Cluster-based dual evolution for multivariate time series: Analyzing COVID-19

Abstract

"This paper proposes a cluster-based method to analyze the evolution of multivariate time series and applies this to the COVID-19 pandemic. On each day, we partition countries into clusters according to both their cases and death counts. The total number of clusters and individual countries’ cluster memberships are algorithmically determined. We study the change in both quantities over time, demonstrating a close similarity in the evolution of cases and deaths. The changing number of clusters of the case counts precedes that of the death counts by 32 days. On the other hand, there is an optimal offset of 16 days with respect to the greatest consistency between cluster groupings, determined by a new method of comparing affinity matrices. With this offset in mind, we identify anomalous countries in the progression from COVID-19 cases to deaths. This analysis can aid in highlighting the most and least significant public policies in minimizing a country’s COVID-19 mortality rate. COVID-19 has resulted in a global pandemic with severe human, social, and economic costs. In order to manage the economic ramifications of prioritizing citizen safety, policymakers have sought a multi-level approach involving social distancing, business closures, and movement restrictions. For this purpose, a careful identification of the most and least successful countries at responding to the spread of COVID-19 is of great relevance. This paper meets such a demand by developing a new method to analyze multivariate time series, in which the variables are the cumulative cases and death counts of each country on each day. We have three goals: first, we analyze the cases and death counts on a country by country basis; second, we analyze the two multivariate time series in conjunction to elucidate their similarity further; and third, we determine anomalous countries relative to cases and deaths."