Generalized matrix means for semisupervised 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.

Please cite this work as:

@inproceedings{mercado2019generalized,
  title={Generalized matrix means for semisupervised learning with multilayer graphs},
  author={Mercado, Pedro and Tudisco, Francesco and Hein, Matthias},
  booktitle={Advances in Neural Information Processing Systems (NeurIPS)},
  year={2019}
}

Keywords: multilayer semi-supervised learning graph laplacian matrix means spectral clustering