1

Jie Tang

Tsinghua University, China

Collaborate with

Jimeng Sun (IBM), Chi Wang (UIUC), and Chenhao Tan (Cornell)

Social Influence Analysis and Action

Prediction via Factor Graph Models

2

Motivation

• 500 million users

• the 3rd largest ―Country‖ in the world

• More visitors than Google

• Action: Update statues, create event

• More than 4 billion images

•Action: Add tags, Add favorites

• 2009, 2 billion tweets per quarter

• 2010, 4 billion tweets per quarter

•Action: Post tweets, Retweet

Social networks already become a bridge to connect

our really daily life and the virtual web space

3

Motivation (cont.)

• Modeling and tracking users’ actions in

social networks is a very important issue

and can benefit many real applications

– Advertising

– Social recommendation

– Marketing

– …

4

Ada

Frank

Eve David

Carol

Bob

George

2

1

14

2

2 33

Marketer Alice

Application—Influence Maximization

Find K nodes (users) in a social network that could maximize the

spread of influence (Domingos, 01; Richardson, 02; Kempe, 03)

Social action and

influence Who are the

opinion leaders

in a community?

5

Ada

Frank

Eve David

Carol

Bob

George

2

1

14

2

2 33

Marketer Alice

Application—Influence Maximization

Find K nodes (users) in a social network that could maximize the

spread of influence (Domingos, 01; Richardson, 02; Kempe, 03)

Social action and

influence Who are the

opinion leaders

in a community?

Questions: - How to quantify the strength of social influence

between users?

- How to predict users’ actions over time?

6

Jie Tang, Jimeng Sun, Chi Wang, and Zi Yang. Social Influence Analysis in

Large-scale Networks. SIGKDD 2009. pp. 807-816.

Social Influence Analysis

7

Topic-based Social Influence Analysis

• Social network -> Topical influence network

Ada

Frank

Eve David

Carol

Bob

George

Input: coauthor network

Ada

Frank

Eve David

Carol

George

Social influence anlaysis

θi1=.5

θi2=.5

Topic

distributiong(v1,y1,z)θi1

θi2

Topic

distribution

Node factor function

f (yi,yj, z)

Edge factor function

rz

az

Output: topic-based social influences

Topic 1: Data mining

Topic 2: Database

Topics:

Bob

Output

Ada

Frank

Eve

BobGeorge

Topic 1: Data mining

Ada

Frank

Eve David

George

Topic 2: Database

. . .

2

1

14

2

2 33

8

How a person

influence a social

community?

Several key challenges: • How to differentiate the social influences from

different angles (topics)?

• How to incorporate different information (e.g.,

topic distribution and network structure) into a

unified model？

• How to estimate the model on real-large networks?

How two persons

Influence each

other?

9

Our Solution: Topical Affinity Propagation

• Topical Affinity Propagation

– Topical Factor Graph model

– Efficient learning algorithm

– Distributed implementation

10

Topical Factor Graph (TFG) Model

Node/user

Nodes that have the

highest influence on

the current node

The problem is cast as identifying which node has the highest probability to

influence another node on a specific topic along with the edge.

Social link

11

• The learning task is to find a configuration

for all {yi} to maximize the joint probability.

Topical Factor Graph (TFG)

Objective function:

1. How to define?

2. How to optimize?

12

How to define (topical) feature functions?

– Node feature function

– Edge feature function

– Global feature function

similarity

or simply binary

13

Model Learning Algorithm

Sum-product:

- Low efficiency!

- Not easy for

distributed learning!

}{~ \~'

)'(')(

\~'

)(')(

)',(i i

ijiiij

iji

iiiiji

y yfy

yfyiyyf

fyf

yyfyfy

myyfm

mm

14

New TAP Learning Algorithm

1. Introduce two new variables r and a, to replace

the original message m.

2. Design new update rules:

mij

15

The TAP Learning Algorithm

16

• Map-Reduce

– Map: (key, value) pairs

• eij /aij ei* /aij; eij /bij ei* /bij; eij /rij e*j /rij .

