Spatial Regionalization Research Articles

Enhancing spatial domain detection in spatial transcriptomics with EnSDD

Advancements in spatial transcriptomics have transformed our understanding of organ function and tissue microenvironment. However, accurately identifying spatial domains to depict genome heterogeneity and cellular interactions remains a challenge. In this study, we propose EnSDD (Ensemble-learning for Spatial Domain Detection), a method that ingeniously integrates eight state-of-the-art spatial domain detection methods to automatically identify spatial domains. A key innovation of EnSDD is its dynamic weighting mechanism within the ensemble learning process, which optimizes the contribution of each base model and provides a performance evaluation metric without the need for ground truth data. By leveraging the spatial domains identified through EnSDD, we incorporate the detection of domain-specific spatially variable genes and the spatial distribution of cell types, thereby providing deeper insights into tissue heterogeneity. We validate EnSDD across diverse spatial transcriptomics datasets from various tissue organizational structures. Our results demonstrate that EnSDD significantly enhances spatial domain identification accuracy, identifies genes with spatial expression patterns, and reveals domain-specific cell type enrichment patterns, offering invaluable insights into tissue spatial heterogeneity and regionalization.

Association between snack intake behaviors of children and neighboring women: A population-based cross-sectional analysis with spatial regionalization

BackgroundAccumulated evidence indicates that neighborhood environments affect children's health behaviors. However, measuring neighborhood environments remains challenging because there exist strengths and weaknesses both in objective and perceived environment measures. Drawing on a recent conceptual model of how environment, perception, and behavior interact, we hypothesized that neighbors' behavioral similarities indicate the combined influence of physical and social environmental opportunities on specific behaviors. We then examined how these similarities (i.e. the behavioral tendencies of children's adult neighbors) relate to children's obesogenic dietary behaviors. MethodsWe used data for 2275 women and 821 elementary schoolchildren from a 2012–2013 population-based survey in greater Tokyo, Japan. Snack intake was defined as the total consumption of various types of snacks, estimated using a validated self-administered diet history questionnaire. Spatial regionalization, a type of spatial clustering, was used to empirically identify segments that could effectively differentiate regional variation in women's snack intake behaviors. We conducted multiple regression analysis to assess the cross-sectional association between children's snack intake and the mean snack intake of neighborhood women, adjusting for mother's intake. ResultsA 1-g increase in the mean snack intake of neighborhood women was associated with a 0.23-g (95% confidence interval: 0.00–0.45) increase in children's intake, while a 1-g increase in mother's intake was associated with a 0.34-g (95% confidence interval: 0.26–0.41) increase in children's intake. DiscussionThe results suggest that the out-of-home physical and social neighborhood environments may have non-ignorable associations with children's dietary behaviors by offering behavioral opportunities in addition to maternal influence.

Improved mapping of heavy metals in agricultural soils using machine learning augmented with spatial regionalization indices

The accurate spatial mapping of heavy metal levels in agricultural soils is crucial for environmental management and food security. However, the inherent limitations of traditional interpolation methods and emerging machine-learning techniques restrict their spatial prediction accuracy. This study aimed to refine the spatial prediction of heavy metal distributions in Guangxi, China, by integrating machine learning models and spatial regionalization indices (SRIs). The results demonstrated that random forest (RF) models incorporating SRIs outperformed artificial neural network and support vector regression models, achieving R2 values exceeding 0.96 for eight heavy metals on the test data. Hierarchical clustering for feature selection further improved the model performance. The optimized RF models accurately predicted the heavy metal distributions in agricultural soils across the province, revealing higher levels in the central-western regions and lower levels in the north and south. Notably, the models identified that 25.78 % of agricultural soils constitute hotspots with multiple co-occurring heavy metals, and over 6.41 million people are exposed to excessive soil heavy metal levels. Our findings provide valuable insights for the development of targeted strategies for soil pollution control and agricultural soil management to safeguard food security and public health.

