + ∑ 𝒓𝒖,𝒊−𝒓𝒖 ∙ 𝒘𝒂,𝒖𝒖∈𝑼∑ 𝒘𝒂,𝒖𝒖∈𝑼

Common items：1,4,6 Rating vectors of common items： a=[1,4,5] b=[2,2,5]

Challenges faced by traditional methods

Matching similar users (computing similarities ): Sparsity and noise Scalability ……

STAR-USER-BASED CF

The MPN users Let A, B, C, D are neighbors of users A, B,

C, D respectively. Then area E is the set of the most

popular neighbors(MPN).

What is star user

Star users are special users who have rated all items with relatively stable standard.

We maintain a small set of star users, and treat them as fixed neighbors of every general user

Problem Formulation

Filling the following matrix ℛ ∈ 𝑅𝐻×𝑁.

𝒊𝟏 … 𝒊𝒊 … 𝒊𝑵

𝒔𝟏 ? . . . ?

… . . . . .

𝒔𝒔 . . 𝑟𝑠,𝑖 . .

... . . . . .

𝒔𝑯 ? . . . ?

Star users(H)

Items (N)

Prediction Model Selecting Star Neighbors:

Generate predictions

based on star users’ ratings:

𝒑𝒖,𝒊 = 𝒓�𝒖 + ∑ 𝒓𝒔,𝒊−𝒓𝒔 ∙ 𝒘𝒖,𝒔𝒔∈𝑺∑ 𝒘𝒖,𝒔𝒔∈𝑺

The parameters are 𝑟𝑠,𝑖 and 𝑤𝑢,𝑠.

𝒖𝟏 … 𝒖𝒊 … 𝒖𝑴

𝒔𝟏 . . . . .

… . . . . .

𝒔𝒔 . . 𝑤𝑢,𝑠 . .

... . . . . .

𝒔𝑯 . . . . .

General Users (M)

Star Users (H

)

Relationship Matrix W

How we get star users（1）

Training Stage: 1. Initialization star user matrix ℛ. 2. Predict each rating �̂�𝑢,𝑖 in the training set:

3. The residual is and the gradient of 𝑒𝑢,𝑖

2 is:

�̂�𝑢,𝑖 = �̅�𝑢 +∑ (𝑟𝑠,𝑖 − �̅�𝑠) × 𝑤𝑢,𝑠𝑠∈𝑆

∑ 𝑤𝑢,𝑠𝑠∈𝑆

𝑒𝑢,𝑖 = 𝑟𝑢,𝑖 − �̂�𝑢,𝑖

𝜕𝜕𝑟𝑠,𝑖

𝑒𝑢,𝑖2 = −2𝑒𝑢,𝑖 ∙

𝑁−1𝑁 ∙𝑤𝑢,𝑠

∑ 𝑤𝑢,𝑠𝑠∈𝑆

How we get star users（2）

Training Stage: 4. Update each element of matrix ℛ:

5. Repeat steps 2 to 4 until convergence.

𝑟𝑠,𝑖 ← 𝑟𝑠,𝑖 + 𝜂 ∙ 𝑒𝑢,𝑖 ∙𝑤𝑢,𝑠

∑ 𝑤𝑢,𝑠𝑠∈𝑆

How we get star users（3）

Parameters: ◦ 𝛼(users):The update frequency of �̅�𝑠 . ◦ 𝛽 𝑖𝑖𝑒𝑟𝑖𝑖𝑖𝑖𝑖𝑠 :The update frequency of 𝑤𝑢,𝑠 ∈ 𝑊for each u, and s.

w𝑢,𝑠 is computed using Pearson Correlation

Maintain the relationship matrix W: 𝑊 ∈ 𝑅𝑀×𝐻

until recommending stage.

EXPERIMENTAL RESULTS

Results on MovieLens Dataset

Time requirement comparison

RMSE of our approach against various H and comparison with kNN

Item-based Model

We firstly train a small set of star items instead of star users.

Predictions are computed as: 𝑝𝑎,𝑖 = �̅�𝑖 +

∑ 𝑟𝑎,𝑠 − 𝑟𝑠� × 𝑤𝑠,𝑗𝑠∈𝑆′

∑ 𝑤𝑠,𝑗𝑠∈𝑆′

Results on Netflix Dataset

Our approach with different values of learning rate

Our approach with different values of H

Discussion

Comparison with kNN

◦ Accuracy ◦ Data Sparsity ◦ Scalability 𝛰 𝑀2 × 𝑁′

→ 𝛰(𝑀 × 𝐻 × 𝑁′) where 𝐻 ≪ 𝑀.

Comparison with SVD

◦ Scientific explanation ◦ Parameters ◦ Updating

CONCLUSION

Summary

We proposed a novel CF model based on star users.

The original intention is to improve traditional neighborhood-based CF model.

Experimental results on two datasets verified the effectiveness of our approach.

Future work

Incorporating contextual information into our model.

Validating our approach in practical applications.

THANK YOU