# Optimal Laplacian regularization for sparse spectral community detection

arXiv: https://arxiv.org/abs/1912.01419 · HTML: https://mlsanity.com/paper/1912.01419/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2019.

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

- [Learning Parametrised Graph Shift Operators](https://mlsanity.com/paper/2101.10050/) (2021)
- [Nishimori meets Bethe: a spectral method for node classification in sparse weighted graphs](https://mlsanity.com/paper/2103.03561/) (2021)
- [Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learning](https://mlsanity.com/paper/2409.09888/) (2024)
- [Enhancing ensemble learning and transfer learning in multimodal data analysis by adaptive dimensionality reduction](https://mlsanity.com/paper/2105.03682/) (2021)
- [A graph representation based on fluid diffusion model for data analysis: theoretical aspects and enhanced community detection](https://mlsanity.com/paper/2112.04388/) (2021)

## Abstract (arXiv)

Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this paper we formally determine a proper regularization which is intimately related to alternative state-of-the-art spectral techniques for sparse graphs.