Link Prediction in (Partially) Aligned Heterogeneous Social Networks
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This document discusses link prediction in homogeneous and heterogeneous social networks. It begins by introducing the problem of link prediction and its applications. It then discusses various unsupervised and supervised methods for link prediction in homogeneous networks. Next, it covers relationship prediction and collective link prediction in heterogeneous networks. It also discusses link prediction in aligned heterogeneous networks using link transfer and anchor link inference. Finally, it outlines future work on this topic.
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References
[1] L. Lü and T. Zhou, "Link prediction in complex networks: A survey," Physica A:
Statistical Mechanics and its Applications, vol. 390, pp. 1150-1170, 2011.
[2] M. Al Hasan, V. Chaoji, S. Salem, and M. Zaki, "Link prediction using supervised
learning," in SDM’06: Workshop on Link Analysis, Counter-terrorism and Security,
2006.
[3] J. Zhang and S. Y. Philip, "Link Prediction across Heterogeneous Social
Networks: A Survey," 2014.
[4] Y. Sun, R. Barber, M. Gupta, C. C. Aggarwal, and J. Han, "Co-author relationship
prediction in heterogeneous bibliographic networks," in Advances in Social
Networks Analysis and Mining (ASONAM), 2011 International Conference on, 2011,
pp. 121-128.
[5] X. Kong, J. Zhang, and P. S. Yu, "Inferring anchor links across multiple
heterogeneous social networks," in Proceedings of the 22nd ACM international
conference on Conference on information & knowledge management, 2013, pp. 179-
188.](https://image.slidesharecdn.com/e38d2aca-e267-4c55-8493-45e77ac39ac3-160513074657/85/Link-Prediction-in-Partially-Aligned-Heterogeneous-Social-Networks-44-320.jpg)
Link Prediction in (Partially) Aligned Heterogeneous Social Networks
- 1. Link Prediction in (Partially) Aligned Heterogeneous Social Networks By: Sina Sajadmanesh Advisor: Dr. Hamid Reza Rabiee
- 2. 2 DMLLink Prediction DMLDMLLink Prediction2 Outline Introduction Problem Formulation Applications Link Prediction in Homogeneous Networks Link Prediction in Heterogeneous Networks Link Prediction in Aligned Networks Future Works
- 3. 3 DMLLink Prediction DMLDMLLink Prediction3 Introduction Problem Based on a snapshot of network, predicting the set of potential links to be formed in the future is formally defined as Link Prediction Problem. First proposed by Liben- Novel and Klienberg in CIKM 2003
- 4. 4 DMLLink Prediction DML4 Applications Social networks and E-commerce Recommender systems Friend recommendation Bioinformatics Prioritization of candidate disease genes Drug discovery Security Identify missing links between criminals Controlling computer viruses
- 5. 5 DMLLink Prediction DMLDMLLink Prediction5 Outline Introduction Link Prediction in Homogeneous Networks Unsupervised methods Supervised methods Link Prediction in Heterogeneous Networks Link Prediction in Aligned Networks Future Works
- 6. 6 DMLLink Prediction DMLDMLLink Prediction6 Link Prediction in Homogeneous Networks Homogeneous Network 𝐺 = (𝑉, 𝐸) If V contains one single type nodes and E contains one single type of links, then G is a homogeneous network
- 7. 7 DMLLink Prediction DMLDMLLink Prediction7 Link Prediction in Homogeneous Networks Unsupervised methods Measuring the closeness among nodes Assuming that close nodes are more likely to be connected Unsupervised Link Predicators Local neighbor based predicators Path based predicators Random-Walk based predicators
- 8. 8 DMLLink Prediction DMLDMLLink Prediction8 Unsupervised Methods Local Neighbor based Link Predicators Preferential Attachment 𝑃𝐴 𝑢, 𝑣 = Γ(𝑢) Γ(𝑣) user 𝑢 neighbor Γ(𝑢)
- 9. 9 DMLLink Prediction DMLDMLLink Prediction9 Unsupervised Methods Local Neighbor based Link Predicators Common Neighbor 𝐶𝑁 𝑢, 𝑣 = Γ(𝑢) ∩ Γ(𝑣) user 𝑢 neighbor Γ(𝑢)
- 10. 10 DMLLink Prediction DMLDMLLink Prediction10 Unsupervised Methods Local Neighbor based Link Predicators Jaccard Coefficient 𝐽𝐶 𝑢, 𝑣 = Γ(𝑢) ∩ Γ(𝑣) Γ(𝑢) ∪ Γ(𝑣) Adamic/Adar 𝐴𝐴 𝑢, 𝑣 = 𝑤∈(Γ(𝑢)∩Γ(𝑣)) 1 log( Γ(𝑤) ) Resource Allocation 𝑅𝐴 𝑢, 𝑣 = 𝑤∈(Γ(𝑢)∩Γ(𝑣)) 1 Γ(𝑤)
