  Mapping of spatial hotspots, i.e., regions with significantly higher rates or
probability density of generating certain events (e.g., disease or crime
cases), is a important task in diverse societal domains, including public
health, public safety, transportation, agriculture, environmental science, etc.
Clustering techniques required by these domains differ from traditional
clustering methods due to the high economic and social costs of spurious
results (e.g., false alarms of crime clusters). As a result, statistical rigor
is needed explicitly to control the rate of spurious detections. To address
this challenge, techniques for statistically-robust clustering have been
extensively studied by the data mining and statistics communities. In this
survey we present an up-to-date and detailed review of the models and
algorithms developed by this field. We first present a general taxonomy of the
clustering process with statistical rigor, covering key steps of data and
statistical modeling, region enumeration and maximization, significance
testing, and data update. We further discuss different paradigms and methods
within each of key steps. Finally, we highlight research gaps and potential
future directions, which may serve as a stepping stone in generating new ideas
and thoughts in this growing field and beyond.
