Signal Processing Over Multilayer Graphs: Theoretical Foundations and Practical Applications

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 data sets and systems, including those in Internet of Things (IoT), are characterized by more complex interactions among distinct entities, which may represent multilevel interactions that are harder to be captured with a single-layer graph, and can be better characterized by multilayers graph connections. Such multilayer or multilevel data structures can be more naturally modeled by high-dimensional multilayer graphs (MLGs). To generalize traditional graph signal processing (GSP) over MLGs for analyzing multilevel signal features and their interactions, this work proposes a tensor-based framework of MLG signal processing (M-GSP). Specifically, we introduce core concepts of M-GSP and study properties of MLG spectral 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 MLGs and M-GSP in practical scenarios.