度校正随机区组模型中群落数的确定
Determining the Number of Communities in Degree-corrected Stochastic Block Models
摘要：
本文提出了基于伪似然比统计量的度校正随机块模型中社区数的估计。为此，我们介绍了一种方法，结合谱聚类与二进制分割。当模型过拟合时，这种方法保证了伪似然比统计量的上限。当模型欠拟合时，我们也得到了它的极限分布。基于这些性质，我们建立了我们的估计的真实社区数的一致性。开发这些理论属性需要平均度的温和条件-以不低于log（n）的速度增长，其中n是节点的数量。我们所提出的方法进一步说明了仿真研究和现实世界的网络分析。数值结果表明，当网络为半稠密网络时，该方法具有令人满意的性能。
英文摘要：
We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio statistic. To this end, we introduce a method that combines spectral clustering with binary segmentation. This approach guarantees an upper bound for the pseudo likelihood ratio statistic when the model is over-fitted. We also derive its limiting distribution when the model is under-fitted. Based on these properties, we establish the consistency of our estimator for the true number of communities. Developing these theoretical properties require a mild condition on the average degrees -- growing at a rate no slower than log(n), where n is the number of nodes. Our proposed method is further illustrated by simulation studies and analysis of real-world networks. The numerical results show that our approach has satisfactory performance when the network is semi-dense.
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