Application of autoencoders artificial neural network and principal component analysis for pattern extraction and spatial regionalization of global temperature data

Spatial regionalization is instrumental in simplifying the spatial complexity of the climate system. To identify regions of significant climate variability, pattern extraction is often required prior to spatial regionalization with a clustering algorithm. In this study, the autoencoder (AE) artificial neural network was applied to extract the inherent patterns of global temperature data (from 1901 to 2021). Subsequently, Fuzzy C-means clustering was applied to the extracted patterns to classify the global temperature regions. Our analysis involved comparing AE-based and principal component analysis (PCA)-based clustering results to assess consistency. We determined the number of clusters by examining the average percentage decrease in Fuzzy Partition Coefficient (FPC) and its 95% confidence interval, seeking a balance between obtaining a high FPC and avoiding over-segmentation. This approach suggested that for a more general model, four clusters is reasonable. The Adjusted Rand Index between the AE-based and PCA-based clusters is 0.75, indicating that the AE-based and PCA-based clusters have considerable overlap. The observed difference between the AE-based clusters and PCA-based clusters is suggested to be associated with AE’s capability to learn and extract complex non-linear patterns, and this attribute, for example, enabled the clustering algorithm to accurately detect the Himalayas region as the ‘third pole’ with similar temperature characteristics as the polar regions. Finally, when the analysis period is divided into two (1901–1960 and 1961–2021), the Adjusted Rand Index between the two clusters is 0.96 which suggests that historical climate change has not significantly affected the defined temperature regions over the two periods. In essence, this study indicates both AE’s potential to enhance our understanding of climate variability and reveals the stability of the historical temperature regions.

Assessment of Irrigation Potential in Jewuha Watershed, Middle Awash River Basin, Ethiopia

Ethiopia is endowed with immense water and land resources that could be tapped and used for irrigation development. However, little has been done so far due mainly to lack of comprehensive knowledge on the potential of these resources. This study was, therefore, taken up to assess the irrigation potential in data scarce Jewuha watershed of the Awash River Basin. To achieve the objective of the study, the suitability of the land for both surface and pressurized irrigations was estimated using a parametric evaluation technique combined with the FAO land evaluation framework in the GIS environment with multi-criteria analysis of irrigation suitability factors. The irrigation water demands of major crops adopted in the area were determined using CROPWAT software. The surface water potential at the sub watershed was estimated using a combination of SWAT model and the spatial proximity regionalization technique. The performance of the SWAT model was checked by statistical parameters. The irrigation suitability analysis reveals that 51372ha of the study area are suitable and 16274ha are unsuitable for surface irrigation system. Furthermore, 52768ha of the area are suitable and 15088ha are unsuitable for a sprinkler irrigation system. For drip irrigation, 52751ha are suitable and 14855ha are unsuitable. The calibration and validation of SWAT model showed that the model has performed well to simulate the hydrology of the watershed with a coefficient of determination (R2), Nash-Sutcliffe efficiency (NSE) and Percent of bias (PBIAS) of 0.74, 0.73 and 0.80 for calibration and 0.71, 0.70 and 7.90 for validation, respectively. From a combined analysis of the available land and water resources, the gross irrigation potential of the area is estimated to be 12,997ha, of which 3098ha of land is exclusively suitable for surface irrigation and 9,899ha is suitable for pressurized irrigation systems.

Development of Synthetic Unit Hydrographs Using Spatial Proximity Regionalization for the Makiling Forest Reserve, Philippines

There is a dearth of streamflow data in the Philippines to generate hydrographs needed for flood forecasting and water resources assessment. A method of generating and calibrating synthetic hydrographs using model simulations and spatial proximity regionalization is presented. Synthetic unit hydrographs of four storm events in the gauged watershed of Makiling Forest Reserve were generated using Soil Conservation Service Unit Hydrograph, Clark Unit Hydrograph, and Snyder’s Unit Hydrograph methods. The generated synthetic hydrographs for each runoff modeling technique were calibrated with the actual hydrographs of the watershed. Snyder’s Unit Hydrograph model results were the most acceptable based on the Nash-Sutcliffe Efficiency, Index of Volumetric Fit, and Relative Error of Peak Flow. The weighted values of the calibrated watershed parameters computed using spatial proximity regionalization technique and the hyetographs derived from the Rainfall Intensity Duration Frequency Curve of the University of the Philippines Los Baños-National Agrometeorological Station were used to generate the synthetic unit hydrographs for three neighboring ungauged watersheds at 2-, 5-, 10-, 15-, 20-, 25-, 50, 100-year return periods. Total runoff volume, the magnitude of peak flows, and time to peak derived from the generated hydrographs can be used in watershed planning, water resources management, flood forecasting and the design of various water control structures.

