Spectral clustering in the dynamic stochastic block model

TL;DR

This paper introduces a spectral clustering method for dynamic stochastic block models that adapts to unknown parameters and provides non-asymptotic guarantees for accurate node clustering over time.

Contribution

It proposes a computationally feasible, adaptive spectral clustering approach for DSBMs with theoretical guarantees, handling unknown smoothness, switching rate, and number of clusters.

Findings

Effective clustering with non-asymptotic error bounds

Adaptive to unknown model parameters

Handles node membership switching over time

Abstract

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.