Latent space models for multiplex networks with shared structure

Summary Latent space models are frequently used for modelling single-layer networks and include many popular special cases, such as the stochastic block model random dot product graph. However, they not well developed more complex network structures, which becoming increasingly common in practice. In this article we propose a new latent multiplex networks, i.e., multiple heterogeneous observed on shared node set. Multiplex can represent sample with labels, evolving over time, or types of edges. The key feature proposed is that it learns from data how much structure between layers pools information across appropriate. We establish identifiability, develop fitting procedure using convex optimization combination nuclear-norm penalty, prove guarantee recovery positions provided there sufficient separation individual subspaces. compare competing methods literature simulated describing worldwide trade agricultural products.