Extreme waves in the Caribbean Sea: spatial regionalization and long-term analysis

The extreme wave height distribution in the Caribbean Sea is studied using a new method based on the maximum basin-wide aggregate of significant wave height, Hs, values per month. Besides, by means of the Self-Organizing Maps (SOM) technique, we identify coherent geographical regions with similar extreme wave height variability in the Caribbean Sea. Our findings revealed three primary regions: the eastern side with comparatively lower values, the central region with intermediate values, and the western side with the highest extreme wave heights. The study also examines the wind forcing conditions driving the spatial and temporal variability of the extreme waves, highlighting the influence of the low-pressure belt dynamics as well as the role played by the Caribbean Low-Level Jet (CLLJ) index, and the impact of cold fronts and hurricanes on extreme wave heights. Additionally, we explore the relationship between the extreme wave height distribution and climatic indices, such as the Atlantic Multidecadal Oscillation (AMO), the Atlantic Meridional Mode (AMM), the North Atlantic Oscillation (NAO) and the Oceanic Niño (ONI). The results reveal that the spatial distribution of extreme wave heights in the Caribbean Sea is mostly ruled by the influence of the CLLJ, with correlations close to 80%. In addition, significant correlations were observed between the extreme wave heights and the ENSO in the central Caribbean, as well as positive correlations between the extreme wave heights and NAO in the eastern part of the basin, and significant values of correlation with the negative phases of AMO and AMM in the whole basin. We show that, unlike conventional (or broadly used) methods deployed to identify extreme wave height, such as percentile 99th, Hs99, our methodology allows a further assessment of the wind and climate forcing conditions associated with the extreme wave events. Although, we acknowledge that the method here presented has limitations to capture extreme wave height outliers, it has the advantage of being used concomitant with the wind forcing to develop multivariate wave climate analysis at basin scale, and could be extended to a more local scale when studying coastal processes.

Examining spatial coordination of human-land-industry-service system from a regionalization approach: A case study of Beijing

Sustainable development requires a better understanding of the coupling relationship among population, urban land use, industry, and city services since they are closely related to the benefits of human beings. However, previous studies tend to focus on population and land use for urbanization-targeted insights without considering city services and industry development from a people-centered on the fine scale. This research aims to fill this gap by examining the spatial coordination of the human-land-industry-service system combining the coupling coordinated degree model and a regionalization approach with Beijing as a case study. Results show that about 3% area of Beijing is enjoying favorable coordination along with over 6% having moderate coordination, and sub-systems like human-land are experiencing better-coordinated development. Though the well-known monocentric structure of Beijing dominated by built-up expansion exists, sub-centers represented by Tongzhou and Changping rise to possibly alleviate the non-capital functions. In addition, Gini coefficients at 200-, 500-, 1000-, and 2000-meter scales decrease, and coarser resolutions present more continuous and smoother patterns. Three points concerning the unbalanced development, the scale effect, and the urbanization pattern of Beijing are further discussed. Our framework could be easily extended to explore interactions in other systems with the ability to consider both the fine details and the general spatial regionalization patterns.

Industrial carbon emission efficiency prediction and carbon emission reduction strategies based on multi-objective particle swarm optimization-backpropagation: A perspective from regional clustering

Against the backdrop of global climate change, industrial carbon emission reduction has become an important pathway to for global low-carbon development. This study constructs a framework of geographic spatial constraints regionalization and multi-objective machine learning to predict future industrial carbon emission efficiency (ICEE) and explore strategies for carbon emission reduction. Firstly, the ICEE of 285 Chinese cities were calculated by the super-efficiency slacks-based measure. Secondly, the cities were classified into four ICEE level regions through the spatially constrained multivariate clustering. Next, the multi-objective particle swarm optimization-BP (MOPSO-BP) model was constructed to predict the future trends of ICEE in the four regions. Finally, the geographical detector and multi-scale geographically weighted regression were employed for exploring driving force and carbon emission reduction strategies in different regions. The results show that most cities had low or medium ICEE, while super efficiency cities were mainly distributed in the east coastal areas. The prediction performance of the MOPSO-BP model for the four regions was better than the ordinary particle swarm optimization-BP and traditional BP model. Except for the Agricultural Production Region, there is considerable room for improving the ICEE of other regions over the next decade. Macroeconomic and microeconomic development have a global effect in promoting regional ICEE improvement, urban construction shows a promoting or inhibiting effect in different regions, and information technology has significant spatial heterogeneity in its influence within each region. The analysis framework developed in the study is a reliable solution for managing and planning ICEE and provides constructive suggestions for future regional low-carbon development.

