Link Mining: Exploring Networks for Information and Insights

1. K I L N I G I N M N Jerry Scripps

2. Overview • What is link mining? • Motivation • Preliminaries • definitions • metrics • network types • Link mining techniques

3. What is Link Mining? Graph Theory Statistics Link Mining Data Mining MachineLearning Social Network Analysis Database

4. What is Link Mining? Examples: • Discovering communities within collaboration networks • Finding authoritative web pages on a given topic • Selecting the most influential people in a social network

5. Link Mining – MotivationEmerging Data Sets • World wide web • Social networking • Collaboration databases • etc.

6. Link Mining – MotivationDirect Applications • What is the community around msu.edu? • What are the authoritative pages? • Who has the most influence? • Who is the likely member of terrorist cell? • Is this a news story about crime, politics or business?

7. Link Mining – MotivationIndirect Applications • Convert ordinary data sets into networks • Integrate link mining techniques into other techniques

8. Preliminaries • Definitions • Metrics • Network Types • Definitions • Metrics • Network Types

9. Definitions Community Node (vertex, point, object) Link (edge, arc)

10. Metrics Network • Characteristic path length • Clustering coefficient • Min-cut Node Pair • Graph distance • Min-cut • Common neighbors • Jaccard’s coef • Adamic/adar • Pref. attachment • Katz • Hitting time • Rooted pageRank • simRank • Bibliographic metrics Node • Degree • Closeness • Betweenness • Clustering coefficient

11. Network Types Watts & Strogatz Small World Random Regular

12. Networks – Scale-free • Barabasi & Bonabeau • Degree follows a power law ~ 1/kn • Can be found in a wide variety of real-world networks

13. Network recap

14. Techniques • Link-Based Classification • Link Prediction • Ranking • Influential Nodes • Community Finding • Link Completion

15. Include features from linked objects: building a single model on all features Fusion of link and attribute models Link-Based Classification ?

16. Link-Based ClassificationChakrabarti, et al. • Copying data from neighboring web pages actually reduced accuracy • Using the label from neighboring page improved accuracy 111011 111011 ? B 101011 B 101011 010010 A 010010 A A 011110 011110 A

17. Link-Based ClassificationLu & Getoor • Define vectors for attributes and links • Attribute data OA(X) • Link data LD(X) constructed using • mode (single feature – class of plurality) • count (feature for each class – count for neighbors) • binary (feature for each class – 0/1 if exists) 111011 ? OA (attr) LD (link) 101011 B 2 1 0 … 1 1 0 … A … 111011 … 010010 A 011110 A Model 1 Model 2 Model

18. Link-Based ClassificationLu & Getoor • Define probabilities for both • Attribute • Link • Class estimation:

19. Link-Based ClassificationSummary • Using class of neighbors improves accuracy • Using separate models for attribute and link data further improves accuracy • Other considerations: • improvements are possible by using community information • knowledge of network type could also benefit classifier

20. Techniques • Link-Based Classification • Link Prediction • Ranking • Influential Nodes • Community Finding • Link Completion

21. Link Prediction

22. Link PredictionLiben-Nowell and Kleinberg Tested node-pair metrics: • Graph distance • Common neighbors • Jaccards coefficient • Adamic/adar • Preferential attachment • Katz • Hitting time • Rooted PageRank • SimRank Neighborhood Ensemble of paths

23. Link Prediction - results

24. Link Prediction – summary • There is room for growth – best predictor has accuracy of only around 9% • Predicting collaborations is difficult • Finding communities could help if most collaborations are intra-community • New problem could be to predict the direction of the link

25. Techniques • Link-Based Classification • Link Prediction • Ranking • Influential Nodes • Community Finding • Link Completion

26. Ranking

27. Ranking – Markov Chain Based • Random-surfer analogy • Problem with cycles • PageRank uses random vector

28. Ranking – summary • Other methods such as HITS and SALSA also based on Markov chain • Ranking has been applied in other areas: • text summarization • anomaly detection

29. Techniques • Link-Based Classification • Link Prediction • Ranking • Influential Nodes • Community Finding • Link Completion

30. Influence

31. Maximizing influence model-based • Problem – finding the k best nodes to activate to maximize the number of nodes activated • Models: • independent cascade – when activated a node has a one-time change to activate neighbors with prob. pij • linear threshold – node becomes activated when the percent of its neighbors crosses a threshold

32. Maximizing influence model-based • Models: independent cascade & linear threshold • A function f:S→S*, can be created using either model • Functions use monte-carlo, hill-climbing solution • Submodular functions, where ST are proven in another work to be NP-C but by using a hill-climbing solution can get to within 1-1/e of optimum.

33. Maximizing influence – cost/benefit • Assumptions: • product x sells for $100 • a discount of 10% can be offered to various prospective customers • If customer purchases profit is: • 90 if discount is offered • 100 if discount is not offered • Expected lift in profit (ELP) from offering discount is: • 90*P(buy|discount) - 100*P(buy|no discount)

34. Maximizing influence – cost/benefit • Goal is to find M that maximizes global ELP • Three approximations used: • single pass • greedy • hill-climbing • Xi is the decision of customer i to buy • Y is vector of product attributes • M is vector of marketing decision • f is a function to set the ith element of M • r0 and r1 are revenue gained • c is the cost of marketing

35. Comparison of approaches • An extension would be to spread influence to the most number of communities • Improvements can be made in speed

36. Techniques • Link-Based Classification • Link Prediction • Ranking • Influential Nodes • Community Finding • Link Completion

37. Communities

38. Gibson, Kleinberg and Raghavan Query Search Engine Root Set Base Set: add forward and back links Use HITS to find top 10 hubs and authorities

39. Reddy and Kitsuregawa • Bipartite graph • Given an initial set of nodes T build I from the nodes pointed to from T • Repeat: • use relax_cocite to expand T and I • prune T and I using dense bipartite graph function DBPG(T,I,α,β) I T u v w

40. Flake, Lawrence and Giles • Uses Min-cut • Start with seed set • Add linked nodes • Find nodes from outgoing links • Create virtual source node • Add virtual sink linking it to all nodes • Find the min-cut of the virtual source and sink

41. Neville, Adler and Jensen A 0 1 1 0 • Distance based on links and attributes • If link exists score is number of common attributes zero otherwise • score(A,B)=2, score(A,C)=1,score(B,C)=0 • Used with 3 partitioning algorithms: • Karger’s Min-Cut • MajorClust • Spectral partitioning by Shi & Malik B 1 1 0 0 C 1 1 0 1

42. Communities - summary • There are many options for building communities around a small group of nodes • Possible future directions • finding communities in networks having different link types • impact of network type on community finding techniques

43. Techniques • Link-Based Classification • Link Prediction • Ranking • Influential Nodes • Community Finding • Link Completion

44. Link Completion

45. Goldenberg, Kubica and Komarek Problem: given a network and n-1 members of a community find the nth • random • counting • popular • NB • NN • cGraph • BayesNet • EBS and LR

46. Conclusions • Link mining is a young, dynamic field of study with problem areas that continue to emerge and morph as techniques continue to evolve • Opportunities for improvements exist in • using community knowledge • using network knowledge • We are the living links in a life force that moves and plays around and through us, binding the deepest soils with the farthest stars. • Alan Chadwick

47. 14 5 3 9 2 15 6 9 4 Ranking • Based on Markov Chain • Rank is sum of node weights from incoming links • Breaks down when cycles exist

48. Ranking - continued • General approach • ap = authority score for p • Bp = backlinks of p • PageRank  • HITS approach • ap = authority score for p • hp = hub score for p • Bp = backlinks of p • Normalize between iterations