Characterizing Covid Waves via Spatio-Temporal Decomposition

In this paper we develop a framework for analyzing patterns of a disease or pandemic such as Covid. Given a dataset which records information about the spread of a disease over a set of locations, we consider the problem of identifying both the disease's intrinsic waves (temporal patterns) and their respective spatial epicenters. To do so we introduce a new method of spatio-temporal decomposition which we call diffusion NMF (D-NMF). Building upon classic matrix factorization methods, D-NMF takes into consideration a spatial structuring of locations (features) in the data and supports the idea that locations which are spatially close are more likely to experience the same set of waves. To illustrate the use of D-NMF, we analyze Covid case data at various spatial granularities. Our results demonstrate that D-NMF is very useful in separating the waves of an epidemic and identifying a few centers for each wave.