Reducing Polarization in Opinion Networks in the Presence of Stubborn Leaders
(2022)Department of Automatic Control
- Abstract
- We study the problem of reducing polarization (variance) of opinions at stationarity in a directed weighted graph with node set divided into two groups: stubborn, initialized with a fixed opinion and regular who repeatedly update their opinion to the average of their out-neighbors, known as the DeGroot model with stubborn nodes. We show how the polarization can be minimized for a number of simple constraints, but that the problem in general is not convex. Theory is developed for the change in opinions at stationarity and the polarization measure for a rank-1 update of the network (encompassing both addition of a directed and undirected link in the network). An algorithm for gradient approximation is presented, given directly by the... (More)
- We study the problem of reducing polarization (variance) of opinions at stationarity in a directed weighted graph with node set divided into two groups: stubborn, initialized with a fixed opinion and regular who repeatedly update their opinion to the average of their out-neighbors, known as the DeGroot model with stubborn nodes. We show how the polarization can be minimized for a number of simple constraints, but that the problem in general is not convex. Theory is developed for the change in opinions at stationarity and the polarization measure for a rank-1 update of the network (encompassing both addition of a directed and undirected link in the network). An algorithm for gradient approximation is presented, given directly by the analytical gradient formulation and method of matrix-vector product estimation. Lastly variations of the algorithm together with other trivial methods of recommending a link are compared for a number of random and real networks. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9075152
- author
- Selleck, Samuel
- supervisor
-
- Giacomo Como LU
- Emma Tegling LU
- organization
- year
- 2022
- type
- H3 - Professional qualifications (4 Years - )
- subject
- report number
- TFRT-6157
- other publication id
- 0280-5316
- language
- English
- id
- 9075152
- date added to LUP
- 2022-02-10 11:50:50
- date last changed
- 2022-02-10 11:50:50
@misc{9075152,
abstract = {{We study the problem of reducing polarization (variance) of opinions at stationarity in a directed weighted graph with node set divided into two groups: stubborn, initialized with a fixed opinion and regular who repeatedly update their opinion to the average of their out-neighbors, known as the DeGroot model with stubborn nodes. We show how the polarization can be minimized for a number of simple constraints, but that the problem in general is not convex. Theory is developed for the change in opinions at stationarity and the polarization measure for a rank-1 update of the network (encompassing both addition of a directed and undirected link in the network). An algorithm for gradient approximation is presented, given directly by the analytical gradient formulation and method of matrix-vector product estimation. Lastly variations of the algorithm together with other trivial methods of recommending a link are compared for a number of random and real networks.}},
author = {{Selleck, Samuel}},
language = {{eng}},
note = {{Student Paper}},
title = {{Reducing Polarization in Opinion Networks in the Presence of Stubborn Leaders}},
year = {{2022}},
}