Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs
This addresses semi-supervised learning for data with multiple graph layers, but it is incremental as it builds on existing matrix mean techniques.
The paper tackles semi-supervised learning on multilayer graphs by proposing a regularizer based on generalized matrix means, which outperforms state-of-the-art methods numerically.
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.