Signal Processing Over Multilayer Graphs: Theoretical Foundations and Practical Applications
Signal Processing Over Multilayer Graphs: Theoretical Foundations and Practical Applications
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DOI：
10.1109/jiot.2023.3294470
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发表时间：
2021-08
影响因子：
10.6
通讯作者：
Songyang Zhang-;Qinwen Deng;Zhi Ding
中科院分区：
文献类型：
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作者：
Songyang Zhang-;Qinwen Deng;Zhi Ding
由于单层图信号处理在揭示数据信号中隐藏的底层结构方面的强大能力，它已成为一种主流工具。然而，许多现实生活中的数据集和系统，包括物联网（IoT）中的那些，其特点是不同实体之间存在更复杂的相互作用，这可能代表着多层相互作用，单层图更难以捕捉这些相互作用，而多层图连接可以更好地对其进行描述。这种多层或多级的数据结构可以通过高维多层图（MLGs）更自然地建模。为了在多层图上推广传统的图信号处理（GSP）以分析多级信号特征及其相互作用，这项工作提出了一个基于张量的多层图信号处理（M - GSP）框架。具体而言，我们引入了M - GSP的核心概念，并研究了多层图频谱空间的性质，接着介绍了基于多层图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，以证明在实际场景中应用多层图和M - GSP的有效性和优势。
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.