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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, theuncertain‐max‐p‐regionsproblem that explicitly incorporates attribute uncertainty and allows its impacts to be evaluated with a degree of statistical certainty. We also detail an efficient solution approach for dealing the problem. The results suggest that the developed problem can out‐perform existing regionalization approaches and that the addition of a measure of statistical confidence can help to facilitate more clarity in planning and policy decisions.
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The max‐ p ‐compact‐regions problem
Abstract The max‐p‐compact‐regions problem involves the aggregation of a set of small areas into an unknown maximum number (p) of compact, homogeneous, and spatially contiguous regions such that a regional attribute value is higher than a predefined threshold. The max‐p‐compact‐regions problem is an extension of the max‐p‐regions problem accounting for compactness. The max‐p‐regions model has been widely used to define study regions in many application cases since it allows users to specify criteria and then to identify a regionalization scheme. However, the max‐p‐regions model does not consider compactness even though compactness is usually a desirable goal in regionalization, implying ideal accessibility and apparent homogeneity. This article discusses how to integrate a compactness measure into the max‐pregionalization process by constructing a multiobjective optimization model that maximizes the number of regions while optimizing the compactness of identified regions. An efficient heuristic algorithm is developed to address the computational intensity of the max‐p‐compact‐regions problem so that it can be applied to large‐scale practical regionalization problems. This new algorithm will be implemented in the open‐source Python Spatial Analysis Library. One hypothetical and one practical application of the max‐p‐compact‐regions problem are introduced to demonstrate the effectiveness and efficiency of the proposed algorithm.
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- Award ID(s):
- 1831615
- PAR ID:
- 10364743
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Transactions in GIS
- Volume:
- 26
- Issue:
- 2
- ISSN:
- 1361-1682
- Page Range / eLocation ID:
- p. 717-734
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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