Belief evolution over signed social networks

Guodong SHI (Royal Institute of Technology, Sweden (KTH))

SYSTEMS AND CONTROL SERIES

DATE: 2013-10-17
TIME: 10:30:00 - 11:30:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU
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ABSTRACT:
In this talk, I will discuss our recent work on opinion dynamics over signed social networks. We consider a social network modeled as a signed graph. The sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends (positive link) or enemies (negative link). Pairs of nodes are randomly selected to interact over time, and when two nodes interact, each of them updates her opinion based on the opinion of the other node in a manner dependent on the sign of the corresponding link. Our model for the opinion dynamics is essentially linear and generalizes DeGroot model to account for negative links a" when two enemies interact, their opinions go in opposite directions. We provide conditions for convergence and divergence in expectation, in mean-square, and in almost sure sense, and exhibit phase transition phenomena for these notions of convergence depending on the parameters of our opinion update model and on the structure of the underlying graph. We establish a no-survivor theorem, stating that the difference in opinions of any two nodes diverges whenever opinions in the network diverge as a whole. We also prove a live-or-die lemma, indicating that almost surely, the opinions either converge to an agreement or diverge. Finally, we extend our analysis to cases where opinions have hard lower and upper limits. In these cases, we study when and how opinions may become asymptotically clustered, and highlight the impact of the structural properties (namely structural balance) of the underlying network on this clustering phenomenon.

BIO:
Guodong Shi received his PhD in 2010 from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China. From Sep. 2010 he has been a postdoctoral researcher with the Automatic Control Lab, KTH Royal Institute of Technology, Stockholm, Sweden. His research focuses on distributed control, computation, and optimization methods over deterministic or random dynamical networks using tools mainly from probability theory, control theory, and convex optimization.