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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
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
6
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
7
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
…
8
OUR CONTRIBUTIONS
9
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
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
11
DIFFUSION MODEL
12
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
CONTRIBUTION FUNCTION
where δ represents the maximum degree in the graph G
15
∑ ∑)0(∈ )0(∈
||||
)(A
jB
jSv Sv
ijij
B
ii ww
Nvf
SIMULATION SETTINGS
19
19
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
CONCLUSION
22
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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