Jerry Scripps

1. R W E T O K N G I I N M N Jerry Scripps

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

3. What is Network Mining? Statistics Computer Science Mathematics Data Mining MachineLearning Pattern Recognition Social Network Analysis Graph Theory Network Mining

4. What is Network Mining?Border Disciplines • Sociology • Military • Biology • Medicine • Chemistry • Business • Statistics • Computer Science • Physics • Math • Psychology • Law Enforcement

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

6. Network Mining – MotivationEmerging Data Sets • World wide web • Social networking • Collaboration databases • Customer or Employee sets • Genomic data • Terrorist sets • Supply Chains • Many more…

7. Network 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?

8. Network Mining – MotivationIndirect Applications • Convert ordinary data sets into networks • Integrate network mining techniques into other techniques

9. Preliminaries • Definitions • Metrics • Network Types • Definitions • Metrics • Network Types

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

11. Metrics Network • Characteristic path length • Clustering coefficient • Min-cut • diameter 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

12. Network Types – Random

13. Network Types – Small World Watts & Strogatz Small World Random Regular

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

15. Network recap

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

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

18. 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

19. 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

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

21. Collective Classification • Uses both attributes and links • Iteratively update the unlabeled instances • message passing, loopy belief nets, etc.

22. 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

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

24. Link Prediction

25. 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

26. Link Prediction - results

27. Link Prediction – newer methods • maximum likelihood • stochastic block model • probabilistic

28. Link Prediction – summary • There is room for growth – best predictor has accuracy of only around 9% • Predicting collaborations is difficult • New problem could be to predict the direction of the link

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

30. Ranking

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

32. 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

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

34. Influence

35. Influence Maximization • Problem: find the best nodes to activate • Approaches: • degree – fast but not effective • greedy – effective but slow • improvements to greedy: degree heuristics and Shapely value • use communities • cost-benefit – probabilistic approach

36. 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

37. 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.

38. 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)

39. 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

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

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

42. Communities

43. 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

44. 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

45. Community Finding • Girvan and Newman – minimize betweenness • Clauset, et al. – agglomerative, uses modularity • Shi & Malik – spectral clustering

46. 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