论文标题
全球和个性化的社区检测不均匀的多层网络
Global and Individualized Community Detection in Inhomogeneous Multilayer Networks
论文作者
论文摘要
在网络应用程序中，以在相同的主题集中观察到的多个网络的形式获得数据集已变得越来越普遍，在这些网络中，每个网络都是在相关但不同的实验条件或应用程序方案中获得的。这样的数据集可以通过多层网络建模，在多层网络中，每个层都是单独的网络本身，而不同的层则关联并共享一些常见信息。本文以风格化但有益的不均匀多层网络模型进行了社区检测。在我们的模型中，层是由不同的随机块模型生成的，其社区结构是（随机）共同的全局结构的扰动，而不同层中的连接概率无关。为了关注对称的两个区块案例，我们建立了对共同结构的全球估计和对层的社区结构的个性化估计的最小值。这两个最小速率都有尖锐的指数。此外，我们还提供了一种有效的算法，该算法同时在轻度条件下对两个估计任务都具有最佳渐近性最小值。最佳速率取决于最有用的层数的奇偶校验，这是由于层次跨层的不均匀性引起的现象。该方法扩展以处理多种且可能不对称的社区案例。我们证明了它在模拟示例和真实多模式的单细胞数据集上的有效性。
In network applications, it has become increasingly common to obtain datasets in the form of multiple networks observed on the same set of subjects, where each network is obtained in a related but different experiment condition or application scenario. Such datasets can be modeled by multilayer networks where each layer is a separate network itself while different layers are associated and share some common information. The present paper studies community detection in a stylized yet informative inhomogeneous multilayer network model. In our model, layers are generated by different stochastic block models, the community structures of which are (random) perturbations of a common global structure while the connecting probabilities in different layers are not related. Focusing on the symmetric two block case, we establish minimax rates for both global estimation of the common structure and individualized estimation of layer-wise community structures. Both minimax rates have sharp exponents. In addition, we provide an efficient algorithm that is simultaneously asymptotic minimax optimal for both estimation tasks under mild conditions. The optimal rates depend on the parity of the number of most informative layers, a phenomenon that is caused by inhomogeneity across layers. The method is extended to handle multiple and potentially asymmetric community cases. We demonstrate its effectiveness on both simulated examples and a real multi-modal single-cell dataset.
