Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

AuthorFeedback »Bibtex »Bibtex »MetaReview »Metadata »Paper »Reviews »Supplemental »


Pedro Mercado, Francesco Tudisco, Matthias Hein


<p>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.</p>