Signal Processing over Multilayer Graphs: Theoretical Foundations and Practical Applications

TL;DR

This paper develops a tensor-based framework for signal processing on multilayer graphs, enabling analysis of complex multi-level data interactions that are difficult to capture with traditional single-layer graph methods.

Contribution

It introduces core concepts and properties of multilayer graph signal processing, extending traditional GSP to multilayer structures with a tensor-based approach.

Findings

Demonstrates the effectiveness of M-GSP in practical applications

Provides theoretical foundations for multilayer graph spectrum analysis

Shows improved modeling of multi-level interactions in data

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.