  In many bio-surveillance and healthcare applications, data sources are
measured from many spatial locations repeatedly over time, say,
daily/weekly/monthly. In these applications, we are typically interested in
detecting hot-spots, which are defined as some structured outliers that are
sparse over the spatial domain but persistent over time. In this paper, we
propose a tensor decomposition method to detect when and where the hot-spots
occur. Our proposed methods represent the observed raw data as a
three-dimensional tensor including a circular time dimension for
daily/weekly/monthly patterns, and then decompose the tensor into three
components: smooth global trend, local hot-spots, and residuals. A combination
of LASSO and fused LASSO is used to estimate the model parameters, and a CUSUM
procedure is applied to detect when and where the hot-spots might occur. The
usefulness of our proposed methodology is validated through numerical
simulation and a real-world dataset in the weekly number of gonorrhea cases
from $2006$ to $2018$ for $50$ states in the United States.
