Influence and Correlation in Social Networks

Xufei wang Nov-7-2008

Outline

 Background, Concepts  Problem statement  Basic idea  Experimental Evaluation  Future directions 2

Proofs of social correlation

• • • People interact with others – Advices, reading, commenting – Communicating with others Non-causal correlation – – Both the CO 2 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 3

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 4

Sources of correlation

• 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.

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Outline

 Background, Concepts  Problem statement  Basic idea  Experimental Evaluation  Future directions 6

Problem statement

• Social correlation and social influence are different concepts • Are they related?

• Maybe yes and Maybe no 7

Outline

 Background, Concepts  Problem statement  Basic idea  Experimental Evaluation  Future directions 8

Social correlation evaluation

• • Influence model: each agent becomes active in each time step independently with probability p(a) , where a the # of active friends.

is Natural choice for p(a): logistic regression function: with ln(a+1) as the explanatory variable. I.e., • Coefficient α measures social correlation .

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Testing for influence

• Shuffle Test: – Chronological property

User

Time

A

1

B

2

C

3 • Edge-Reversal Test: – Asymmetry property C A B

User

Time

A

2 A

B

3 C B

C

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Outline

 Background, Concepts  Problem statement  Basic idea  Experimental Evaluation  Future directions 11

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 12

Simulation results Shuffle test, influence model 13

Simulation results Edge-reversal test, influence model 14

Simulation results Shuffle test , correlation model 15

Simulation results Edge-reversal test, correlation model 16

Shuffle test on Flickr data

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Edge-reversal test on Flickr data

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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 19

Outline

 Background, Concepts  Problem statement  Basic idea  Experimental Evaluation  Future directions 20

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?

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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??

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