A Study of social influence in diffusion of innovation over Facebook

Shaomei Wu

sw475@cornell.edu

Information Science

Cornell University

Information Science Breakfast, Dec 5, 2008

Diffusion of Innovation

“ Diffusion is the process in which an innovation is communicated through certain channels over time among the members of a social system. ”

–––– Everett M. Rogers *

“innovation”: Friendship Quiz – a Facebook application “Communicated”: Invitations among Facebook friends “time”: September 25, 2008 – Now “social system”: Facebook

* Rogers, Everett M. (2003). Diffusion of Innovations, 5th ed.. New York, NY: Free Press, pp 5-6

Basic Diffusion Models

Threshold Model Cascade Model⇔

Statistically Equivalent *

*David Kempe, Jon Kleinberg, Eva Tardos. Maximizing the Spread of Influence through a Social Network. KDD, 2003

Cascade Model

Each recommendation will succeed with certain probability.

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pab

pagpac

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non-adopter

adopter

social link

recommendationQuestion: how to estimate puv ?

Question: how to estimate puv?

Current practice Constant [1]

Based on ONLY network structure (e.g., in/out-degree) [2]

[1] Jure Leskovec, Mary McGlohon, Christos Faloutsos, Natalie Glance, Matthew Hurst, Cascading Behavior in Large Blog Graphs. SDM 2007.

[2] Jure Leskovec, Lada Adamic, Bernardo Huberman. The Dynamics of Viral Marketing. ACM Conference on Electronic Commerce (EC) 2006.

Do individuals and the social relationship among them matter?

Theories from Empirical Diffusion Research:

Opinion leaders: who own “greater exposure to mass media than their followers”, “are more cosmopolite”, “have greater social participation” , “have higher socioeconomic status”, and “are more innovative” [Rogers 2003, pp 316-318].

The importance of heterophily between participants on certain attributes (i.e., education and socioeconomic status) at determining the efficiency of diffusion, despite the fact that “more effective communication occurs when two or more individuals are homophilous” [Rogers, 2003, pp19]

This project is to…

Model puv’s for cascade model Identify the most influential factors at determining puv

Predict the success of contagion

Exploit Facebook data A real-world, ongoing diffusion instance; Rich and (most of the time) trustable profile information of

individuals and their social connections/activities; Precisely timestamped diffusion process, a complete log of

events;

Status

Launched: Sep 25, 2008. Currently used data is until: Nov 25, 2008.

216 adopters, 375 individuals, 737 edges between 266 pairs of people, 90 successful infection 178 failed infection

Network Evolution (in the first month after release)

political view distribution

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erva

tive

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ratic

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lican

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# of people

adopters

non-adopters

Religious View Distribution

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Christian Muslim Other

Religion

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t adopters

non-adopters

Gender distribution

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adopters non-adopters

# o

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male

Age distribution

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Non-adopter

Adopter

Predict the success of invitation with SVM

A Binary classifier: each invitation is either successful or failed.

Features Individual features Pair features (homophily/heterophily)

Individual Features

# of events attended/invited# of photo tagged

# of wall posts# of networks

# of groups participated# of notesReligion

Political ViewGender

AgeCulture BackgroundRelationship Status

Work InfoEducation Info

Social Activeness

Socioeconomics

Education

Innovativeness

Pair-wise Features

Age differenceSame gender?

Same political view?Same religion?

Same culture background?# of same networks

# of photos both tagged# of groups both participated

# of events both attendedSame education level?

Same high school?Same college?

Same workplace?Same current city?

Biological traits

Socioeconomics

Proximity

Belief

time sender receiver classsender

featuresreceiver features

pair features

2008-09-25 18:25:41

589483260 3621185 1 1:22 2:1 3:0 4:0 5:0 6:1 … …

35:1 47:0 48:0 49:0 50:0 51:0

… …

68:0 69:0 70:0 74:1 76:1

… …

2008-09-25 18:25:49

3621185 571023231 -1 … … …

… … … … … … …

… … … … … … …

2008-11-24 02:40:34

768059413 81405257 -1 … … …

Training Data

Each invitation is a training example - machine learning.