- 11. 11 DMLLink Prediction DMLDMLLink Prediction11 Unsupervised Methods Path based Link Predicators Shortest Path 𝑆𝑃 𝑢, 𝑣 = min{ 𝑃𝑢↝𝑣 } Katz Score 𝐾𝑎𝑡𝑧 𝑢, 𝑣 = 𝑙=1 ∞ 𝛽 𝑙 𝑃𝑢↝𝑣 𝑙 = (𝐼 − 𝛽𝐴)−1−𝐼
- 12. 12 DMLLink Prediction DMLDMLLink Prediction12 Unsupervised Methods Random-Walk based Link Predicators Hitting Time 𝐻𝑇 𝑢, 𝑣 = 1 + 𝑤∈Γ(𝑢) 𝑃𝑢,𝑤 𝐻𝑇(𝑤, 𝑣) Commute Time 𝐶𝑇 𝑢, 𝑣 = 𝐻𝑇 𝑢, 𝑣 + 𝐻𝑇(𝑣, 𝑢)
- 13. 13 DMLLink Prediction DMLDMLLink Prediction13 Link Prediction in Homogeneous Networks Other Unsupervised Methods Matrix Factorization methods Maximum Likelihood Methods Probabilistic Methods
- 14. 14 DMLLink Prediction DMLDMLLink Prediction14 Link Prediction in Homogeneous Networks Supervised Link Prediction Learning a binary classifier that will predict whether a link exists between a given pair of nodes or not. First proposed by Hassan et. al in SDM 2006
- 15. 15 DMLLink Prediction DMLDMLLink Prediction15 Supervised Link Prediction Dataset We need two snapshot of the network for training Positive Samples Links that are missing in former snapshot, but are formed in latter snapshot Negative Samples Links that are missing in both snapshots
- 16. 16 DMLLink Prediction DMLDMLLink Prediction16 Supervised Link Prediction Features Topological Features Attribute-based Features Classifiers SVM Decision Trees Multilayer Perceptron KNN Naïve Bayes
- 17. 17 DMLLink Prediction DMLDMLLink Prediction17 Outline Introduction Link Prediction in Homogeneous Networks Link Prediction in Heterogeneous Networks Relationship Prediction Collective Link Prediction Link Prediction in Aligned Networks Future Works
- 18. 18 DMLLink Prediction DMLDMLLink Prediction18 Link Prediction in Heterogeneous Networks Heterogeneous Network 𝐺 = (𝑉, 𝐸) 𝑉 = 𝑖 𝑉𝑖 is the sets of various kinds of nodes and 𝑉𝑖 is the 𝑖 𝑡ℎ kind of nodes in G 𝐸 = 𝑗 𝐸𝑗 is the sets of various types of links and 𝐸𝑗 is the 𝑗𝑡ℎ kind of links in G
- 19. 19 DMLLink Prediction DMLDMLLink Prediction19 Link Prediction in Heterogeneous Networks Heterogeneous Network Schema
- 20. 20 DMLLink Prediction DMLDMLLink Prediction20 Link Prediction in Heterogeneous Networks From Link Prediction to Relationship Prediction A relationship between two objects could be a composition of two or more links • E.g. two authors have a co-author relationship if they have co-written a paper Need to redesign topological features in heterogeneous networks
- 21. 21 DMLLink Prediction DMLDMLLink Prediction21 Supervised Relationship Prediction Feature Extraction Heterogeneous Features • Based on heterogeneous structure of network Meta-Path based Features • Uses the concepts of meta-paths • Different meta paths represent different semantic meanings • Number of path instanced of a meta-path Φ
- 22. 22 DMLLink Prediction DMLDMLLink Prediction22 Supervised Relationship Prediction Case Study Social Link Prediction
- 23. 23 DMLLink Prediction DMLDMLLink Prediction23 Supervised Relationship Prediction Heterogeneous Features Social Features • Common Neighbor • Jaccard Coefficient • Adamic/Adar Spatial Features • Common Locations • Jaccard Coefficient of Common Locations • Average Geographic distance of locations • …
- 24. 24 DMLLink Prediction DMLDMLLink Prediction24 Supervised Relationship Prediction Heterogeneous Features Temporal Features • Let T(u) be 24 hour activity vector of user u • Inner product of T(u) and T(v) • Cosine similarity of T(u) and T(v) Text Content Features • Let w(u) be the bag-of-words vector of user u weighted by TF-IDF • Inner product of w(u) and w(v) • Cosine similarity of w(u) and w(v)
- 25. 25 DMLLink Prediction DMLDMLLink Prediction25 Supervised Relationship Prediction Meta-Path based Features Φ1: Follower of Follower • UUU Φ2: Common Out Neighbor • UUU Φ3: Common In Neighbor • UUU Φ4: Common Words • UPWPU Φ5: Common Timestamps • UPTPU Φ6: Common Location Check-ins • UPLPU
- 26. 26 DMLLink Prediction DMLDMLLink Prediction26 Link Prediction in Heterogeneous Networks Collective Link Prediction Conventional link prediction approaches assume that links are independent identically distributed (i.i.d). But in heterogeneous networks, different type of links are correlated and mutually influential.
