POSITIVE OPINION INFLUENTIAL NODE SET

SELECTION FOR SOCIAL NETWORKS:

CONSIDERING BOTH POSITIVE AND NEGATIVE

RELATIONSHIPS

Presenter: Jing (Selena) He

Department of Computer Science,

Kennesaw State University

Kennesaw, GA, USA

WCNA 2014

OUTLINE

Motivation

Problem Definition

Greedy Algorithm

Performance Evaluation

Conclusion

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OUTLINE

Motivation

Problem Definition

Greedy Algorithm

Performance Evaluation

Conclusion

3

4

INTRODUCTION

What is a social network?

o The graph of relationships and interactions within a group of

individuals

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, …)5

MOTIVATION

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o 900 million users, Apr. 2012

o the 3rd largest ― “Country” in the world

o More visitors than Google

o Action: Update statues, Create event

o More than 4 billion images

o Action: Add tags, Add favorites

o 2009, 2 billion tweets per quarter

o 2010, 4 billion tweets per quarter

o Action: Post tweets, Retweet

Social networks already become a bridge to connect

our daily life and the virtual web space

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Who are the positively

influential leaders in a

community?

Marketer Alice

EXAMPLE

Find minimum-sized node (user) set in a social network that

could positively influence every node in the network

APPLICATIONS

Smoking intervention program

Political Campaign

Advertising

Social recommendation

Expert finding

…

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OUR CONTRIBUTIONS

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Consider both positive and negative influences

New optimization problem - Positive Opinion

Influential Node Set (POINS) selection problem

o node set with size k that could maximizes the

spread of positive opinion influences

Propose a greedy algorithm to solve POINS

Conduct simulations to validate the proposed

algorithm

OUTLINE

Motivation

Problem Definition

Greedy Algorithm

Performance Evaluation

Conclusion

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NETWORK MODEL

A social network is represented as a undirected graph

Nodes are divided to two sets

VA positive node sets

VB negative node sets

Social influence represented by the weights on the edges

Positive influence: friendship relationship

Negative influence: foe relationship

Nodes start either active or inactive

An active node may trigger activation of neighboring nodes based on a pre-defined threshold θ

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DIFFUSION MODEL

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otherwise ),(

||w when ),(

||w when ),(

)1( )1(ij

)1( )1(ij

tS

wtS

wtS

v

IN

tSv tSvB

iijB

tSv tSvA

iijA

iB

jA

j

Aj

Bj

POSITIVE OPINION INFLUENCE NODE SET

SELECTION PROBLEM (POINS)

Given

o a social network

o thresholds θiA and θi

B

Objective

o find an initial active node set with opinion A

represented by SA(0) of size at most k that

maximize the expected value of the number of

active nodes with opinion A denoted by ρ(t),

i.e., 13

G = (V, E, W), SB (0), and k

)( max argk(0)|S| A

t

OUTLINE

Motivation

Problem Definition

Greedy Algorithm

Performance Evaluation

Conclusion

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CONTRIBUTION FUNCTION

where δ represents the maximum degree in the graph G

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∑ ∑)0(∈ )0(∈

||||

)(A

jB

jSv Sv

ijij

B

ii ww

Nvf

GREEDY ALGORITHM

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17

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OUTLINE

Motivation

Problem Definition

Greedy Algorithm

Performance Evaluation

Conclusion

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SIMULATION SETTINGS

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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

SIMULATION RESULTS

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The default setting is n=15, p=0.5, and θ=0.5

OUTLINE

Motivation

Problem Definition

Greedy Algorithm

Performance Evaluation

Conclusion

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CONCLUSION

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Positive Opinion Influential Node Set (POINS)

selection problem is proposed and studied

A greedy algorithm to solve POINS

Implement simulations to validate proposed

algorithm on random graphs

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Q & A