1. Learning with Green’s Function with Application to Semi-Supervised Learning and Recommender System ----Chris Ding, R. Jin, T. Li and H.D. Simon. A Learning Framework using Green’s Function and Kernel Regularization with Application to Recommender System. KDD’07.

2. Outline Green’s Function Graph-Based Semi-supervised Learning with Green’s Function Item-Based Recommendation Using Green’s Function Extension

3. Green’s Function  Given a weighted graph G=(V,E), W= D=  The Graph Laplacian matrix L= D-W. 1 2 4 3 5

4. Green’s Function  Defined as the inverse of L = D-W with zero- mode discarded. discard

5. Semi-Supervised with Green’s Function Green’s Function  Interpreted as an electric resistor network 1 2 3 5 4  Viewed as a similarity metric on a graph

6. Semi-Supervised with Green’s Function Label Propagation  Labeled data &, unlabeled data labeled data unlabeled data  For 2-class problems: For k-class problems: Label Propagation

7. Semi-Supervised with Green’s Function Compared to Harmonic Function  Harmonic Function is an iterative procedure  Outperforms Harmonic Function  7 datasets, 10% as labeled data

8. Recommendation with Green’s Function Item-based Recommendation  To calculate unknown rating by averaging rating of similar items by test users  User-item matrix R, : rates  Item Graph G=(V,E) typical similarity: cosine similarity, conditional probability…

9. Recommendation with Green’s Function 1 2 3 4 56 7

10. Experiments:  Dataset: Movielens : 943 users; 1682 movies; ratings from 1 to 5 Training set: 90,570 records Test set: 9,430 records

11. Recommendation with Green’s Function Results compared to traditional methods: MAE: Mean Absolute Error M0E: Mean Zero-one Error

12. Extension Combination between semi-supervised learning and recommendation? Combine with other recommendation algorithms? Improve graph-based semi-supervised learning with other algorithm?

13. Discussion and Suggestion

14. Thank You!