Accelerated Graph Learning from Smooth Signals

TL;DR

This paper introduces a fast, globally convergent dual-based proximal gradient algorithm for network topology identification from smooth signals, significantly improving speed and accuracy over existing methods.

Contribution

The paper presents a novel, efficient algorithm with convergence guarantees for graph learning from smooth signals, outperforming current state-of-the-art techniques.

Findings

Demonstrates faster graph recovery in simulations

Achieves high accuracy in real-world graph reconstruction

Provides convergence guarantees without step-size tuning

Abstract

We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network inverse problem known to yield high-quality graph solutions. Unlike existing solvers, the novel iterations come with global convergence rate guarantees and do not require additional step-size tuning. Reproducible simulated tests demonstrate the effectiveness of the proposed method in accurately recovering random and real-world graphs, markedly faster than state-of-the-art alternatives and without incurring an extra computational burden.