# The Power Mean Laplacian for Multilayer Graph Clustering

arXiv: https://arxiv.org/abs/1803.00491 · HTML: https://mlsanity.com/paper/1803.00491/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2018.

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

- [ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Network](https://mlsanity.com/paper/2102.10226/) (2021)
- [Laplacian Change Point Detection for Single and Multi-view Dynamic Graphs](https://mlsanity.com/paper/2302.01204/) (2023)
- [Federated Myopic Community Detection with One-shot Communication](https://mlsanity.com/paper/2106.07255/) (2021)
- [Mixture of multilayer stochastic block models for multiview clustering](https://mlsanity.com/paper/2401.04682/) (2024)
- [A Spectral Framework for Tracking Communities in Evolving Networks](https://mlsanity.com/paper/2412.07378/) (2024)

## Abstract (arXiv)

Multilayer graphs encode different kind of interactions between the same set of entities. When one wants to cluster such a multilayer graph, the natural question arises how one should merge the information different layers. We introduce in this paper a one-parameter family of matrix power means for merging the Laplacians from different layers and analyze it in expectation in the stochastic block model. We show that this family allows to recover ground truth clusters under different settings and verify this in real world data. While computing the matrix power mean can be very expensive for large graphs, we introduce a numerical scheme to efficiently compute its eigenvectors for the case of large sparse graphs.