Download Minimum-sized Positive Influential Node Set

IPCCC 2013
Minimum-sized Positive Influential Node Set
Selection for Social Networks:
Considering Both Positive and Negative
Influences
Jing (Selena) He and Hisham M. Haddad
Department of Computer Science, Kennesaw State University
Shouling Ji, Xiaojing Liao, and Raheem Beyah
School of Electrical and Computer Engineering, Georgia Institute of Technology
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OUTLINE



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
Motivation
Problem Definition
Greedy Algorithm
Performance Evaluation
Conclusion
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Motivation
o Example & Applications
o Related Work
o Contributions
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Motivation
INTRODUCTION

What is a social network?
o
The graph of relationships and interactions within a group of
individuals
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Motivation
SOCIAL NETWORK AND SPREAD OF
INFLUENCE
 Social
network plays a fundamental
role as a medium for the spread of
INFLUENCE among its members
o
Opinions, ideas, information,
innovation…
 Direct
Marketing takes the “word-of-mouth”
effects to significantly increase profits
(facebook, twitter, myspace, …)
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Motivation
MOTIVATION
o
o
o
o
900 million users, Apr. 2012
the 3rd largest ― “Country” in the world
More visitors than Google
Action: Update statues, Create event
o More than 4 billion images
o Action: Add tags, Add favorites
Social networks already become a bridge to connect
our daily life and the virtual web space
o 2009, 2 billion tweets per quarter
o 2010, 4 billion tweets per quarter
o Action: Post tweets, Retweet
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Motivation
EXAMPLE
Who are the positively
influential leaders in a
community?
Marketer Alice
Find minimum-sized node (user) set in a social network that
could positively influence every node in the network
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Motivation
APPLICATIONS

Smoking intervention program
 Promote new products
 Advertising
 Social recommendation
 Expert finding
 …
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Motivation
RELATED WORK

Influence Maximization (IM) Problem [Kempe03]
o Select k nodes, maximize the expected number of
influenced individuals

Positive Influence Dominating Set (PIDS) [Wang11]
o Minimum-sized nominating set D, every other
node has at least half of its neighbors in D
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Motivation
OUR CONTRIBUTIONS
 Consider
both positive and negative influences
 New
optimization problem - Minimum-sized
Positive Influential Node Set (MPINS)
o
Minimum-sized node set that could positively
influence every node in the network no less than a
threshold θ
 Propose
a greedy algorithm to solve MPINS
 Conduct
simulations to validate the proposed
algorithm
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Problem Definition
o Network Model
o Diffusion Model
o Problem Definition
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Problem Definition
NETWORK MODEL
 A social
 Social
network is represented as a undirected graph
influence represented by the weights on the
edges
o
Positive influence
o
Negative influence
 Nodes
start either active or inactive
 An
active node may trigger activation of neighboring
nodes based on a pre-defined threshold θ
 Monotonicity
deactivate
assumption: active nodes never
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Problem Definition
DIFFUSION MODEL
 Positive
influence
 Negative
influence
 Ultimate
influence
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Problem Definition
MINIMUM-SIZED POSITIVE INFLUENCE NODE
SET SELECTION PROBLEM (MPINS)
 Given
a social network
o a threshold θ
 Goal
o The initially selected active node set denoted
by I could positively influence every other
node in the network
o
,
 Objective
o Minimize the size of I
o
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Greedy Algorithm
o Contribution Function
o Example
o Correctness Proof
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Greedy algorithm
CONTRIBUTION FUNCTION

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Greedy algorithm
TWO-PHASE ALGORITHM

Maximal Independent Set (M)

Greedy algorithm
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Greedy algorithm
EXAMPLE
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Greedy algorithm
CORRECTNESS PROOF

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Performance Evaluation
o Simulation Settings
o Simulation Results
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Performance Evaluation
SIMULATION SETTINGS
 Generate
random graph
 Randomly
generate the weighs on the edges
 For
each specific setting, generate 100 instances of the
graph. The results are the average values of these 100
instances
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Performance Evaluation
SIMULATION RESULTS – SMALL SCALE
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Performance Evaluation
SIMULATION RESULTS – LARGE SCALE
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Performance Evaluation
SIMULATION RESULTS
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Conclusion
CONCLUSION
 We
study MPINS selection problem considering both
positive and negative influences, which has useful
commercial applications in social networks
 We
propose a greedy algorithm to solve the problem
 We
validate the proposed algorithm through
simulations on random graphs representing small and
large size networks
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RELATED REFERENCES
 [Kempe03]
D. Kempe, J. Kleinberg, and E. Tardos,
Maximizing the Spread of Influence through a Social
Network, KDD, 2003.
 [Wang11]
F. Wang, H. Du, E. Camacho, K. Xu, W.
Lee, Yan, Shi, and S. Shan, On Positive Influence
Dominating Sets in Social Networks, TCS, 2011.
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Q&A
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