Link Prediction and Recommendation across Multiple ...

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Yuxiao Dong*$, Jie Tang$, Sen Wu$, Jilei Tian# Nitesh V. Chawla*, Jinghai Rao#, Huanhuan Cao#

Link Prediction and Recommendation across

Multiple Heterogeneous Networks

*University of Notre Dame $Tsinghua University #Nokia Research China

Yuxiao Dong, Jie Tang, Sen Wu, Jilei Tian, Nitesh V. Chawla, Jinghai Rao, Huanhuan Cao. Link Prediction and Recommendation across Heterogeneous Social networks. In IEEE ICDM'12.

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Introduction Link prediction and recommendation is ubiquitous …

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Topic: Transfer Link Prediction Framework

General Features

Transfer Model

Source network Target network

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Link Prediction and Recommendation

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Link Prediction and Recommendation

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G=(V, E): social network vs: a particular user C: candidates for vs

Y: candidates’ rank

Input: G, vs, C Output: f: (G, vs, C) à Y

What is link prediction?

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y13

y14 y12

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Link Prediction and Recommendation Basic Idea

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Attribute factor

Social factor

Ranking Factor Graph Model (RFG)

Latent Variable

Joint distribution: Attribute factors Social factors

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Ranking Factor Graph Model

p  Joint distribution: Attributes Social factors

p  Attribute factor:

p  Social factor:

p  Exponential-linear functions to initialize factors

Model Initialization

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Ranking Factor Graph Model

p  RFG objective function:

p  Learning[1]:

1. Wenbin Tang, Honglei Zhuang, Jie Tang. Learning to infer social ties in large networks. In ECML/PKDD'11, pp 381-397.

Objective function and model learning

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Still Problems?

– Unbalanced Data: the number of potential candidates grows exponentially (d(vs)n-1) as the number of hops n increases.

– Few Training Data: obtaining sufficient training data is difficult.

Challenges in traditional link prediction problem

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Transfer Link Prediction and Recommendation

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Link Prediction Framework

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Features

Model

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Transfer Link Prediction Framework

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General Features

Transfer Model

Source network Target network

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General social factors

p  What are the general factors driving people make friends in real world and form links in social networks? p  Homophily p  Social Balance p  Preferential Triad Closure

How do we create social connections?

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General social factors

The principle of homophily suggests that users with similar characteristics tend to associate with each other.

Homophily / Social Balance / Preferential Triad Closure

1. The likelihood of two users creating a link increases when the number of their common neighbors increases in the four networks. 2. This effect of homophily is more pronounced when the number reaches 100, where the probabilities are all higher than 50% in the four networks.

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Social balance theory is based on the principles that “the friend of my friend is my friend” and “the enemy of my enemy is my friend”.

It is more likely (more than 80% likelihood) for users to establish balanced triangle of friendships in all four online networks.

General social factors Homophily / Social Balance / Preferential Triad Closure

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Preferential attachment and triadic closure are the basic models, concerning the nature of human social interactions and agency on a local scale.

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x Lady Gaga

Barack Obama student

student

Why?


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Four networks share a very similar distribution on probabilities of close triad formation in all six cases, though the four networks are totally different.

The enumeration is conditioned on whether X, Y, Z are opinion leaders (green means it is an opinion leader).


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Transfer Ranking Factor Graph Model

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p  TRFG Objective function:

Attributes factor in source network

Attributes factor in target network

General social factors across source and target networks

Transfer Ranking Factor Graph Model p  RFG Objective function:

Bridge source & target networks

General social factors across source and target networks

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Experiment Setup

–  Randomly select 2000 nodes as the source users[2] from the network. –  For each source user, we generate the candidate list for her/him.

1. Epinions, Slashdot, Wikivote are available at http://snap.stanford.edu and Twitter available at http://arnetminer.org/reciprocal 2. Lars Backstrom, Jure Leskovec. Supervised Random Walks: Predicting and Recommending Links in social Networks. In WSDM’11

#nodes #edges +edges description

Epinions 131,828 841,372 85% Who-trust-whom online social website

Slashdot 82,144 549,202 78% User community based technology news website

Wikivote 7,115 103,689 79% Who-vote-whom network for admins in Wikipedia

Twitter 63,803 153,098 38% Who-follow-whom micro-blogging networks

Facebook 4,039 88,234 100% Facebook friendship networks

Networks and Candidate Generation

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Experiment Setup Features

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Experiment Setup

p  Unsupervised methods •  Common neighbors

•  Adamic/Adar

•  Jaccard Index

•  Preferential Attachment

p  Supervised methods •  SVMRank (SVM-light) •  Logistic Regression (Weka) •  Ranking Factor Graph Model

Baseline Predictors

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Results

Precision @ 30

AUC

Non-transfer case

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Results Transfer: one source network to one target network

1 source networks

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Results Transfer: multiple source networks to one target network

4 source networks

3 source networks

2 source networks

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Summary

Study the novel problem of Transfer Link Prediction across Multiple Heterogeneous Networks

Propose transfer ranking factor graph model to leverage the observed general factors, and demonstrate the effectiveness of it in five real-world networks

Discovery general social theories on link formation across networks, including homophily, social balance and preferential triadic closure

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Thanks

Yuxiao Dong, Jie Tang, Sen Wu, Jilei Tian, Nitesh V. Chawla, Jinghai Rao, Huanhuan Cao. Link Prediction and Recommendation across Heterogeneous Social networks. In IEEE ICDM'12.

Link Prediction and Recommendation across Multiple ...

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