# Randomized Spectral Clustering in Large-Scale Stochastic Block Models

arXiv: https://arxiv.org/abs/2002.00839 · HTML: https://mlsanity.com/paper/2002.00839/

## Key facts

- Cited by 9 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 20 Jan 2020.

## Built on by (most cited first, 9 of 9)

- [Community detection for weighted bipartite networks](https://mlsanity.com/paper/2109.10319/) (2021)
- [FedPower: Privacy-Preserving Distributed Eigenspace Estimation](https://mlsanity.com/paper/2103.00704/) (2021)
- [Bipartite mixed membership distribution-free model. A novel model for community detection in overlapping bipartite weighted networks](https://mlsanity.com/paper/2211.00912/) (2022)
- [Mixed membership distribution-free model](https://mlsanity.com/paper/2112.04389/) (2021)
- [Privacy-Preserving Community Detection for Locally Distributed Multiple Networks](https://mlsanity.com/paper/2306.15709/) (2023)
- [Latent class analysis with weighted responses](https://mlsanity.com/paper/2310.10984/) (2023)
- [Simultaneous estimation of connectivity and dimensionality in samples of networks](https://mlsanity.com/paper/2508.12483/) (2025)
- [A Subsampled Davis-Kahan Bound for Large-Scale Eigenspace Estimation](https://mlsanity.com/paper/2609.09211/) (2026)
- [Randomized SVD Approximations for Spectral Co-Clustering of Word-Document Matrices](https://mlsanity.com/paper/2609.19243/) (2026)

## Abstract (arXiv)

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statistical perspective, where we typically assume the network data are generated from a stochastic block model that is not necessarily of full rank. To do this, we first use the recently developed sketching algorithms to obtain two randomized spectral clustering algorithms, namely, the random projection-based and the random sampling-based spectral clustering. Then we study the theoretical bounds of the resulting algorithms in terms of the approximation error for the population adjacency matrix, the misclassification error, and the estimation error for the link probability matrix. It turns out that, under mild conditions, the randomized spectral clustering algorithms lead to the same theoretical bounds as those of the original spectral clustering algorithm. We also extend the results to degree-corrected stochastic block models. Numerical experiments support our theoretical findings and show the efficiency of randomized methods. A new R package called Rclust is developed and made available to the public.