Efficient Regionalization For Spatially Explicit Neighborhood Delineation

Neighborhood delineation is increasingly relied upon in urban social science research to identify the most appropriate spatial unit. In problems of this type, the true number of neighborhoods (typically called the k parameter) is unknown and analysts often require algorithmic approaches to determine k endogenously. Existing approaches for neighborhood delineation that do not require pre-specification of a k-parameter, however, are either nonspatial or lead to noncontiguous or overlapping regions. In this paper, we propose the use of max-p-regions for neighborhood delineation so that the geographic space can be partitioned into a set of homogeneous and geographically contiguous neighborhoods. In addition, we developed a new efficient algorithm to address the computational challenges associated with solving the max-p-regions so that it can be applied for large-scale neighborhood delineation. This new algorithm is implemented in the open-source Python Spatial Analysis Library (PySAL). Computational experiments based on both simulated and realistic data sets are performed and the results demonstrate its effectiveness and efficiency.