The process of regionalization involves clustering a set of spatial areas into spatially contiguous regions. Given the NP-hard nature of regionalization problems, all existing algorithms yield approximate solutions. To ascertain the quality of these approximations, it is crucial for domain experts to obtain statistically significant evidence on optimizing the objective function, in comparison to a random reference distribution derived from all potential sample solutions. In this paper, we propose a novel spatial regionalization problem, denoted as SISR (Statistical Inference for Spatial Regionalization), which generates random sample solutions with a predetermined region cardinality. The driving motivation behind SISR is to conduct statistical inference on any given regionalization scheme. To address SISR, we present a parallel technique named PRRP (P-Regionalization through Recursive Partitioning). PRRP operates over three phases: the region-growing phase constructs initial regions with a predetermined region cardinality, while the region merging and region-splitting phases ensure the spatial contiguity of unassigned areas, allowing for the growth of subsequent regions with predetermined cardinalities. An extensive evaluation shows the effectiveness of PRRP using various real datasets.
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A Probabilistic Approach to Address Data Uncertainty in Regionalization
Spatial data regularly suffer from error and uncertainty, ranging from poorly georeferenced coordinate pairs to sampling error associated with American Community Survey data. Geographic information systems can amplify and propagate error and uncertainty through the abstraction and representation of spatial data, as can the manipulation, processing, and analysis of spatial data using exploratory and confirmatory statistical techniques. The purpose of this article is to explore and address uncertainty in regionalization, a fundamental spatial analytical method that aggregates spatial units (e.g., tracts) into a set of contiguous regions for strategic purposes, including school districting, habitat areas, and the like. Specifically, we develop a new regionalization method, the
- Award ID(s):
- 1831615
- NSF-PAR ID:
- 10366423
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Geographical Analysis
- Volume:
- 54
- Issue:
- 2
- ISSN:
- 0016-7363
- Page Range / eLocation ID:
- p. 405-426
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The max‐
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Abstract Models of bathymetry derived from satellite radar altimetry are essential for modeling many marine processes. They are affected by uncertainties which require quantification. We propose an uncertainty model that assumes errors are caused by the lack of high‐wavenumber content within the altimetry data. The model is then applied to a tsunami hazard assessment. We build a bathymetry uncertainty model for northern Chile. Statistical properties of the altimetry‐predicted bathymetry error are obtained using multibeam data. We find that a Von Karman correlation function and a Laplacian marginal distribution can be used to define an uncertainty model based on a random field. We also propose a method for generating synthetic bathymetry samples conditional to shipboard measurements. The method is further extended to account for interpolation uncertainties, when bathymetry data resolution is finer than
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