We consider the problem of detecting latent community information of mixed membership weighted network in which nodes have mixed memberships and edges connecting between nodes can be finite real numbers. We propose a general mixed membership distribution-free model for this problem. The model has no distribution constraints of edges but only the expected values, and can be viewed as generalizations of some previous models. We use an efficient spectral algorithm to estimate community memberships under the model. We also derive the convergence rate of the proposed algorithm under the model using delicate spectral analysis. We demonstrate the advantages of mixed membership distribution-free model with applications to a small scale of simulated networks when edges follow different distributions.
翻译:我们考虑了发现混合成员加权网络的潜在社区信息的问题,在这种网络中,节点具有混合成员,节点之间连接的边缘可以是实际数目的有限。我们建议对这个问题采用一个普遍混合成员分配模式。该模式没有边缘分布限制,但只有预期值,可以被视为以前一些模式的概括。我们使用高效的光谱算法来估计模式下的社区成员。我们还利用微妙的光谱分析得出模型下的拟议算法的趋同率。我们展示了混合成员分配模式的优点,在边缘跟随不同分布时,可将其应用于小规模模拟网络。