Clustering US States by Time Series of COVID-19 New Case Counts in the Early Months with Non-Negative Matrix Factorization

The spreading pattern of COVID-19 in the early months of the pandemic differs a lot across the states in the US under different quarantine measures and reopening policies. We proposed to cluster the US states into distinct communities based on the daily new confirmed case counts from March 22 to July 25 via a nonnegative matrix factorization (NMF) followed by a k-means clustering procedure on the coefficients of the NMF basis. A cross-validation method was employed to select the rank of the NMF. The method clustered the 49 continental states (including the District of Columbia) into 7 groups, two of which contained a single state. To investigate the dynamics of the clustering results over time, the same method was successively applied to the time periods with an increment of one week, starting from the period of March 22 to March 28. The results suggested a change point in the clustering in the week starting on May 30, caused by a combined impact of both quarantine measures and reopening policies.