  Regionalization, spatially contiguous clustering, provides a means to reduce
the effect of noise in sampled data and identify homogeneous areas for policy
development among many other applications. Existing regionalization methods
require user input such as the number of regions or a similarity measure
between regions, which does not allow for the extraction of the natural regions
defined solely by the data itself. Here we view the problem of regionalization
as one of data compression and develop an efficient, parameter-free
regionalization algorithm based on the minimum description length principle. We
demonstrate that our method is capable of recovering planted spatial clusters
in noisy synthetic data, and that it can meaningfully coarse-grain real
demographic data. Using our description length formulation, we find that
spatial ethnoracial data in U.S. metropolitan areas has become less
compressible over the period from 1980 to 2010, reflecting the rising
complexity of urban segregation patterns in these metros.
