Feedback Effects between Similarity and Social Influence in Online Communities

Authors: David Crandall, Dan Cosley, Daniel Huttenlocher, Jon Kleinberg, Siddharth Suri

Cornell University Ithaca, NY

2008 KDD: Proceeding of the 14th ACM KDD international conference on Knowledge discovery and data mining

#citations at 2010/04/09 from Google Scholar:44

Presenter: Paolo Massa, SoNet group, http://sonet.fbk.eu

SoNet Research MeetingsThese slides were used for an internal presentation of

the SoNet group.

Every week, one member of the SoNet group presents a research papers to the other members. The mentioned paper(s) are hence written by other researchers.

Being internal presentations, these slides might be a bit rough and unpolished.

You can find more information (including this presentation) about the SoNet group at http://sonet.fbk.eu

These slides

Some of these slides are taken from http://carbon.videolectures.net/2008/contrib/kdd08_las_vegas/crandall_fessioc/kdd08_crandall_fessioc_01.ppt

Thanks to the authors for sharing their slides, of course the real presentation is more polished and you can find it at the previous link

Interdisciplinary Team!• Cornell University

• David Crandall (computer vision)

• Dan Cosley (helping people make sense of and manage information, both individually and as group)

• Daniel Huttenlocher (computer vision)

• Jon Kleinberg (networks genius, recently wrote “Governance in Social Media: A case study of the Wikipedia promotion process. Proc. 4th International AAAI Conference on Weblogs and Social Media, 2010.” and “ Predicting Positive and Negative Links in Online Social Networks. Proc. 19th International World Wide Web Conference, 2010.” (using a dataset released by me!!!)

– Note for me: ask him the wikipedia voting dataset!

• Siddharth Suri (social networks and algorithmic game theory)

Homophily in social networks• “Birds of a feather flock together”

– Plato used the phrase in The Republic, 360 B.C.E, "I will tell you, Socrates, he said, what my own feeling is. Men of my age flock together; we are birds of a feather, as the old proverb says;

Caused by two related social forces [Friedkin98, Lazarsfeld54]

– Social influence: People become similar to those they interact with• Interaction → similarity

– Selection: People seek out similar people to interact with• Similarity → interaction

• Both processes contribute to homophily, but– Social influence leads to community-wide homogeneity– Selection leads to fragmentation of the community

fragmentationhomogeneity

Main questions• How do similarity and social ties compare as predictors

of future behavior?– viral marketing relies upon social influence affecting

behavior– recommender systems predict behavior based on

similarity– like social influence and selection, these are in

tension• Can we quantify and model the way in which selection

and social influence interact to create social networks?– important for understanding health, trajectory of a

community

• How does first interaction affect similarity?

• Wikipedia: a large collaborative social network– users interact by posting to each others’ user-talk pages– user interests revealed by article edit patterns– rich, publicly-available, fine-grained log

Interplay between influence and similarity

Social influence dominates? Selection dominates? Transient effect?

time

similarit

y

firstinteraction

time

similarit

y

firstinteraction

time

similarit

y

first interaction

Wikipedia dataset• Registered users English Wikipedia who have a user

discussion page (~510,000 users as of April 2, 2007)• Responsible for 61% of edits to the roughly 3.4 million

articles.• We ignore actions by users without discussion pages, who

tend to have very few social connections.

Wikipedia dataset• user’s activity vector v(t): number of times that he or she

has edited each article up to that point in time t• time of first meeting for two users u and v = time at which

one of them first makes a post on the user discussion page of the other.

• In principle, we could also try to infer social interactions based on posting to the interactions based on posting to the same article’s discussion page. Moreover, we found that using simple heuristics to infer interaction based on posts to article discussion pages produced closely analogous results to what we obtain from analyzing user discussion pages.

Results

Results

Slower, long-term increase after first interaction

(social influence)

Slower, long-term increase after first interaction

(social influence)

Rapid increase in similarity before first interaction

(selection)

Rapid increase in similarity before first interaction

(selection)

Results

Effect is qualitatively stable– across populations (admins/non-admins, heavy/light users, etc.)– across different time scales, similarity metrics, languages, etc.– See for k<10 etc...

Slower, long-term increase after first interaction

(social influence)

Slower, long-term increase after first interaction

(social influence)

Rapid increase in similarity before first interaction

(selection)

Rapid increase in similarity before first interaction

(selection)

After describing ...• ... modelling!

• Mental framework: the goal is to understand the rules governing the world

Simpler model [ Holme and Newman]

• Each user holds a single mutable opinion. • In each time step of their model, a user u is chosen.

With probability φ, u changes its opinion to match a random neighbor’s (social influence), and with probability 1 − φ, u re-wires one of its links to connect to a random user who holds the same opinion (selection).