* all numerical features are normalized across examples.

AdaBoost (with DecisionDump) A popular way to do feature selection.

Selected Features sender wall post count sender group count sender network count receiver age receiver group count sender & receiver common group count

Performance (10-fold cross validation) Accuracy: 83.6%

Class precision Recall

-1 83.5% 93.8%

1 83.8% 63.3%

SVM performance SVM-light (10-fold cross-validation)

fold accuracy precision recall

1 80.77 100 58.33

2 80.77 100 44.44

3 88.46 100 62.5

4 76.92 50 33.33

5 73.08 100 30

6 84.62 100 50

7 69.23 50 50

8 76.92 100 53.85

9 88.46 100 66.67

10 88.24 80 57.14

average 80.747 88 50.626

Weights from SVM

feature weight distribution

sender_isOther

sender_isInARelationshipreceiver_isAtheist/Agnostic

receiver_isWorking

receiver_eventCount

receiver_groupCount

receiver_photoTagged

sameWorkPlace

receiver_age

sameReligionsameCollege

receiver_isMiddleEasternreceiver_isMuslim

receiver_isChristian

sender_isCollegesender_isWorking

sender_isChristian

sender_isModerate

sender_age receiver_isRepublicsender_wallCount

sender_isMarried

receiver_noteCount

sender_networkCount

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

feature

wei

gh

t

Result

SVM-light performance 209 records into 5 folds, 4 for training, 1 for testing. Performance on the testing set:

Accuracy: 71.43% (30 correct, 12 incorrect, 42 total) Precision/recall: 55.56%/38.46%

Feature weights distribution

Feature Weights

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5 6

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12 171819202122 242526

27

2830313233

34

35

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Top weighted features:

8, sender_events_invited,4, sender_friend_count,11, sender_gender35, receiver_is_It's Complicated5, sender_wall_post_count,9, sender_note_count27. sender_is_In a Relationship

So, the story can be: when a sender who has been invited to greater number of events in Facebook, has more friends, wrote more Facebook notes (blog entries), is female, has less wall posts, in a relationship, tried to infect a person whose relationship status is “it’s complicated”, it’s more like the infection will happen compared to other cases.

SVM with features selected by AdaBoost

fold accuracy precision recall

1 80.77 100 58.33

2 80.77 83.33 55.56

3 88.46 100 62.5

4 73.08 0 0

5 76.92 100 40

6 84.62 83.33 62.5

7 76.92 66.67 50

8 80.77 100 61.54

9 96.15 100 88.89

10 91.18 83.33 71.43

average 82.96 81.67 55.075

Background

Diffusion of Innovation

Question: How does it work in large online social networks? What are the key factors at determining the

success of infection? Can we predict the propagation path?

Hypothesis Social influence depends on 5 dimensions of similarities:

geographical distance current location(country/state/city), current school, current major, year of class, current workplace, current courses enrolled;

background similarity sex, sexual preference, dating interest, relationship interest, relationship status, birthday, political view, religious view, hometown address, previous school, previous workplace;

social similarity number of mutual networks they belong to, number of mutual friends; interest similarity

activities, favorite books, favorite music, favorite movies, favorite TV shows, favorite quotas;

social status distance difference of numbers of friends, difference of wallpost counts, difference of counts

of message sent and received, difference of counts of notes.

Project Description

Objectives Identify the key factors for social influence; Predict occurrence of adoption based on the key

factors. Friendship Quiz

A Facebook application we developed; Enable users to make quizzes and send to their

friends (take a peek!); We track the spread of application.

Highlights

A real-world diffusion of innovation; Rich and (most of the time) trustful profile

information of individuals and their social connections/activities;

Precisely timestamped diffusion process, a complete log of events;

Ongoing diffusion process

Backup: Threshold Model