抽象消息传递与分布式图信号处理
Abstract message passing and distributed graph signal processing
摘要：
图信号处理是处理图结构化数据的框架。其基本概念是图形移位算子，从而产生了图形傅里叶变换。虽然图形傅里叶变换是一个集中式过程，但需要分布式图形信号处理算法来解决诸如可扩展性和隐私等挑战。在本文中，我们开发了一个理论的分布式图信号处理的消息传递的经典概念的基础上。然而，我们概括了消息的定义，以允许更抽象的数学对象。该框架提供了一种替代的观点，避免了现有的分布式图信号处理方法的迭代性质。此外，我们的框架有利于研究理论问题，如分布式问题的解决方案。
英文摘要：
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.
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