多层图上的信号处理：理论基础与实际应用
Signal Processing over Multilayer Graphs: Theoretical Foundations and Practical Applications
摘要：
单层图上的信号处理由于其在揭示数据信号中的模糊底层结构方面的能力而已经成为主流工具。然而，许多现实生活中的数据集和系统（包括物联网（IoT）中的数据集和系统）的特征在于不同实体之间的更复杂的交互，这可能表示难以用单层图捕获的多级交互，并且可以通过多层图连接更好地表征。这种多层或多级数据结构可以更自然地由高维多层图（MLG）建模。为了将传统的图信号处理（GSP）推广到多层图上以分析多层信号特征及其相互作用，提出了一种基于张量的多层图信号处理（M-GSP）框架.具体来说，我们介绍了M-GSP的核心概念和MLG频谱空间的研究性质，其次是MLG为基础的滤波器设计的基本原理。为了说明M-GSP的新方面，我们进一步探讨了它与传统信号处理和GSP的联系。我们提供了示例应用程序来演示在实际场景中应用多层图和M-GSP的有效性和好处。
英文摘要：
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.
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