Identification and mapping of surface irrigation potential in the data-scarce Jewuha watershed, Middle Awash River Basin, Ethiopia

Abstract This study was conducted to identify and map the surface irrigation potential in the data-scarce Jewuha watershed of the Awash Basin, Ethiopia. The suitability of the land, based on the soil characteristics and slope, was first assessed by the parametric evaluation technique. The overall suitability of the land was then evaluated considering additional factors including land use land cover, proximity to a water source and road using weighted overlay analysis through the analytic hierarchical process (AHP). Water diversion sites as the source of water supply points were selected based on theoretical site selection criteria with the help of a geographic information system (GIS) and physical observation. The surface water available at the diversion sites was estimated using the Soil and Water Assessment Tool (SWAT) model combined with the spatial proximity regionalization technique. The land suitability analysis revealed that 16.7% (11,359 ha) of the study area is suitable for surface irrigation. Five diversion sites were identified as sources of water supply and the total flows at these sites were 12.92 Mm3. It was found that only 27.3% (3,098 ha) of the suitable land, 5% of the total area of the watershed, can be effectively developed by surface irrigation.

Am I Crossing a Border? Spatial Regionalization and Route Choice Depends on Perceived Landmark Categorization

ABSTRACT We investigated the role of semantic similarities of place names in forming larger regions. The environment´s place names allowed two alternative semantic categorizations corresponding to two equally valid regionalizations. In a priming phase, participants were biased to one or the other categorization scheme. Region perception was assessed by having participants choose between two equidistant routes crossing different numbers of region boundaries. Participants selected routes with a lower number of region crossings according to the primed categorization in 61% of all cases. The results show that perceived semantic similarity of place names affects route choice and the formation of spatial regions.

Motor unit placement in a realistic muscle cross section model: performance of a new algorithm and effects of muscle architecture on surface EMG power spectral components

Objetive. Surface electromyogram (sEMG) characteristics are strongly dependent on the spatial localization of motor units (MU). Thus, the definition of the muscle architecture is a crucial step in the simulation of sEMG. Muscles cross section or even the shape of the MU territories is not a regular geometric figure. Moreover, MU may have different fibre densities, and its distribution may not be random but follow a spatial regionalization by type. Despite these prior conditions, the method for MU placement in a muscle model should be able to achieve constant muscle fibre density, which is a generally accepted property of any muscle. Approach. An algorithm was developed that meets the previously established requirements for the distribution of MU in a muscle model. The algorithm considers the muscle cross section and MU territories as bitmaps and encodes the muscle fibre density distribution by pixel brightness. This allowed the use of digital image processing techniques to optimally distribute the MU. The impact of the different muscle architectures on sEMG was investigated using one of the most accepted models of motor unit pool recruitment combined with a model of MU action potential simulation. element-citationitalic Main results. The algorithm produced a completely regionalized architecture with constant muscle fibre density in a muscle with both an irregular cross-section and elliptic MU territory. Significance. In addition to the improvement in the realism of the muscle simulations, the algorithm allowed the investigation of the influence of the spatial distribution of MU on the sEMG power spectrum, thus helping to explain the existing inability to detect changes in motor unit recruitment strategies through the spectral analysis of interference patterns.

Modeling and Assessing Surface Water Potential Using Combined SWAT Model and Spatial Proximity Regionalization Technique for Ungauged Subwatershed of Jewuha Watershed, Awash Basin, Ethiopia

Surface water potential is the availability of water on the surface of the Earth. It is a finite renewable resource, of which the quantity and quality are both space- and time-dependent. Careful estimation of the surface water potential of a river basin is very essential for the future development of any kind of water-related project in countries like Ethiopia. The surface water potential of the ungauged subwatershed of Jewuha watershed was estimated using the hydrological model of Soil and Water Assessment Tool (SWAT) and simple regionalization techniques. The study used different data inputs collected from various sources and field observations. The performance of the hydrological model was analyzed using performance checker parameters. After calibrating and simulating using observed flow, the model showed it was very well to simulate the hydrology of the watershed with a coefficient of determination (R2), Nash–Sutcliffe efficiency (NSE), and percent of bias (PBIAS) of 0.74, 0.73, and 0.80 for calibration and 0.71, 0.70, and 7.90 for validation, respectively, in Jewuha watershed. From the total watershed area of 680 km2, 163.68 million m3 of runoff was generated by the model annually. In conclusion, the watershed has high surface water potential, and the rivers in the subwatershed also have enough surface water that may be used for agricultural development.

