# Signal Processing over Multilayer Graphs: Theoretical Foundations and Practical Applications

arXiv: https://arxiv.org/abs/2108.13638 · HTML: https://mlsanity.com/paper/2108.13638/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2021.

## Built on by (most cited first, 1 of 1)

- [PFL-GAN: When Client Heterogeneity Meets Generative Models in Personalized Federated Learning](https://mlsanity.com/paper/2308.12454/) (2023)

## Abstract (arXiv)

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.