The process of aggregating areal units into contiguous clusters, known as regionalization, is central to the analysis of spatial data. Regionalization provides a means to reduce the effect of noise or outliers in sampled data, identify socioeconomically homogeneous areas for policy development, and simplify the visualization of data in maps among many other applications. Most existing regionalization methods require a substantial amount of manual input, such as the number of desired regions or a similarity measure among regional populations, which may be desirable for some applications but does not allow us to extract the natural regions defined solely by the data itself. Here we view the problem of regionalization as one of data compression. We define the optimal partition of spatial units with corresponding distributional data as the one that minimizes the description length required to transmit the data, and develop an efficient, parameter-free greedy optimization algorithm to identify this partition. We demonstrate that our method is capable of recovering planted spatial clusters in noisy synthetic distributional data, and that it identifies meaningful ethnoracial boundaries in real demographic data. Using our description length formulation, we find that the information contained in spatial ethnoracial data in metropolitan areas across the U.S. has become more difficult to compress over the period from 1980 to 2010, which reflects the rising complexity of urban segregation patterns of these metros. We identify the increasing overall diversity of these metros as a major contributor to this lower data compressibility, while the spatial scale of ethnoracial clustering does not appear to be a significant factor.