What are the main environmental impacts and products contributing to the biodiversity footprint of EU consumption? A comparison of life cycle impact assessment methods and models

PurposeRecent developments in life cycle impact assessment (LCIA) target at better addressing biodiversity impacts, including the extended modeling of drivers of biodiversity loss. This led to the development of multiple LCIA methods addressing the area of protection of ecosystem quality (i.e, biodiversity loss) over time. This paper aims at systematically comparing available operational LCIA methods and models for assessing the main drivers of biodiversity impacts of EU consumption and unveiling similarities and differences among current methods.MethodsThis paper compares the biodiversity impacts of EU consumption by implementing eight LCIA methods and models: five full LCIA methods (namely, LC-IMPACT, Impact World + , Ecological Scarcity 2013, ReCiPe 2016, and Stepwise), a land-use intensity-specific LCIA model, and two approaches based on the GLOBIO model. The EU Consumption Footprint model is adopted as case study. The comparative analysis between the assessed methods aimed at identifying convergent and divergent results regarding the drivers of biodiversity impacts of EU consumption. The analysis focused on four different levels: impact category, representative product (modeled consumed products), inventory process, and elementary flow. The agreement among the methods in defining an element as relevant was evaluated. Finally, gaps among methods were assessed in terms of coverage of impact categories and elementary flows.Results and discussionThe analysis unveiled that there is a certain level of agreement among available LCIA methods and models regarding the most contributing impact categories and products to the overall biodiversity footprint due to EU consumption. Land use, climate change, and ecotoxicity had a major contribution to overall impacts, thereby highlighting their role as drivers of biodiversity loss. Biodiversity impacts were due to a limited number of consumed products, where food (meat), mobility, and household goods were identified as top contributors. Most contributing inventory processes and elementary flows were associated to most contributing representative products (e.g, animal feed). The relevance and presence of elementary flows in LCIA methods and models were heterogeneous for most of the impact categories.ConclusionsThe results of this study highlight the importance of impact category coverage in the assessment of biodiversity impacts. Limited coverage of impact categories (e.g, methods limited to assess land use) might underestimate the impacts of other drivers of biodiversity loss, especially climate change and ecotoxicity. Further efforts are required to assess the effects of spatial regionalization and the inclusion of missing drivers, recently developed in LCIA.

EnDecon: cell type deconvolution of spatially resolved transcriptomics data via ensemble learning.

Spatially resolved gene expression profiles are the key to exploring the cell type spatial distributions and understanding the architecture of tissues. Many spatially resolved transcriptomics (SRT) techniques do not provide single-cell resolutions, but they measure gene expression profiles on captured locations (spots) instead, which are mixtures of potentially heterogeneous cell types. Currently, several cell-type deconvolution methods have been proposed to deconvolute SRT data. Due to the different model strategies of these methods, their deconvolution results also vary. Leveraging the strengths of multiple deconvolution methods, we introduce a new weighted ensemble learning deconvolution method, EnDecon, to predict cell-type compositions on SRT data in this work. EnDecon integrates multiple base deconvolution results using a weighted optimization model to generate a more accurate result. Simulation studies demonstrate that EnDecon outperforms the competing methods and the learned weights assigned to base deconvolution methods have high positive correlations with the performances of these base methods. Applied to real datasets from different spatial techniques, EnDecon identifies multiple cell types on spots, localizes these cell types to specific spatial regions and distinguishes distinct spatial colocalization and enrichment patterns, providing valuable insights into spatial heterogeneity and regionalization of tissues. The source code is available at https://github.com/Zhangxf-ccnu/EnDecon. Supplementary data are available at Bioinformatics online.

