Signal Processing over Multilayer Graphs: Theoretical Foundations and Practical Applications (2108.13638v6)

Abstract: Signal processing over single-layer graphs has become a mainstream tool owing to its power in revealing obscure underlying structures within data signals. However, many real-life datasets and systems, {including those in Internet of Things (IoT)}, are characterized by more complex interactions among distinct entities, which may represent multi-level interactions that are harder to be captured with a single-layer graph, and can be better characterized by multilayers graph connections. Such multilayer or multi-level data structure can be more naturally modeled by high-dimensional multilayer graphs (MLG)}. To generalize traditional graph signal processing (GSP) over multilayer graphs for analyzing multi-level signal features and their interactions, this work proposes a tensor-based framework of multilayer graph signal processing (M-GSP). Specifically, we introduce core concepts of M-GSP and study properties of MLG spectrum space, followed by fundamentals of MLG-based filter design. To illustrate novel aspects of M-GSP, we further explore its link with traditional signal processing and GSP. We provide example applications to demonstrate the efficacy and benefits of applying multilayer graphs and M-GSP in practical scenarios.