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 IPCCC Minimum-sized Positive Influential Node Set Selection for Social Networks: Considering Both Positive and Negative Influences

O UTLINE Motivation Problem Definition Greedy Algorithm Performance Evaluation Conclusions 2

3 Motivation Example & Applications Related Work Contributions

4 I NTRODUCTION What is a social network? The graph of relationships and interactions within a group of individuals. Motivation

S OCIAL N ETWORK AND S PREAD OF I NFLUENCE 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, …) 5 Motivation

M OTIVATION million users, Apr the 3 rd 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 Motivation

7 Who are the opinion leaders in a community? Marketer Alice E XAMPLE Find minimum-sized node (user) set in a social network that could positively influence on every node in the network Motivation

A PPLICATIONS Smoking intervention program Promote new products Advertising Social recommendation Expert finding … 8 Motivation

R ELATED W ORK 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 9 Motivation

O UR C ONTRIBUTIONS 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 10 Motivation

11 Problem Definition Network Model Diffusion Model Problem Definition

N ETWORK M ODEL 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 12 Problem Definition

D IFFUSION M ODEL Positive influence Negative influence Ultimate influence 13 Problem Definition

M INIMUM - SIZED P OSITIVE I NFLUENCE N ODE S ET (MPINS) Given a social network a threshold θ Goal The 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

15 Greedy Algorithm Contribution function Example Correctness proof

C ONTRIBUTION FUNCTION 16 Greedy algorithm

T WO - PHASE ALGORITHM Maximal Independent Set (M) Greedy algorithm 17 Greedy algorithm

18 E XAMPLE Greedy algorithm

C ORRECTNESS P ROOF 19 Greedy algorithm

20 Performance Evaluation Simulation settings Simulation results

S IMULATION S ETTINGS 21 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

S IMULATION R ESULTS – SMALL SCALE 22 Performance Evaluation

S IMULATION R ESULTS – L ARGE SCALE 23 Performance Evaluation

S IMULATION R ESULTS 24 Performance Evaluation

C ONCLUSIONS 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. 25 Conclusions

26 Q & A