  The spreading pattern of COVID-19 differ a lot across the US states 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 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. Applying the method to the
entire study period from March 22 to July 25, we clustered the 49 continental
states (including 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 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,
which might be explained by a combined impact of both quarantine measures and
reopening policies.