• Then ask yourself, the world I created with this simple model is “similar” to the observed world?

A model of user behavior• We model systems where people interact & do activities

– each user u has a history of k most recent activities, Ek(u)

• At each time step, user u either,– interacts with another user, choosing – (1) someone who has engaged in a common activity or– (2) someone at random– performs an activity, choosing as follows:

• Of the model parameters θ = (φ, ψ, β, γ, α, δ, k), two can be estimated by direct observation of the Wikipedia data: φ is the ratio of user discussion page edits to total edits, and β is the proportion of edits that create new articles.

• We use maximum-likelihood estimation to set the values of the unobservable parameters ψ, α, γ, and δ (of which only three are independent.

• Given the model parameters θ it is straightforward to estimate the likelihood of the actual Wikipedia data W given the model, P (W |θ).

• We seek parameter values that maximize the probability of the Wikipedia data given our model. We estimate these parameters by brute force search over a grid of quantized values. To make this tractable, we first search over a relatively coarse quantization grid: for each parameter we search over the range (0, 1) at a spacing of 0.05. We then conduct a finer-scale search around the maximizing parameter values using a quantization of 0.005 for each parameter.

• We performed this parameter learning procedure on the entire history of Wikipedia through April 1, 2007, which consists of roughly 49 million article edit events and 3 million user interaction events.

Simulation results• We used the model to simulate user behavior in Wikipedia

– using maximum-likelihood estimates of the parameters– simpler models (e.g. [Holme-Newman06]) do not

produce this effect

interacting users interacting users

Simulated Wikipedia result Actual Wikipedia result

Estimated parameters (results)• First, the vast majority of activities are edits (94%) rather

than interactions (6%).• In the interaction case, the user to communicate with is

chosen randomly from the overall set of users with probability δ = 0.71 (71%).

• In choosing what to edit users are most influenced by the overall distribution of editing in Wikipedia (50%), then by their own edit history (35%), and finally by the the edit history of their neighbors (8%). In addition, 7% of the time they choose to start a new article rather than editing anything that already exists.

Insight from Selected Interactions• We randomly selected 30 instances of two users meeting for the first time.

We examined the content of the initial communication and any reply, looking for references to specific articles or other artifacts in Wikipedia. We also compared the edit history of the two users.

• Of the 30 messages, 26 referenced a specific article, image, or topic. In 21 cases, the users had both recently worked on the artifact that was the subject of conversation.

• The gap between co-activity and communication was usually short, often less than a day, though it stretched back three months in one case.

• Informally, communications tended to fall into a few broad categories: o ering thanks and praise, making requests for help, or trying to ffunderstand the editing.behavior of the other person.

• This sample of interactions suggests that people most often come to talk to each other in Wikipedia when they become aware of the other person through recent shared activity around an artifact. Awareness then leads to communication, and often coordination.

Up to now ...• FIRST they observed the world• Second they modeled the world• Now they are going to PREDICT the world!!! i.e. compare similarity and social ties in predicting behavior

• OMG!!!!!!!

In particular, we create two networks, one based on social interaction and one based on similarity of past behavior (directed)

• For the interaction network, we create directed edges (v, w) between any users v and w such that v has edited w’s user discussion page at some point before a given reference time t1.

• We then create a similarity network with the same ordered degree sequence: if node v has dv outneighbors in the interaction network, we connect it to thedv nodes whose activity vectors are the most similar to v’sactivity vector v(t1 ).

• vector similarity measure = weighted Jaccard coe cientffi

Compare similarity and social ties in predicting behavior

• Once we create the networks, we use them to estimate the probability of future activities as follows.

• For either network, we say that an individual u is k-exposed to an activity a at time t1 if that individual is a non-adopter of a at t1 and has exactly k neighbors who are adopters at t1 .

• We then see whether u adopts a sometime between t1 and a later time t2 . Let p(k) be the fraction of cases in which a user was k-exposed to activity a at t1 and then adopted that behavior between t1 and t2 .

Why just Wikipedia?!?• They predicted on 2 datasets!!!• The first is Wikipedia, with the definitions of interactions

and activities as defined previously; • The second is LiveJournal, where we define interactions

based on declared friendship links, and each Live-Journal community defines an activity that a user can engage in simply by joining the community.

Probability of joining a community based on k exposure via social ties versus similarity ties

• [Backstrom06] found that the more friends in a community, the higher a user’s probability of joining that community

• We compare similarity and social ties in predicting behavior– in Wikipedia, social ties are more predictive– in LiveJournal, interest similarity is more predictive

social tiessimilarity

social tiessimilarity

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