Spectral clustering in the dynamic stochastic block model
Spectral clustering in the dynamic stochastic block model
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DOI：
10.1214/19-ejs1533
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发表时间：
2017-05
影响因子：
1.1
通讯作者：
M. Pensky;Teng Zhang
中科院分区：
文献类型：
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作者：
M. Pensky;Teng Zhang
本文研究了一个动态随机块模型（DSBM），该模型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5个节点可以切换它们的类隶属关系。利用核函数估计边缘概率张量，利用谱聚类提取节点的群隶属度。该方法计算可行，适应功能连接概率的未知平滑性、成员切换速率$s$和未知簇数。此外，它还具有估计和聚类精度的非渐近保证。
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.