  The patterns of particulate matter with diameters that are generally 2.5
micrometers and smaller (PM2.5) are heterogeneous in China nationwide but can
be homogeneous region-wide. To reduce the adverse effects from PM2.5,
policymakers need to develop location-specific regulations based on nationwide
clustering analysis of PM2.5 concentrations. However, such an analysis is
challenging because the data have complex structures and are usually noisy. In
this study, we propose a robust clustering framework using a novel concept of
depth, which can handle both magnitude and shape outliers effectively and
incorporate spatial information. We apply this framework to a PM2.5 dataset and
reveal ten regions in China that have distinct PM2.5 patterns, and the
homogeneity within each cluster is also confirmed. The clusters have clearly
visible boundaries and enable policymakers to develop local emission control
policies and establish regional collaborative systems to control air pollution
in China.
