Learning Multiplex Graph With Inter-Layer Coupling

In many real-life systems, the interactions among entities are complex and varied. This necessitates the use of a multiplex graph model with heterogeneous layers of graphs to effectively describe these interactions. The current paper focuses on incorporating high-order relations, specifically inter-layer couplings or connections, in multiplex graph learning. Through developing a high-order smoothness criterion, we propose an algorithm that integrates inter-layer connections to perform inference from multi-attribute graph signals. We show that it is essential to consider high-order interactions in the inference process. We validate our claims through numerical experiments, demonstrating their efficacy in capturing the intricate relationships within multiplex networks.