Dissensus Algorithms for Opinion Dynamics on the Sphere

TL;DR

This paper introduces novel dissensus algorithms based on PCA flow for opinion dynamics on the sphere, achieving dissensus equilibria without negative interactions, with stability analysis and simulation validation.

Contribution

It presents a new PCA-based dissensus algorithm for opinion dynamics on the sphere, differing from traditional signed graph approaches, with stability analysis and simulation results.

Findings

Achieves dissensus equilibrium without negative graph weights

Provides stability analysis for both consensus and dissensus states

Demonstrates effectiveness through multi-agent system simulations

Abstract

In this paper, novel dissensus algorithms based on the Oja principal component analysis (PCA) flow are proposed to model opinion dynamics on the unit sphere. The information of the covariance formed by the opinion state of each agent is used to achieve a dissensus equilibrium on unsigned graphs. This differs from most of the existing work where antagonistic interactions represented by negative weights in signed graphs are used to achieve a dissensus equilibrium. The nonlinear algorithm is analyzed under both constant covariance and time-varying covariance leading to different behaviors. Stability analysis for the unstable consensus and stable dissensus equilibria is provided under various conditions. The performance of the algorithm is illustrated through a simulation experiment of a multi-agent system.