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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
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Outline
Social Network
• Introduction• Models of social correlation• Methodology• Simulations• Experiments on real data
Influence and Correlation in Social Networks Azad University Kurdistan
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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 Network Influence and Correlation in Social Networks Azad University Kurdistan
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Social correlation
• There has been some theoretical and empirical work on how a user's actions can be correlated to his/her social affliations.
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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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 Network Influence and Correlation in Social Networks Azad University Kurdistan
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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.
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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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 Network Influence and Correlation in Social Networks Azad University Kurdistan
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Models of social correlation
• 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.
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Models of social correlation
• 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.
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Models of social correlation
• 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.
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Example: obesity study
• Data set of 12,067 people from 1971 to 2003 as part of Framingham Heart Study
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Example: obesity study
• Results
– Having an obese friend increases chance of obesity by 57%.
– obese sibling ! 40%, obese spouse ! 37%
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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.
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Models of social influence
-Probabilistic models• Probabilistic models are more predictive
– allows optimization (find the best “seed set”)– allows fitting the data to estimate parameters of the system
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Models of social influence
• 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
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Models of social influence
• probability p(x), where x is the active contacts
Social Network
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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.
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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
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Social Network Influence and Correlation in Social Networks Azad University Kurdistan
Sample
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Social Network Influence and Correlation in Social Networks Azad University Kurdistan
Sample
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Social Network Influence and Correlation in Social Networks Azad University Kurdistan
Sample
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Test
• Shuffle
• Edge-Reversal
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simulations
• Generative models
• Measuring correlation
• Distinguishing influence
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• 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
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
Generative models
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Simulation results, baseline
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Distribution of for the influence model
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Distribution of for the correlation model
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Shuffle test, influence model
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Shuffle test, correlation model
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Edge-reversal test, influence model
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Edge-reversal test, correlation model
Social Network Influence and Correlation in Social Networks Azad University Kurdistan
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Experiments on real data
• The Flickr dataset
• Measuring correlation
• Distinguishing influence
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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.
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Distribution of for the Flickr social network.
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Shuffle test on Flickr data
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Edge-reversal test on Flickr data
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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.
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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.
Social Network Influence and Correlation in Social Networks Azad University Kurdistan