Abstract message passing and distributed graph signal processing

TL;DR

This paper introduces a generalized message passing framework for distributed graph signal processing, enabling scalable, privacy-preserving algorithms and facilitating theoretical analysis of problem solvability.

Contribution

It develops a novel, abstract message passing theory for distributed graph signal processing, moving beyond iterative methods and allowing deeper theoretical insights.

Findings

Framework avoids iterative procedures common in existing methods

Enables analysis of the solvability of distributed graph problems

Provides a new perspective on distributed graph signal processing

Abstract

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.