Distributed Graph Learning with Smooth Data Priors

TL;DR

This paper introduces a distributed graph learning algorithm that infers graphs from smooth data signals with reduced communication costs, suitable for large or communication-constrained networks.

Contribution

It presents a novel distributed optimization method for graph inference that minimizes communication while maintaining accuracy, especially effective for sparse and large networks.

Findings

Distributed approach reduces communication costs compared to centralized methods.

The algorithm maintains high accuracy in graph inference.

Scales efficiently with network size, particularly for sparse graphs.

Abstract

Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely the data that lives on the graph nodes. However, there are settings where data cannot be collected easily or only with a non-negligible communication cost. In such cases, distributed processing appears as a natural solution, where the data stays mostly local and all processing is performed among neighbours nodes on the communication graph. We propose here a novel distributed graph learning algorithm, which permits to infer a graph from signal observations on the nodes under the assumption that the data is smooth on the target graph. We solve a distributed optimization problem with local projection constraints to infer a valid graph while limiting the communication costs. Our results show that the distributed approach has a lower communication cost than a centralised algorithm without compromising the accuracy in the inferred graph. It also scales better in communication costs with the increase of the network size, especially for sparse networks.