# Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs

arXiv: https://arxiv.org/abs/1910.13951 · HTML: https://mlsanity.com/paper/1910.13951/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2019.

## Built on by (most cited first, 4 of 4)

- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)
- [Graph-based Multi-View Fusion and Local Adaptation: Mitigating Within-Household Confusability for Speaker Identification](https://mlsanity.com/paper/2207.04081/) (2022)
- [Laplacian-based Semi-Supervised Learning in Multilayer Hypergraphs by Coordinate Descent](https://mlsanity.com/paper/2301.12184/) (2023)
- [Learning the Right Layers: a Data-Driven Layer-Aggregation Strategy for Semi-Supervised Learning on Multilayer Graphs](https://mlsanity.com/paper/2306.00152/) (2023)

## Abstract (arXiv)

We study the task of semi-supervised learning on multilayer graphs by taking into account both labeled and unlabeled observations together with the information encoded by each individual graph layer. We propose a regularizer based on the generalized matrix mean, which is a one-parameter family of matrix means that includes the arithmetic, geometric and harmonic means as particular cases. We analyze it in expectation under a Multilayer Stochastic Block Model and verify numerically that it outperforms state of the art methods. Moreover, we introduce a matrix-free numerical scheme based on contour integral quadratures and Krylov subspace solvers that scales to large sparse multilayer graphs.