An official website of the United States government
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.
more »
« less
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, 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.
more »
« less
- Award ID(s):
- 1831615
- 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
More Like this
-
-
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.more » « less
-
Regionalization techniques group spatial areas into a set of homogeneous regions to analyze and draw conclusions about spatial phenomena. A recent regionalization problem, called MP-regions, groups spatial areas to produce a maximum number of regions by enforcing a user-defined constraint at the regional level. The MP-regions problem is NP-hard. Existing approximate algorithms for MP-regions do not scale for large datasets due to their high computational cost and inherently centralized approaches to process data. This article introduces a parallel scalable regionalization framework (PAGE) to support MP-regions on large datasets. The proposed framework works in two stages. The first stage finds an initial solution through randomized search, and the second stage improves this solution through efficient heuristic search. To build an initial solution efficiently, we extend traditional spatial partitioning techniques to enable parallelized region building without violating the spatial constraints. Furthermore, we optimize the region building efficiency and quality by tuning the randomized area selection to trade off runtime with region homogeneity. The experimental evaluation shows the superiority of our framework to support an order of magnitude larger datasets efficiently compared to the state-of-the-art techniques while producing high-quality solutions.more » « less
-
Abstract Finding similarities between model parameters across different catchments has proved to be challenging. Existing approaches struggle due to catchment heterogeneity and non‐linear dynamics. In particular, attempts to correlate catchment attributes with hydrological responses have failed due to interdependencies among variables and consequent equifinality. Machine Learning (ML), particularly the Long Short‐Term Memory (LSTM) approach, has demonstrated strong predictive and spatial regionalization performance. However, understanding the nature of the regionalization relationships remains difficult. This study proposes a novel approach to partially decouple learning the representation of (a) catchment dynamics by using theHydroLSTMarchitecture and (b) spatial regionalization relationships by using aRandom Forest(RF) clustering approach to learn the relationships between the catchment attributes and dynamics. This coupled approach, calledRegional HydroLSTM, learns a representation of “potential streamflow” using a single cell‐state, while the output gate corrects it to correspond to the temporal context of the current hydrologic regime. RF clusters mediate the relationship between catchment attributes and dynamics, allowing identification of spatially consistent hydrological regions, thereby providing insight into the factors driving spatial and temporal hydrological variability. Results suggest that by combining complementary architectures, we can enhance the interpretability of regional machine learning models in hydrology, offering a new perspective on the “catchment classification” problem. We conclude that an improved understanding of the underlying nature of hydrologic systems can be achieved by careful design of ML architectures to target the specific things we are seeking to learn from the data.more » « less
-
This paper introduces a generalized spatial regionalization problem, namely, PRUC ( P -Regions with User-defined Constraint) that partitions spatial areas into homogeneous regions. PRUC accounts for user-defined constraints imposed over aggregate region properties. We show that PRUC is an NP-Hard problem. To solve PRUC, we introduce GSLO (Global Search with Local Optimization), a parallel stochastic regionalization algorithm. GSLO is composed of two phases: (1) Global Search that initially partitions areas into regions that satisfy a user-defined constraint, and (2) Local Optimization that further improves the quality of the partitioning with respect to intra-region similarity. We conduct an extensive experimental study using real datasets to evaluate the performance of GSLO. Experimental results show that GSLO is up to 100× faster than the state-of-the-art algorithms. GSLO provides partitioning that is up to 6× better with respect to intra-region similarity. Furthermore, GSLO is able to handle 4× larger datasets than the state-of-the-art algorithms.more » « less
