social influence analysis and action prediction via factor
TRANSCRIPT
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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
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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
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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
– …
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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?
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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?
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Jie Tang, Jimeng Sun, Chi Wang, and Zi Yang. Social Influence Analysis in
Large-scale Networks. SIGKDD 2009. pp. 807-816.
Social Influence Analysis
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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
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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?
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Our Solution: Topical Affinity Propagation
• Topical Affinity Propagation
– Topical Factor Graph model
– Efficient learning algorithm
– Distributed implementation
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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
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• 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?
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How to define (topical) feature functions?
– Node feature function
– Edge feature function
– Global feature function
similarity
or simply binary
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Model Learning Algorithm
Sum-product:
- Low efficiency!
- Not easy for
distributed learning!
}{~ \~'
)'(')(
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)(')(
)',(i i
ijiiij
iji
iiiiji
y yfy
yfyiyyf
fyf
yyfyfy
myyfm
mm
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New TAP Learning Algorithm
1. Introduce two new variables r and a, to replace
the original message m.
2. Design new update rules:
mij
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The TAP Learning Algorithm
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• 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
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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
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Scalability Performance
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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
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Influential nodes on different topics
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Social Influence Sub-graph on ―Data mining‖
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Application—Expert Finding
Expert finding data from (Tang, KDD08; ICDM08)
http://arnetminer.org/lab-datasets/expertfinding/
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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.
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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
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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
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NTT-FGM Model
Continuous latent action state Personal attributes
Correlation
Dependence
Influence
Action Personal attributes
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How to estimate the parameters?
Model Instantiation
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Model Learning—Two-step learning
Extremely time costing!!
Our solution: distributed learning (MPI)
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• 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
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Performance Analysis
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Factor Contribution Analysis
• NTT-FGM: Our model
• NTT-FGM-I: Our model ignoring influence
• NTT-FGM-CI: Our model ignoring influence and correlation
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Efficiency Performance
With
5x4
cores
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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)
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Thank you!
QA?
Data & Code:
http://arnetminer.org/lab-datasets/soinf
http://arnetminer.org/stnt
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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
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Statistical Study: Dependence Y-axis: the likelihood that a user performs an action
X-axis: different time windows
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Statistical Study: Correlation Y-axis: the likelihood that two friends(random) perform an action together
X-axis: different time windows
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Appendix
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Appendix
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Appendix
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Prediction
• Based on the learning parameters we just
need to solve the following equations:
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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)
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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]
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• 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