基于样本协方差矩阵的网络时间序列谱聚类
Spectral clustering of network time series via the sample covariance matrix
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中文总结 AI 辅助
本文针对依赖结构由未观测随机块模型决定的多变量时间序列，提出基于样本协方差矩阵的谱聚类方法，实现了潜在社区的精确恢复，其理论扩展了矩阵扰动理论至依赖数据场景。
中文摘要 AI 辅助
本文针对由未观测随机块模型决定依赖结构的多变量时间序列模型，分析用于社区检测的谱聚类方法。研究表明，样本协方差矩阵的谱聚类可实现对潜在社区的精确恢复，恢复率明确依赖于网络规模、样本长度、块分离度和数据依赖程度。这证明即使邻接矩阵未被观测，在随机块模型下仍可实现精确的社区恢复。本文的理论将经典和细粒度矩阵扰动理论扩展到依赖数据场景，具有独立研究价值。
英文摘要
Spectral clustering for community detection is analysed in multivariate time series models whose dependence structure is determined by an unobserved stochastic blockmodel. We establish that spectral clustering of the sample covariance matrix achieves exact recovery of the underlying communities. The recovery rates depend explicitly on the network size, sample length, block separation, and degree of data dependence. This demonstrates that exact community recovery under a stochastic blockmodel is possible even when the adjacency matrix is unobserved. Our theory provides extensions of both classical and fine-grained matrix perturbation theory to the setting of dependent data, which may be of independent interest.
