Influence and Correlation in Social Networks

Xufei wangNov-7-2008

2

Background, ConceptsProblem statementBasic ideaExperimental EvaluationFuture directions

Outline

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 IPhone after 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

• Social influence: One person performing an action can cause her contacts to do the same.– A bought an IPhone after B told him it’s cool

• Homophily: Similar individuals are more likely to become friends.– Example: two mathematicians are more likely to become

friends.

• Confounding factors: 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.

Sources of correlation

6

Background, ConceptsProblem statementBasic ideaExperimental EvaluationFuture directions

Outline

7

• Social correlation and social influence are different concepts

• Are they related?

• Maybe yes and Maybe no

Problem statement

8

Background, ConceptsProblem statementBasic ideaExperimental EvaluationFuture directions

Outline

9

• 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.

Social correlation evaluation

10

• Shuffle Test: – Chronological property

• Edge-Reversal Test: – Asymmetry property

Testing for influence

User A B C

Time 1 2 3

User A B C

Time 2 3 1

A

B

C

A

B

C

11

Background, ConceptsProblem statementBasic ideaExperimental EvaluationFuture directions

Outline

12

• 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

Experimental setup

13

Simulation results Shuffle test, influence model

14

Simulation results Edge-reversal test, influence model

15

Simulation results Shuffle test, correlation model

16

Simulation results Edge-reversal test, 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

Background, ConceptsProblem statementBasic ideaExperimental EvaluationFuture directions

Outline

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??