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Learning with Green’s Function with Application to Semi-Supervised Learning and Recommender System

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. Outline. Green’s Function

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Learning with Green’s Function with Application to Semi-Supervised Learning and Recommender System

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

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

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

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

  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 2 3 1 7 4 6 • Recommendation with Green’s Function 5

  10. Recommendation with Green’s Function • 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 Any Suggestion? Any Inspiration?

  14. Thank You!

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