French-DeGroot社会网络模型的结构辨识与参数估计

Structure inference and parameter identification for French-DeGroot type of social networks

中文关键词  社会网络  最小二乘算法  参数估计  结构辨识

英文关键词  social network  least squares algorithm  parameter estimation  structure identification

中文摘要

      近年来社会网络的研究受到越来越多的关注, 本文研究基于French-DeGroot模型的社会网络参数和结构辨识问题, 通过网络中个体对话题所持的观点来判断个体间是否存在影响关系、进一步估计个体之间影响的大小. 具体而言: 假设网络存在固执个体(stubborn agents)和非固执个体(non-stubborn agents) 两类, 当固执个体的观点为零均值独立同分布随机变量序列时, 利用最小二乘算法估计网络未知参数, 证明了估计的强一致性并给出收敛速度; 进一步, 构造结构辨识算法判断个体间是否存在影响关系, 证明了结构辨识算法的有限时间收敛性. 最后给出仿真例子验证算法的有效性.

英文摘要

      In recent years, the research for social networks has attracted more and more attention. In this paper we consider the parameter and structure identification of social networks based on the French-DeGroot model. We assume that there are two types of agents in the network, i.e., stubborn agents and non-stubborn agents. Based on the assumption that the opinions of the stubborn agents are a sequence of independent and identically distributed random variables with zero expectation, the parameter matrix of the French-DeGroot model is recursively estimated by the least-square algorithm, and strong consistency of estimates as well as convergence rate are established. Then structure identification algorithm for the network is proposed and it is proved that with the estimates we can infer the structure of the network, i.e., whether mutual influence existing between agents can be exactly identified with finite number of observations. Finally, numerical examples are given to testify performance of the algorithms.