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Influence and Correlation in Social Networks

Influence and Correlation in Social Networks Azad University KurdistanSocial Network

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Proffessor: Dr shaykh Esmaili

Presenters: Alireza ZandiAsrin Mohammadi Somaye Yosefi

Social Network Influence and Correlation in Social Networks Azad University Kurdistan



Outline

Social Network

• Introduction• Models of social correlation• Methodology• Simulations• Experiments on real data

Influence and Correlation in Social Networks Azad University Kurdistan



Social systems

• Online social networks: are playing an ever-important role in shaping the behavior of users on the web.– Network of professional contacts (e.g., for finding jobs)– Network of colleagues (e.g., for learning new techniques)– Web 2.0 systems:

• Online social networks: facebook, myspace, orkut, IM, linkedIn, twitter, …

• Content sharing: flickr, del.icio.us, youtube, weblogs, …• Content creation: wikipedia




Social correlation

• There has been some theoretical and empirical work on how a user's actions can be correlated to his/her social affliations.




correlation in social networks

• Causes of correlation in social networks can be categorized into roughly three types.

– The first is influence,where the action of a user is triggered by one of his/her friend's recent actions.

– The second is homophily,which means that individuals often befriend others who are similar to them.

– The third is environment (also known as confounding factors or external influence).




Social influence

• Given the signficance of social influence.– This is a particularly difficult problem in online settings.– We overcome this problem by taking advantage of the

availability of data about the timing of actions in online settings.

– We propose a statistical test (called the shuffle test).

– We also show the efectiveness of our test using simula-

tions. Our test cases are based on a large social network

from Flickr.




Models of social correlation

• We study a setting where a group of individuals (also

called agents or users) are nodes of a social network G.– G is generated from an unknown probability distribution

this means that for two nodes u and v that are adjacent in G, the events that u becomes active is correlated with v

becoming active..





• Social correlation– Is correlation between the behavior of aliated agents in a

social network is a well-known phenomenon.

• There are three primary explanations for this phenomenon:– homophily, the environment , and social inuence.





• Homophily– Homophily is the tendency of individuals tochoose friends

with similar characteristics

• Confounding – The second explanation for correlation between actions of

adjacent agents in a social network is external inuence from

elements in the environment.





• Influence– The third, and perhaps the most consequential explanation

for social correlation is social inuence. This refers to the phenomenon that the action of individuals can induce their friends to act in a similar way.




Example: obesity study

• Data set of 12,067 people from 1971 to 2003 as part of Framingham Heart Study




Example: obesity study

• Results

– Having an obese friend increases chance of obesity by 57%.

– obese sibling ! 40%, obese spouse ! 37%




Models of social influence

• Many models proposed in different settings– Game-theoretic models

• Each agent modeled as a player in a “game”.• The utility that an agent derives depends on what

his/her friends do.• Agents decide whether to become active to

maximize their utility.





-Probabilistic models• Probabilistic models are more predictive

– allows optimization (find the best “seed set”)– allows fitting the data to estimate parameters of the system





• Influence Model• Graph (static or dynamic)• Edge (u,v): Node u can influence node v• Discrete time: t = 0, 1, 2, …• For each t, every inactive node becomes active

with





• probability p(x), where x is the active contacts

Social Network



Model

• 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.




Measuring social correlation

• We compute the maximum likelihood estimate for parameters α and β.

• Let Ya = pairs (user u, time t) where u is not active and has a active friends at the beginning of time step t, and becomes active in this step.

• Let Na = …… does not become active in this step.• Find α, β to maximize





Sample



Test

• Shuffle

• Edge-Reversal




simulations

• Generative models

• Measuring correlation

• Distinguishing influence




• no-correlation model: actions generated randomly to follow the pattern of one of the real tags, but ignoring network

• Influence model: same as described, with a variety of (α,β) values

• Correlation model(no-influence): pick a # of random centers, let W be the union of balls of radius 2 around these centers


Generative models



Simulation results, baseline




Distribution of for the influence model




Distribution of for the correlation model




Shuffle test, influence model




Shuffle test, correlation model




Edge-reversal test, influence model




Edge-reversal test, correlation model




Experiments on real data

• The Flickr dataset

• Measuring correlation

• Distinguishing influence




Flickr tags

• ~10K tags • We focus on a set of 1700• Different growth patterns:

– bursty (“halloween” or “katrina”)– smooth (“landscape” or “bw”)– periodic (“moon”)

• For each tag, define an action corresponding to using the tag for the first time.




Distribution of for the Flickr social network.




Shuffle test on Flickr data




Edge-reversal test on Flickr data




Conclusions

• Our contributions– Defined two models that exhibit correlation, one with and

the other without social influence.– Developed statistical tests to distinguish the two– Theoretical justification for one of the tests.– Simulations suggest that the tests “work” in practice.– On Flickr, we conclude that despite considerable

correlation, no social influence can be detected.




Conclusions

• Discussion– cannot conclusively say there is influence without

controlled experiments (example: flu shot)– still can rule out potential candidates– Open: develop algorithms to find “influential”

nodes/communities given a pattern of spread.




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