1. 1 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.

2. 2 Introduction Link prediction and recommendation is ubiquitous …

3. 3 x ? ? x Topic: Transfer Link Prediction Framework General Features Transfer Model Source network Target network x 1 2 3

4. 4 Link Prediction and Recommendation

5. 5 ? ? G=(V, E): social network v s : a particular user C: candidates for v s Y: candidates’ rank Input: G, v s, C Output: f: (G, v s, C)  Y What is link prediction?

6. 6 y 13 y 14 y 12 ?? Link Prediction and Recommendation Basic Idea

7. 7 Attribute factor Social factor Ranking Factor Graph Model (RFG) Latent Variable Joint distribution: Attribute factors Social factors

8. 8 Ranking Factor Graph Model  Joint distribution: Attributes Social factors  Attribute factor:  Social factor:  Exponential-linear functions to initialize factors Model Initialization

9. 9 Ranking Factor Graph Model  RFG objective function:  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

10. 10 Still Problems? –Unbalanced Data: the number of potential candidates grows exponentially (d(v s ) n-1 ) as the number of hops n increases. –Few Training Data: obtaining sufficient training data is difficult. Challenges in traditional link prediction problem

11. 11 Transfer Link Prediction and Recommendation

12. 12 Link Prediction Framework ? ? x Features Model 1 2 3

13. 13 Transfer Link Prediction Framework x ? ? x General Features Transfer Model Source network Target network x 1 2 3

14. 14 General social factors  What are the general factors driving people make friends in real world and form links in social networks?  Homophily  Social Balance  Preferential Triad Closure How do we create social connections?

15. 15 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.

16. 16 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

17. 17 Preferential attachment and triadic closure are the basic models, concerning the nature of human social interactions and agency on a local scale. x x Lady Gaga Barack Obama student Why ? General social factors Homophily / Social Balance / Preferential Triad Closure

18. 18 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). General social factors Homophily / Social Balance / Preferential Triad Closure

19. 19 Transfer Ranking Factor Graph Model

20. 20  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  RFG Objective function: Bridge source & target networks General social factors across source and target networks

21. 21 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/reciprocalhttp://snap.stanford.eduhttp://arnetminer.org/reciprocal 2. Lars Backstrom, Jure Leskovec. Supervised Random Walks: Predicting and Recommending Links in social Networks. In WSDM’11 #nodes#edges+edgesdescription Epinions131,828841,37285%Who-trust-whom online social website Slashdot82,144549,20278%User community based technology news website Wikivote7,115103,68979%Who-vote-whom network for admins in Wikipedia Twitter63,803153,09838%Who-follow-whom micro-blogging networks Facebook4,03988,234100%Facebook friendship networks Networks and Candidate Generation

22. 22 Experiment Setup Features

23. 23 Experiment Setup  Unsupervised methods Common neighbors Adamic/Adar Jaccard Index Preferential Attachment  Supervised methods SVMRank (SVM-light) Logistic Regression (Weka) Ranking Factor Graph Model Baseline Predictors

24. 24 Results Precision @ 30 AUC Non-transfer case

25. 25 Results Transfer: one source network to one target network 1 source networks

26. 26 Results Transfer: multiple source networks to one target network 4 source networks 3 source networks 2 source networks

27. 27 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

28. 28 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.