Spatial regionalization based on optimal information compression

Regionalization, spatially contiguous clustering, provides a means to reduce the effect of noise in sampled data and identify homogeneous areas for policy development among many other applications. Existing regionalization methods require user input such as the number of regions or a similarity measure between regions, which does not allow for the extraction of the natural regions defined solely by the data itself. Here we view the problem of regionalization as one of data compression and develop an efficient, parameter-free regionalization algorithm based on the minimum description length principle. We demonstrate that our method is capable of recovering planted spatial clusters in noisy synthetic data, and that it can meaningfully coarse-grain real demographic data. Using our description length formulation, we find that spatial ethnoracial data in U.S. metropolitan areas has become less compressible over the period from 1980 to 2010, reflecting the rising complexity of urban segregation patterns in these metros.

A global analysis of mosses reveals low phylogenetic endemism and highlights the importance of long‐distance dispersal

AbstractAimDigitization of herbarium specimens and DNA sequencing efforts in the past decade have enabled integrative analyses of patterns of diversity and endemism in a phylogenetic context. Here, we compare the best available floristic databases to a comprehensive specimen database to examine spatial patterns of moss phylogenetic assembly. We test the hypotheses that (1) mosses exhibit phylogenetic regionalization, (2) islands contain significantly high phylogenetic diversity and (3) that moss phylogenetic endemism is low on a global scale.LocationGlobal.TaxonMosses.MethodsWe developed a phylogeny of 3654 moss species using 25 markers and compiled a global specimen database from online repositories. We calculated floristic and phylogenetic measures of diversity and endemism and performed randomizations to test for significant deviations from expectations. We use rarefaction and extrapolation to alleviate substantial differences in sampling effort across the globe. We used both phylogenetic and floristic methods to test for spatial regionalization. We compare our specimen‐based results to those obtained using a floristic dataset.ResultsPhylogenetic diversity is more robust to missing data than species richness. Mean phylogenetic distance was significantly higher than expected in areas with high species richness, indicating that reported richness in these areas is likely a product of repeated colonization. Phylogenetic endemism is low globally. Phylogenetic regionalizations cluster into a Holarctic/Holantarctic temperate region, a pantropical region, and a region composed of Australia, New Zealand and South Africa.Main ConclusionsFuture efforts for collecting, sequencing and databasing moss species should focus on the tropics, particularly Africa and Southeast Asia. We provide further evidence to support several important theories developed in moss biogeography, including the role of long‐distance dispersal in shaping floristic patterns, the dominance of anagenesis in driving patterns of island diversity, and the role of climatic instability in driving patterns of assembly in the Holarctic.

A framework for spatial regionalization composed of novel clustering‐based algorithms under spatial contiguity constraints

AbstractTraditionally, the geospatial regionalization task consists of aggregating into regions, geographically connected areas that share similar characteristics. Although various spatial optimization approaches have been proposed for finding exact regionalization solutions, these approaches are not practical when applied to a large number of areas or problems for online aggregation, due to the long execution times using hardware with low resources. In this article, we present a framework for executing spatial regionalization tasks. The pre‐condition for using our framework is the definition of a map describing the neighborhood relations—as spatial contiguity constraints—among the areas (or objects) to be regionalized. In our framework we implemented three clustering algorithms with spatial contiguity constraints: RegK‐Means and Agglomerative Hierarchical Regionalization (AHR), our adaptation of k‐means partition‐based clustering and hierarchical‐based clustering algorithms, respectively; and the Automatic Zoning Procedure (AZP), a traditional algorithm for regionalization that also has the premise of simplifying the neighborhood relation representation. We conducted an exploratory analysis composed of two different experiments. Our results showed that our framework leads to a faster way of executing regionalization tasks in the experimental analysis, allowing us to observe a significant gain of AHR and RegK‐Means over AZP in execution time, while showing better or similar results in other metrics, such as figure of merit.

Supervised Spatial Regionalization using the Karhunen-Loève Expansion and Minimum Spanning Trees

The article presents a methodology for supervised regionalization of data on a spatial domain. Defining a spatial process at multiple scales leads to the famous ecological fallacy problem. Here, we use the ecological fallacy as the basis for a minimization criterion to obtain the intended regions. The Karhunen-Loève Expansion of the spatial process maintains the relationship between the realizations from multiple resolutions. Specifically, we use the Karhunen-Loève Expansion to define the regionalization error so that the ecological fallacy is minimized. The contiguous regionalization is done using the minimum spanning tree formed from the spatial locations and the data. Then, regionalization becomes similar to pruning edges from the minimum spanning tree. The methodology is demonstrated using simulated and real data examples.

PRUC

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.