- 27. 27 DMLLink Prediction DMLDMLLink Prediction27 Link Prediction in Heterogeneous Networks Input Social Network
- 28. 28 DMLLink Prediction DMLDMLLink Prediction28 Link Prediction in Heterogeneous Networks Independent Social and Location Link Prediction
- 29. 29 DMLLink Prediction DMLDMLLink Prediction29 Link Prediction in Heterogeneous Networks Traditional Link Prediction 𝑌𝑠 = 𝑎𝑟𝑔 max 𝑌𝑠 𝑃(𝑦 𝐿 𝑠 = 𝑌𝑠) 𝑌𝑙 = 𝑎𝑟𝑔 max 𝑌 𝑙 𝑃(𝑦 𝐿𝑙 = 𝑌𝑙) 𝐿 𝑠 and 𝐿𝑙 are the sets of potential social and location links 𝑃 𝑦 𝐿 𝑠 = 𝑌𝑠 is the probability scores achieved when links in 𝐿 𝑠 are assigned with Labels 𝑌𝑠 𝑌𝑠 and 𝑌𝑙 are the sets of optimal labels
- 30. 30 DMLLink Prediction DMLDMLLink Prediction30 Link Prediction in Heterogeneous Networks Collective Link Prediction 𝑌𝑠, 𝑌𝑙 = 𝑎𝑟𝑔 max 𝑌𝑠,𝑌 𝑙 𝑃(𝑦 𝐿 𝑠 = 𝑌𝑠|𝑦 𝐿𝑙 = 𝑌𝑙) × 𝑃(𝑦 𝐿𝑙 = 𝑌𝑙|𝑦 𝐿 𝑠 = 𝑌𝑠) 𝑌𝑠 (𝑡) = 𝑎𝑟𝑔 max 𝑌𝑠 𝑃(𝑦 𝐿 𝑠 = 𝑌𝑠 | 𝑦 𝐿 𝑠 = 𝑌𝑠 𝑡−1 , 𝑦 𝐿𝑙 = 𝑌𝑙 𝑡−1 ) 𝑌𝑙 (𝑡) = 𝑎𝑟𝑔 max 𝑌 𝑙 𝑃(𝑦 𝐿𝑙 = 𝑌𝑙 | 𝑦 𝐿 𝑠 = 𝑌𝑠 𝑡 , 𝑦 𝐿𝑙 = 𝑌𝑙 𝑡−1 ) IterativeSolution
- 31. 31 DMLLink Prediction DMLDMLLink Prediction31 Outline Introduction Link Prediction in Homogeneous Networks Link Prediction in Heterogeneous Networks Link Prediction in Aligned Networks Link Transfer Anchor Link Inference Future Works
- 32. 32 DMLLink Prediction DMLDMLLink Prediction32 Link Prediction in Aligned Networks Multi Aligned Heterogeneous Social Networks
- 33. 33 DMLLink Prediction DMLDMLLink Prediction33 Link Prediction in Aligned Networks Link Transfer Information Sparsity • New Network Problem • Cold Start Problem Need to transfer knowledge from another domain • Transfer Learning • Use aligned network as a source Context • Fully aligned networks • Partially aligned networks
- 34. 34 DMLLink Prediction DMLDMLLink Prediction34 Link Prediction in Aligned Networks Link Transfer across Fully Aligned Networks Prediction using only the target network: 𝑃 𝑦 𝑢 𝑡, 𝑣 𝑡 = 1|𝐺 𝑡 = 𝑃 𝑦 𝑢 𝑡, 𝑣 𝑡 = 1|𝑥 𝑢 𝑡, 𝑣 𝑡 Prediction using source and target network: 𝑃 𝑦 𝑢 𝑡, 𝑣 𝑡 = 1|𝐺 𝑡, 𝐺 𝑠 = 𝑃 𝑦 𝑢 𝑡 , 𝑣 𝑡 = 1| 𝑥 𝑢 𝑡 , 𝑣 𝑡 𝑇 , 𝑥 𝑢 𝑠 , 𝑣 𝑠 𝑇 , 𝑦 𝑢 𝑠 , 𝑣 𝑠 𝑇
- 35. 35 DMLLink Prediction DMLDMLLink Prediction35 Link Prediction in Aligned Networks Link Transfer across Partially Aligned Networks Solution: Inter-Network Meta-Paths Let 𝛾 𝑈 𝑡, 𝑈 𝑠 be the anchor meta-path Ψ1: 𝛾 𝑈 𝑡, 𝑈 𝑠 − Φ 𝑈 𝑠, 𝑈 𝑠 − 𝛾 𝑈 𝑠, 𝑈 𝑡 Ψ2: Φ 𝑈 𝑡, 𝑈 𝑡 − 𝛾 𝑈 𝑡, 𝑈 𝑠 − Φ 𝑈 𝑠, 𝑈 𝑠 − 𝛾 𝑈 𝑠, 𝑈 𝑡 Ψ3: 𝛾 𝑈 𝑡, 𝑈 𝑠 − Φ 𝑈 𝑠, 𝑈 𝑠 − 𝛾 𝑈 𝑠, 𝑈 𝑡 − Φ 𝑈 𝑡, 𝑈 𝑡 Ψ3: Φ 𝑈 𝑡 , 𝑈 𝑡 − 𝛾 𝑈 𝑡 , 𝑈 𝑠 − Φ 𝑈 𝑠 , 𝑈 𝑠 − 𝛾 𝑈 𝑠, 𝑈 𝑡 − Φ 𝑈 𝑡, 𝑈 𝑡
