标题： 动态随机块模型中的谱聚类 显示英文标题

标题： Spectral clustering in the dynamic stochastic block model

摘要： 本文研究了一种动态随机块模型（DSBM），假设连接概率作为时间的函数是光滑的，并且在两个连续的时间点之间最多有 $s$ 个节点可以改变它们的类别成员资格。 我们通过一种核型过程估计边概率张量，并通过谱聚类提取节点的群体成员资格。该过程在计算上可行，能够适应未知的功能性连接概率的平滑程度、成员切换速率 $s$ 和未知的聚类数量。 此外，还提供了非渐近保证来确保估计和聚类的精确性。 显示英文摘要

摘要： In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most $s$ nodes can switch their class memberships between two consecutive time points. We estimate the edge probability tensor by a kernel-type procedure and extract the group memberships of the nodes by spectral clustering. The procedure is computationally viable, adaptive to the unknown smoothness of the functional connection probabilities, to the rate $s$ of membership switching and to the unknown number of clusters. In addition, it is accompanied by non-asymptotic guarantees for the precision of estimation and clustering.