Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs
Abstract
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.
Cite
Text
Mercado et al. "Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs." Neural Information Processing Systems, 2019.Markdown
[Mercado et al. "Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs." Neural Information Processing Systems, 2019.](https://mlanthology.org/neurips/2019/mercado2019neurips-generalized/)BibTeX
@inproceedings{mercado2019neurips-generalized,
title = {{Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs}},
author = {Mercado, Pedro and Tudisco, Francesco and Hein, Matthias},
booktitle = {Neural Information Processing Systems},
year = {2019},
pages = {14877-14886},
url = {https://mlanthology.org/neurips/2019/mercado2019neurips-generalized/}
}