an enhanced semi supervised recommendation model based on green s function
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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
  • Background
  • Motivation
  • An Enhanced Model
  • Experimental Analysis
  • Conclusion

ICONIP 2010, Sydney, Australia

background
Background
  • Recommendation in Collaborative Filtering

Recommendation

ICONIP 2010, Sydney, Australia

background1
Background
  • Significance
    • Consumer Satisfaction
    • Profit
  • Mathematical Form
    • User-item matrix complete task
    • Rating prediction

Rating for Prediction

User

Item

ICONIP 2010, Sydney, Australia

background2
Background
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Local Similarity Calculation
    • Cosine Similarity
    • Pearson Correlation Coefficient (PCC)

ICONIP 2010, Sydney, Australia

an enhanced model4
An Enhanced Model
  • 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 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 Calculation
    • Defined as the inverse of matrix L with zero-mode discarded

without

ICONIP 2010, Sydney, Australia

an enhanced model7
An Enhanced Model
  • Label Propagation Recommendation
    • rating as label ;
    • Closed form label propagation:

Label Propagation

Label data

Unlabeled data

ICONIP 2010, Sydney, Australia

experimental analysis
Experimental Analysis
  • 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
  • Impact of Weight Parameter

k=5

k=10

ICONIP 2010, Sydney, Australia

experimental analysis2
Experimental Analysis
  • 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
  • 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

slide20
Q&A

Thank you!

ICONIP 2010, Sydney, Australia

slide21
PMF
  • Probabilistic Matrix Factorization
    • Define a conditional distribution over the observed ratings as:

Gaussian Distribution

ICONIP 2010, Sydney, Australia

slide22
PMF
  • PMF
    • Assume zero-mean spherical Gaussian priors on user and item feature
    • By Bayesian Inference:

ICONIP 2010, Sydney, Australia

slide23
PMF
  • 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
  • Algorithm

ICONIP 2010, Sydney, Australia

ad