Learning%20with%20Green

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Learning with Greens Function with Application
to Semi-Supervised Learning and Recommender System

• ----Chris Ding, R. Jin, T. Li and H.D. Simon.
• A Learning Framework using Greens Function and
  Kernel Regularization with Application to
  Recommender System. KDD07.

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Outline

• Greens Function
• Graph-Based Semi-supervised Learning with Greens
  Function
• Item-Based Recommendation Using Greens Function
• Extension

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Greens Function

• Greens Function
• Given a weighted graph G(V,E),
• W
• D
• The Graph Laplacian matrix L D-W.

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Greens Function

• Greens Function
• Defined as the inverse of L D-W with zero-mode
  discarded.
• discard

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Semi-Supervised with Greens Function

• Greens Function
• Interpreted as an electric resistor network

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• Viewed as a similarity metric on a graph

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Semi-Supervised with Greens Function

• Label Propagation
• Labeled data , unlabeled
  data
• labeled data unlabeled
  data
• For 2-class problems For k-class problems

Label Propagation
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Semi-Supervised with Greens Function

• Compared to Harmonic Function
• Harmonic Function is an iterative procedure
• Outperforms Harmonic Function
• 7 datasets, 10 as labeled data

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Recommendation with Greens 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

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Recommendation with Greens Function

• Recommendation with Greens Function

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Recommendation with Greens Function

• Experiments
• Dataset
• Movielens 943 users 1682 movies
• ratings from 1 to 5
• Training set 90,570 records
• Test set 9,430 records

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Recommendation with Greens Function

• Results compared to traditional methods
• MAE Mean Absolute Error
• M0E Mean Zero-one Error

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Extension

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

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Discussion and Suggestion

Any Suggestion? Any
Inspiration?
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• Thank You!