On the Minimization of Sobolev Norms of Time-Varying Graph Signals: Estimation of New Coronavirus Disease 2019 Cases

TL;DR

This paper introduces a novel Sobolev norm minimization approach for reconstructing time-varying graph signals, specifically applied to modeling COVID-19 case data, outperforming existing methods and demonstrating faster convergence.

Contribution

The paper presents a new Sobolev norm minimization technique for graph signal reconstruction, tailored for COVID-19 data, with proven convergence benefits and superior performance.

Findings

Outperforms state-of-the-art algorithms on COVID-19 datasets

Proves faster convergence due to better condition number of the Hessian

Effectively models spatial-temporal COVID-19 case data

Abstract

The mathematical modeling of infectious diseases is a fundamental research field for the planning of strategies to contain outbreaks. The models associated with this field of study usually have exponential prior assumptions in the number of new cases, while the exploration of spatial data has been little analyzed in these models. In this paper, we model the number of new cases of the Coronavirus Disease 2019 (COVID-19) as a problem of reconstruction of time-varying graph signals. To this end, we proposed a new method based on the minimization of the Sobolev norm in graph signal processing. Our method outperforms state-of-the-art algorithms in two COVID-19 databases provided by Johns Hopkins University. In the same way, we prove the benefits of the convergence rate of the Sobolev reconstruction method by relying on the condition number of the Hessian associated with the underlying optimization problem of our method.