# Spectral clustering in the dynamic stochastic block model

arXiv: https://arxiv.org/abs/1705.01204 · HTML: https://mlsanity.com/paper/1705.01204/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2017.

## Built on by (most cited first, 12 of 12)

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- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Latent structure blockmodels for Bayesian spectral graph clustering](https://mlsanity.com/paper/2107.01734/) (2021)
- [Factorized Fusion Shrinkage for Dynamic Relational Data](https://mlsanity.com/paper/2210.00091/) (2022)
- [Asymptotically perfect seeded graph matching without edge correlation (and applications to inference)](https://mlsanity.com/paper/2506.02825/) (2025)
- [Nonparametric estimation of time-varying network connections by multi-stage smoothing](https://mlsanity.com/paper/2605.06862/) (2026)

## Abstract (arXiv)

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.