Spectral clustering of network time series via the sample covariance matrix

2026-08-03

AI Summary

This study addresses the fundamental challenge of accurately recovering community structure generated by a latent stochastic block model from network time series when the adjacency matrix is unobserved. The work proposes a spectral clustering method based on the sample covariance matrix and establishes, for the first time, that exact community recovery is achievable without direct access to the adjacency matrix, under the assumption that node dependencies are governed by a latent stochastic block model. The core theoretical contribution lies in extending both classical and fine-grained matrix perturbation analyses to the setting of dependent time series, yielding explicit recovery guarantees that precisely quantify the roles of network size, sample length, inter-block separation, and the strength of temporal dependence.

Abstract

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.

Problem

• spectral clustering
• community detection
• stochastic blockmodel
• network time series
• sample covariance matrix

Innovation

• spectral clustering
• stochastic blockmodel
• sample covariance matrix
• community detection
• dependent time series