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.

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Presentation transcript:

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

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

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

Semi-Supervised with Green’s Function Green’s Function  Interpreted as an electric resistor network  Viewed as a similarity metric on a graph

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

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

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…

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

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

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

Discussion and Suggestion

Thank You!