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Jing (Selena) He and Hisham M. HaddadDepartment of Computer Science, Kennesaw State University
Shouling Ji, Xiaojing Liao, and Raheem BeyahSchool of Electrical and Computer Engineering, Georgia Institute of Technology
IPCCC 2013
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Minimum-sized Positive Influential Node Set Selection for Social Networks:
Considering Both Positive and Negative Influences
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OUTLINE
MotivationProblem DefinitionGreedy AlgorithmPerformance EvaluationConclusions
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Motivation• Example & Applications• Related Work• Contributions
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INTRODUCTION
What is a social network? The graph of relationships and interactions within a group of
individuals.
Motivation
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SOCIAL NETWORK AND SPREAD OF INFLUENCE Social network plays a fundamental
role as a medium for the spread of INFLUENCE among its members Opinions, ideas, information,
innovation…
Direct Marketing takes the “word-of-mouth” effects to significantly increase profits (facebook, twitter, myspace, …)
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Motivation
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MOTIVATION
• 900 million users, Apr. 2012• 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 connectour really daily life and the virtual web space
Motivation
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Who are the opinion leaders in a community?
Marketer Alice
EXAMPLE
Find minimum-sized node (user) set in a social network that could positively influence on every node in the network
Motivation
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APPLICATIONS
Smoking intervention program Promote new products Advertising Social recommendation Expert finding …
Motivation
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RELATED WORK
Influence Maximization (IM) Problem [Kempe03]Select k nodes, maximize the expected number
of influenced individuals
Positive Influence Dominating Set (PIDS) [Wang11]Minimum-sized nominating set D, every other
node has at least half of its neighbors in D
Motivation
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OUR CONTRIBUTIONS
o Consider both positive and negative influences
o 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
o Propose a greedy algorithm to solve MPINS
o Conduct simulations to validate the proposed algorithm
Motivation
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Problem Definition• Network Model• Diffusion Model• Problem Definition
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NETWORK MODEL
A social network is represented as an undirected graph Social influence represented by weights on the edges
Positive influence 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 assumption: active nodes never deactivate
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Problem Definition
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DIFFUSION MODEL
Positive influence
Negative influence
Ultimate influence
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Problem Definition
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MINIMUM-SIZED POSITIVE INFLUENCE NODE SET (MPINS)
Givena social networka threshold θ
GoalThe initially selected active node set denoted
by I could positively influence every other node in the network
, Objective
Minimize the size of I 14
Problem Definition
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Greedy Algorithm• Contribution function• Example• Correctness proof
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CONTRIBUTION FUNCTION
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Greedy algorithm
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TWO-PHASE ALGORITHM
Maximal Independent Set (M)
Greedy algorithm
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Greedy algorithm
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EXAMPLE
Greedy algorithm
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CORRECTNESS PROOF
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Greedy algorithm
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Performance Evaluation• Simulation settings• Simulation results
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SIMULATION SETTINGS
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Performance Evaluation
Generate random graph
The weighs on edges are randomly generated
For each specific setting, 100 instances are generated. The results are the average values of these 100 instances
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SIMULATION RESULTS – SMALL SCALE
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Performance Evaluation
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SIMULATION RESULTS – LARGE SCALE
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Performance Evaluation
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SIMULATION RESULTS
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Performance Evaluation
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CONCLUSIONS
We study MPINS selection problem which has useful commercial applications in social networks.
We propose a greedy algorithm to solve the problem.
We validate the proposed algorithm through simulation on random graphs representing small size and large size networks.
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Conclusions
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Q & A