– Reduce: (key, value) pairs

• eij / * new rij; eij/* new aij

• For the global feature function

Distributed TAP Learning

17

Experiment

• Data set: (http://arnetminer.org/lab-datasets/soinf/)

• Evaluation measures

– CPU time

– Case study

– Application

Data set #Nodes #Edges

Coauthor 640,134 1,554,643

Citation 2,329,760 12,710,347

Film 18,518 films

7,211 directors

10,128 actors

9,784 writers

142,426

18

Scalability Performance

19

Speedup results

0 170K 540K 1M 1.7M0

1

2

3

4

5

6

7

1 2 3 4 5 61

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Perfect

Our method

Speedup vs. Dataset

size

Speedup vs. #Computer

nodes

20

Influential nodes on different topics

21

Social Influence Sub-graph on ―Data mining‖

22

Application—Expert Finding

Expert finding data from (Tang, KDD08; ICDM08)

http://arnetminer.org/lab-datasets/expertfinding/

23

Social Action Prediction

Chenhao Tan, Jie Tang, Jimeng Sun, Quan Lin, and Fengjiao Wang. Social

Action Tracking via Noise Tolerant Time-varying Factor Graphs. SIGKDD 2010.

pp. 1049-1058.

24

John

Time t

John

Time t+1

Action Prediction：

Will John post a tweet on ―Haiti Earthquake‖?

Personal attributes:

1. Always watch news

2. Enjoy sports

3. ….

Influence 1

Action bias 4

Dependence 2

Social Action Modeling and Prediction

Correlation 3

25

Problem formulation

Gt =(Vt, Et, Xt, Yt)

Input:

Gt =(Vt, Et, Xt, Yt) t = 1,2,…T

Output:

F: f(Gt) ->Yt

Nodes at time t

Edges at time t

Attribute matrix at time t

Actions at time t

26

NTT-FGM Model

Continuous latent action state Personal attributes

Correlation

Dependence

Influence

Action Personal attributes

27

How to estimate the parameters?

Model Instantiation

28

Model Learning—Two-step learning

Extremely time costing!!

Our solution: distributed learning (MPI)

29

• Data Set (http://arnetminer.org/stnt)

• Baseline

– SVM

– wvRN (Macskassy, 2003)

• Evaluation Measure:

Precision, Recall, F1-Measure

Action Nodes #Edges Action Stats

Twitter Post tweets on

―Haiti Earthquake‖ 7,521 304,275 730,568

Flickr Add photos into

favorite list 8,721 485,253 485,253

Arnetminer Issue publications

on KDD 2,062 34,986 2,960

Experiment

30

Performance Analysis

31

Factor Contribution Analysis

• NTT-FGM: Our model

• NTT-FGM-I: Our model ignoring influence

• NTT-FGM-CI: Our model ignoring influence and correlation

32

Efficiency Performance

With

5x4

cores

33

Conclusion

• Formalize a novel problem of topic-based social

influence analysis and propose a Topical Factor

Graph model to solve this problem

• Propose a unified model: NTT-FGM to model and

predict social actions

• Distributed model learning:

– For TFG model: Map-reduce (hadoop)

– For NTT-FGM: MPI (Message Passing Interface)

34

Thank you！

QA?

Data & Code:

http://arnetminer.org/lab-datasets/soinf

http://arnetminer.org/stnt

35

Statistical Study: Influence Y-axis: the likelihood that the user also performs the action at t

X-axis: the percentage of one’s friends who perform an action at t − 1

36

Statistical Study: Dependence Y-axis: the likelihood that a user performs an action

X-axis: different time windows

37

Statistical Study: Correlation Y-axis: the likelihood that two friends(random) perform an action together

X-axis: different time windows

38

Appendix

39

Appendix

40

Appendix

41

Prediction

• Based on the learning parameters we just

need to solve the following equations:

42

Latent State Analysis

Action Bias Factor: f(y12|z1

2)

Influence Factor: g(z11,z1

2)

Correlation Factor: h(z12,z2

2), h(z12,x1

2)

43

Related Work—Social networks and influences

• Social network

– Metrics to characterize a social network

– Web community discovery [Flake,2000]

• Influence in social network

– The existence of influence. [Singla, 2008]

[Anagnostopoulos, 2008]

– The correlation between social similarity and

interactions [Crandall, 2008]

44

• Factor graph models – A graph model [Kschischang, 2001]

– Computing marginal function [Frey, 2006]

– Message passing/affinity propagation [Frey, 2007]

• Distributed programming model – Map-reduce [J. Dean, 2004]

Related Work—large-scale mining