# Spectral Detection in the Censored Block Model

arXiv: https://arxiv.org/abs/1502.00163 · HTML: https://mlsanity.com/paper/1502.00163/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2015.

## Built on by (most cited first, 5 of 5)

- [Semidefinite Programming for Community Detection with Side Information](https://mlsanity.com/paper/2105.02816/) (2021)
- [Low coordinate degree algorithms II: Categorical signals and generalized stochastic block models](https://mlsanity.com/paper/2412.21155/) (2024)
- [Community Detection: Exact Recovery in Weighted Graphs](https://mlsanity.com/paper/2102.04439/) (2021)
- [Community Detection with Known, Unknown, or Partially Known Auxiliary Latent Variables](https://mlsanity.com/paper/2301.04088/) (2023)
- [Computational and statistical lower bounds for low-rank estimation under general inhomogeneous noise](https://mlsanity.com/paper/2510.08541/) (2025)

## Abstract (arXiv)

We consider the problem of partially recovering hidden binary variables from the observation of (few) censored edge weights, a problem with applications in community detection, correlation clustering and synchronization. We describe two spectral algorithms for this task based on the non-backtracking and the Bethe Hessian operators. These algorithms are shown to be asymptotically optimal for the partial recovery problem, in that they detect the hidden assignment as soon as it is information theoretically possible to do so.