Graph Signal Processing Over a Probability Space of Shift Operators
Graph Signal Processing Over a Probability Space of Shift Operators
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DOI：
10.1109/tsp.2023.3263675
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发表时间：
2021-08
影响因子：
5.4
通讯作者：
Feng Ji;Wee Peng Tay;Antonio Ortega
中科院分区：
文献类型：
--
作者：
Feng Ji;Wee Peng Tay;Antonio Ortega
图信号处理（GSP）使用移位算子来定义一组图信号的傅里叶基。移位运算符通常用于捕获图拓扑。然而，在许多应用中，图拓扑可能是先验未知的，其结构不确定，或者是从每个观测的预定义集合随机生成的。每个图拓扑都会产生一个不同的移位算子。在本文中，我们在移位算子的概率空间上建立了一个GSP框架。我们发展了相应的傅里叶变换、MFC滤波器和带通滤波器的概念，将经典GSP理论作为概率空间由单个移位算子组成的特殊情况。我们表明，在此框架下的MFC滤波器是经典GSP中随机卷积滤波器的期望，而带宽限制的概念需要额外的摆动空间，而不仅仅是带通滤波器的固定点。我们开发了一种机制，便于从移位操作符的一个空间映射到另一个空间，从而允许我们的框架应用于丰富的场景集。我们通过使用合成数据集和真实数据集来演示如何应用该理论。
Graph signal processing (GSP) uses a shift operator to define a Fourier basis for the set of graph signals. The shift operator is often chosen to capture the graph topology. However, in many applications, the graph topology may be unknown a priori, its structure uncertain, or generated randomly from a predefined set for each observation. Each graph topology gives rise to a different shift operator. In this paper, we develop a GSP framework over a probability space of shift operators. We develop the corresponding notions of Fourier transform, MFC filters, and band-pass filters, which subsumes classical GSP theory as the special case where the probability space consists of a single shift operator. We show that an MFC filter under this framework is the expectation of random convolution filters in classical GSP, while the notion of bandlimitedness requires additional wiggle room from being simply a fixed point of a band-pass filter. We develop a mechanism that facilitates mapping from one space of shift operators to another, which allows our framework to be applied to a rich set of scenarios. We demonstrate how the theory can be applied by using both synthetic and real datasets.