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An Enhanced Semi-supervised Recommendation Model Based on Green’s Function. Dingyan Wang and Irwin King Dept. of Computer Science & Engineering The Chinese University of Hong Kong. Outline. Background Motivation An Enhanced Model Experimental Analysis Conclusion. Background.

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An enhanced semi supervised recommendation model based on green s function

An Enhanced Semi-supervised Recommendation Model Based on Green’s Function

Dingyan Wang and Irwin King

Dept. of Computer Science & Engineering

The Chinese University of Hong Kong

ICONIP 2010, Sydney, Australia


Outline
Outline Green’s Function

  • Background

  • Motivation

  • An Enhanced Model

  • Experimental Analysis

  • Conclusion

ICONIP 2010, Sydney, Australia


Background
Background Green’s Function

  • Recommendation in Collaborative Filtering

Recommendation

ICONIP 2010, Sydney, Australia


Background1
Background Green’s Function

  • Significance

    • Consumer Satisfaction

    • Profit

  • Mathematical Form

    • User-item matrix complete task

    • Rating prediction

Rating for Prediction

User

Item

ICONIP 2010, Sydney, Australia


Background2
Background Green’s Function

  • Traditional Recommendation Methods

    • Memory-based method

      • Item-based method, WWW ’01 & SIGIR ’06

      • User-based method, SIGIR ’06

    • Model-based method

      • Probabilistic matrix factorization, SIGIR ’07 & 04

ICONIP 2010, Sydney, Australia


Background3
Background Green’s Function

  • A Novel View of Recommendation [Green’s function recommendation, KDD ’07 & WWW10]

    • Label propagation on a graph

    • Label prediction with semi-supervised learning

2

1

3

4

5

ICONIP 2010, Sydney, Australia


Motivation
Motivation Green’s Function

  • Higher accuracy in label propagation recommendation

  • Importance of graph construction

  • Accuracy Reduction

    • Data Sparsity

      • Some items have no similarity information

    • Information Loss

      • Similarity in a local view

ICONIP 2010, Sydney, Australia


An enhanced model
An Enhanced Model Green’s Function

  • An Enhanced Model Based on Green’s Function

User-Item Rating

Matrix

Predicted User-item

Matrix

Enhanced Item-Graph

Construction

Green’s Function

Calculation

Label

Propagation

ICONIP 2010, Sydney, Australia


An enhanced model1
An Enhanced Model Green’s Function

  • Enhanced Item-Graph Construction

    • Global similarity between items

      • Latent-feature vector similarity

    • Local similarity between items

      • Similarity derived from ratings

    • Global and local consistent similarity

      • Linear combination of global and local similarity

ICONIP 2010, Sydney, Australia


An enhanced model2
An Enhanced Model Green’s Function

  • Global Similarity Calculation

    • Latent features extraction

      • Probabilistic matrix factorization (PMF), NIPS ’08

: M*N rating matrix ; : K*N item-latent matrix : M*K user-latent

: rating of user i for item j; : indicator to show whether user i rated item j.

ICONIP 2010, Sydney, Australia


An enhanced model3
An Enhanced Model Green’s Function

  • Local Similarity Calculation

    • Cosine Similarity

    • Pearson Correlation Coefficient (PCC)

ICONIP 2010, Sydney, Australia


An enhanced model4
An Enhanced Model Green’s Function

  • Global And Local Consistent Similarity (GLCS)

    • Global similarity from item latent matrix

    • Global and Local similarity combination

    • Weighted undirected item-graph

ICONIP 2010, Sydney, Australia


An enhanced model5
An Enhanced Model Green’s Function

  • Green’s Function Calculation (An Example)

    • Given an item-graph

    • Calculate the Laplacian matrix L= D-W

W=

1

2

3

4

D=

5

ICONIP 2010, Sydney, Australia


An enhanced model6
An Enhanced Model Green’s Function

  • Green’s Function Calculation

    • Defined as the inverse of matrix L with zero-mode discarded

without

ICONIP 2010, Sydney, Australia


An enhanced model7
An Enhanced Model Green’s Function

  • Label Propagation Recommendation

    • rating as label ;

    • Closed form label propagation:

Label Propagation

Label data

Unlabeled data

ICONIP 2010, Sydney, Australia


Experimental analysis
Experimental Analysis Green’s Function

  • Dataset

    • MovieLens dataset

  • Metrics

    • Mean Absolute Error (MAE)

    • Mean Zero-one Error (MZOE)

    • Rooted Mean Squared Error (RMSE)

ICONIP 2010, Sydney, Australia


Experimental analysis1
Experimental Analysis Green’s Function

  • Impact of Weight Parameter

k=5

k=10

ICONIP 2010, Sydney, Australia


Experimental analysis2
Experimental Analysis Green’s Function

  • Performance Comparison

    • Previous Green’s function model (GCOS, GPCC), [KDD ’07]

    • Item-based recommendation (ICOS, IPCC)

    • User-based recommendation (UCOS, UPCC)

ICONIP 2010, Sydney, Australia


Conclusion
Conclusion Green’s Function

  • Latent features provide global similarity.

  • Global and local consistent similarity can improve item-graph construction.

  • The enhanced model outperformed other memory-based methods and previous model.

ICONIP 2010, Sydney, Australia


Q Green’s Function&A

Thank you!

ICONIP 2010, Sydney, Australia


P Green’s FunctionMF

  • Probabilistic Matrix Factorization

    • Define a conditional distribution over the observed ratings as:

Gaussian Distribution

ICONIP 2010, Sydney, Australia


P Green’s FunctionMF

  • PMF

    • Assume zero-mean spherical Gaussian priors on user and item feature

    • By Bayesian Inference:

ICONIP 2010, Sydney, Australia


P Green’s FunctionMF

  • PMF

    • Optimization: to maximize the log likelihood of the posterior distribution:

    • Using Gradient Decent in Y, U, V to get local optimal.

ICONIP 2010, Sydney, Australia


Algorithm
Algorithm Green’s Function

  • Algorithm

ICONIP 2010, Sydney, Australia


ICONIP 2010, Sydney, Australia Green’s Function


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