Graph signal processing is a framework to handle graph structured data. The fundamental concept is graph shift operator, giving rise to the graph Fourier transform. While the graph Fourier transform is a centralized procedure, distributed graph signal processing algorithms are needed to address challenges such as scalability and privacy. In this paper, we develop a theory of distributed graph signal processing based on the classical notion of message passing. However, we generalize the definition of a message to permit more abstract mathematical objects. The framework provides an alternative point of view that avoids the iterative nature of existing approaches to distributed graph signal processing. Moreover, our framework facilitates investigating theoretical questions such as solubility of distributed problems.
翻译:图形信号处理是处理图形结构化数据的框架。 基本概念是图形转换操作器, 由此产生图 Fourier 变换。 虽然图 Fourier 变换是一个集中程序, 需要分布的图形信号处理算法来应对可缩放性和隐私等挑战。 在本文件中, 我们根据传统的电文传递概念, 开发了分布式图形信号处理理论。 然而, 我们将电文的定义概括化, 以便允许更抽象的数学天体。 框架提供了另一个观点, 避免了分布式图形信号处理现有方法的迭接性。 此外, 我们的框架有助于研究理论问题, 如分布式问题的可溶性 。