Signal Recovery on Graphs: Variation Minimization

TL;DR

This paper introduces a unified approach for recovering signals on graphs, using variation minimization and optimization techniques, applicable to various real-world problems like classification, temperature estimation, and anomaly detection.

Contribution

It proposes a novel graph signal recovery model and optimization framework, connecting various data recovery tasks under a common methodology with theoretical analysis.

Findings

Effective signal recovery demonstrated on multiple real-world datasets

Unified framework improves robustness to noise and corruption

Theoretical guarantees support the proposed methods

Abstract

We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a corresponding optimization problem. We provide a general solution by using the alternating direction methods of multipliers. We next show how signal inpainting, matrix completion, robust principal component analysis, and anomaly detection all relate to graph signal recovery, and provide corresponding specific solutions and theoretical analysis. Finally, we validate the proposed methods on real-world recovery problems, including online blog classification, bridge condition identification, temperature estimation, recommender system, and expert opinion combination of online blog classification.