- 36. 36 DMLLink Prediction DMLDMLLink Prediction36 Link Prediction in Aligned Networks Anchor Link Inference
- 37. 37 DMLLink Prediction DMLDMLLink Prediction37 Anchor Link Inference Supervised Method Social Features • Extended Common Neighbors • Extended Jaccard Coefficient • Extended Adamic/Adar Spatial Features Temporal Features Text Content Features
- 38. 38 DMLLink Prediction DMLDMLLink Prediction38 Anchor Link Inference Inference w.r.t One-to-One Constraint Predicted Scores
- 39. 39 DMLLink Prediction DMLDMLLink Prediction39 Anchor Link Inference Inference w.r.t One-to-One Constraint Conventional Link Prediction
- 40. 40 DMLLink Prediction DMLDMLLink Prediction40 Anchor Link Inference Inference w.r.t One-to-One Constraint Max sum of scores
- 41. 41 DMLLink Prediction DMLDMLLink Prediction41 Anchor Link Inference Inference w.r.t One-to-One Constraint Stable Matching
- 42. 42 DMLLink Prediction DMLDMLLink Prediction42 Outline Introduction Link Prediction in Homogeneous Networks Link Prediction in Heterogeneous Networks Link Prediction in Aligned Networks Future Works
- 43. 43 DMLLink Prediction DMLDMLLink Prediction43 Future Works Anchor Link Formation Prediction Predicting whether a user in the source network will join the target network in the future This depends on the amount of influence he/she receives from the target network An influence model can be learned using the training data Positive-Unlabeled learning can improve the prediction performance
- 44. 44 DMLLink Prediction DMLDMLLink Prediction44 References [1] L. Lü and T. Zhou, "Link prediction in complex networks: A survey," Physica A: Statistical Mechanics and its Applications, vol. 390, pp. 1150-1170, 2011. [2] M. Al Hasan, V. Chaoji, S. Salem, and M. Zaki, "Link prediction using supervised learning," in SDM’06: Workshop on Link Analysis, Counter-terrorism and Security, 2006. [3] J. Zhang and S. Y. Philip, "Link Prediction across Heterogeneous Social Networks: A Survey," 2014. [4] Y. Sun, R. Barber, M. Gupta, C. C. Aggarwal, and J. Han, "Co-author relationship prediction in heterogeneous bibliographic networks," in Advances in Social Networks Analysis and Mining (ASONAM), 2011 International Conference on, 2011, pp. 121-128. [5] X. Kong, J. Zhang, and P. S. Yu, "Inferring anchor links across multiple heterogeneous social networks," in Proceedings of the 22nd ACM international conference on Conference on information & knowledge management, 2013, pp. 179- 188.
- 45. Q&A