随机块模型上流言意见动力学中的几乎精确恢复
Almost Exact Recovery in Gossip Opinion Dynamics over Stochastic Block Models
AI总结：
本文研究随机块模型上流言意见动力学中的社区检测问题，提出基于瞬时状态聚类和时间平均状态聚类的两种算法，并证明在不同顽固智能体影响条件下均可实现几乎精确恢复。
摘要：
我们研究基于随机块模型（SBM）上流言意见动力学的状态观测进行社区检测。假设网络由一个双社区随机块模型生成，其中每个智能体具有一个社区标签，每条边以取决于其端点标签的概率存在。随后，一个流言过程在采样得到的网络上演化。我们提出两种算法，从该过程的单条轨迹中检测社区。研究表明，当顽固智能体的影响较小且社区内部的连边概率较大时，一种基于对瞬时智能体状态进行聚类的算法能够实现社区的几乎精确恢复。也就是说，该算法能够以高概率恢复除消失比例之外的所有社区标签。相比之下，当顽固智能体的影响较大时，另一种基于对智能体状态的时间平均进行聚类的算法能够实现几乎精确恢复。文中给出数值实验以说明这两种算法及本文的理论结果。
英文摘要：
We study community detection based on state observations from gossip opinion dynamics over stochastic block models (SBM). It is assumed that a network is generated from a two-community SBM where each agent has a community label and each edge exists with probability depending on its endpoints' labels. A gossip process then evolves over the sampled network. We propose two algorithms to detect the communities out of a single trajectory of the process. It is shown that, when the influence of stubborn agents is small and the link probability within communities is large, an algorithm based on clustering transient agent states can achieve almost exact recovery of the communities. That is, the algorithm can recover all but a vanishing part of community labels with high probability. In contrast, when the influence of stubborn agents is large, another algorithm based on clustering time average of agent states can achieve almost exact recovery. Numerical experiments are given for illustration of the two algorithms and the theoretical results of the paper.
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