Spatial regionalization based on optimal information compression

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.