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Register a new userDetecting Communities in a Gossip Model with Stubborn Agents
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We consider a community detection problem in a gossip model, where agents randomly interact pairwise, with stubborn agents never changing their states. It is assumed that the agents can be divided into two communities based on their interaction probability with others. Such a model can illustrate how disagreement and opinion fluctuation arise in a social network. The considered problem is twofold: to infer which community each agent belongs to, and to estimate interaction probabilities between agents, by only observing their state evolution. First, stability and limit theorems of the model are derived. An integrated detection and estimation algorithm is then proposed to infer the two communities and to estimate the interaction probabilities, based on agent states. It is verified that the community detector of the algorithm converges in finite time, and the interaction estimator converges almost surely. In addition, non-asymptotic property is obtained for the former, and convergence rate is analyzed for the latter. Simulations are presented to illustrate the performance of the proposed algorithm.
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We consider a community detection problem for gossip dynamics with stubborn agents in this paper. It is assumed that the communication probability matrix for agent pairs has a block structure. More specifically, we assume that the network can be divided into two communities, and the communication probability of two agents depends on whether they are in the same community. Stability of the model is investigated, and expectation of stationary distribution is characterized, indicating under the block assumption, the stationary behaviors of agents in the same community are similar. It is also shown that agents in different communities display distinct behaviors if and only if state averages of stubborn agents in different communities are not identical. A community detection algorithm is then proposed to recover community structure and to estimate communication probability parameters. It is verified that the community detection part converges in finite time, and the parameter estimation part converges almost surely. Simulations are given to illustrate algorithm performance.
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