Influence and Correlation in Social Networks

1. Influence and Correlation in Social Networks Xufeiwang Nov-7-2008

2. Outline • Background, Concepts • Problem statement • Basic idea • Experimental Evaluation • Future directions

3. Proofs of social correlation • People interact with others • Advices, reading, commenting • Communicating with others • Non-causal correlation • Both the CO2 level and crime level have increased sharply • Both beer and diaper sales well in a super market • Causal correlation • I bought an IPhone after I’m recommended by my friend

4. Social influence • A bought an IPhoneafter B told him it’s cool • Directed: B influences A, not A influences B • Chronological: A is influenced after B told him • Asymmetry: B has influence to A doesn’t imply A has the same influence to B

5. Sources of correlation • Socialinfluence: One person performing an action can cause her contacts to do the same. • A bought an IPhoneafter B told him it’s cool • Homophily: Similar individuals are more likely to become friends. • Example: two mathematicians are more likely to become friends. • Confoundingfactors: External influence from elements in the environment. • Example: friends live in the same area, thus attend and take pictures of similar events, and tag them with similar tags.

6. Outline • Background, Concepts • Problem statement • Basic idea • Experimental Evaluation • Future directions

7. Problem statement • Social correlation and social influence are different concepts • Are they related? • Maybe yes and Maybe no

8. Outline • Background, Concepts • Problem statement • Basic idea • Experimental Evaluation • Future directions

9. Social correlation evaluation • Influence model: each agent becomes active in each time step independently with probability p(a), where a is the # of active friends. • Natural choice for p(a): logistic regression function: with ln(a+1) as the explanatory variable. I.e., • Coefficient α measures social correlation.

10. Testing for influence • Shuffle Test: • Chronological property • Edge-Reversal Test: • Asymmetry property C C A A B B

11. Outline • Background, Concepts • Problem statement • Basic idea • Experimental Evaluation • Future directions

12. Experimental setup • Influence model • Only use the influence factor • Current node A has “a” active friends, its probability to be active is related with the # of active friends • Correlation model • Use the homophily and confounding factors • Init S nodes as centers randomly, add a ball of radius 2 to each node in S, according to the data on Flickr, randomly pick the same # of nodes to be active

13. Simulation results Shuffle test, influence model

14. Simulation results Edge-reversaltest, influence model

15. Simulation results Shuffle test, correlation model

16. Simulation results Edge-reversaltest, correlation model

17. Shuffle test on Flickr data

18. Edge-reversal test on Flickr data

19. Explanations • The users’ tagging actions are independent • The users either seldom visit their friends’ pages • Or the users visit pages but only care about the content rather than the tags

20. Outline • Background, Concepts • Problem statement • Basic idea • Experimental Evaluation • Future directions

21. Future directions I • The relationship in the internet is weak! • How weak it is? • So I think it’s interesting to search close communities, based on strong correlation, in blogosphere • How to define the “strongness” • How the “strongness” among the users • Do we have reasonable datasets • “strongness” is related with time?

22. Future Directions II • Most of the users don’t contact frequently • How about the contact distribution • Search for stable relationships is also interesting. Seeking stable communities • How to define stable? • Stable relationship can be strong or weak connection • Contact infrequently but regularly • The group can be small • Hold for a long time??