Showing papers on "Spatial analysis published in 2013"

Advances in Spectral-Spatial Classification of Hyperspectral Images

Abstract: Recent advances in spectral-spatial classification of hyperspectral images are presented in this paper. Several techniques are investigated for combining both spatial and spectral information. Spatial information is extracted at the object (set of pixels) level rather than at the conventional pixel level. Mathematical morphology is first used to derive the morphological profile of the image, which includes characteristics about the size, orientation, and contrast of the spatial structures present in the image. Then, the morphological neighborhood is defined and used to derive additional features for classification. Classification is performed with support vector machines (SVMs) using the available spectral information and the extracted spatial information. Spatial postprocessing is next investigated to build more homogeneous and spatially consistent thematic maps. To that end, three presegmentation techniques are applied to define regions that are used to regularize the preliminary pixel-wise thematic map. Finally, a multiple-classifier (MC) system is defined to produce relevant markers that are exploited to segment the hyperspectral image with the minimum spanning forest algorithm. Experimental results conducted on three real hyperspectral images with different spatial and spectral resolutions and corresponding to various contexts are presented. They highlight the importance of spectral-spatial strategies for the accurate classification of hyperspectral images and validate the proposed methods.

Estimating Uncertain Spatial Relationships in Robotics

Abstract: In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map contains the estimates of relationships among objects in the map, and their uncertainties, given all the available information. The procedures provide a general solution to the problem of estimating uncertain relative spatial relationships. The estimates are probabilistic in nature, an advance over the previous, very conservative, worst-case approaches to the problem. Finally, the procedures are developed in the context of state-estimation and filtering theory, which provides a solid basis for numerous extensions.

Hadoop GIS: a high performance spatial data warehousing system over mapreduce

Abstract: Support of high performance queries on large volumes of spatial data becomes increasingly important in many application domains, including geospatial problems in numerous fields, location based services, and emerging scientific applications that are increasingly data- and compute-intensive. The emergence of massive scale spatial data is due to the proliferation of cost effective and ubiquitous positioning technologies, development of high resolution imaging technologies, and contribution from a large number of community users. There are two major challenges for managing and querying massive spatial data to support spatial queries: the explosion of spatial data, and the high computational complexity of spatial queries. In this paper, we present Hadoop-GIS - a scalable and high performance spatial data warehousing system for running large scale spatial queries on Hadoop. Hadoop-GIS supports multiple types of spatial queries on MapReduce through spatial partitioning, customizable spatial query engine RESQUE, implicit parallel spatial query execution on MapReduce, and effective methods for amending query results through handling boundary objects. Hadoop-GIS utilizes global partition indexing and customizable on demand local spatial indexing to achieve efficient query processing. Hadoop-GIS is integrated into Hive to support declarative spatial queries with an integrated architecture. Our experiments have demonstrated the high efficiency of Hadoop-GIS on query response and high scalability to run on commodity clusters. Our comparative experiments have showed that performance of Hadoop-GIS is on par with parallel SDBMS and outperforms SDBMS for compute-intensive queries. Hadoop-GIS is available as a set of library for processing spatial queries, and as an integrated software package in Hive.

Principal Component Analysis on Spatial Data: An Overview

Abstract: This article considers critically how one of the oldest and most widely applied statistical methods, principal components analysis (PCA), is employed with spatial data. We first provide a brief guide to how PCA works: This includes robust and compositional PCA variants, links to factor analysis, latent variable modeling, and multilevel PCA. We then present two different approaches to using PCA with spatial data. First we look at the nonspatial approach, which avoids challenges posed by spatial data by using a standard PCA on attribute space only. Within this approach we identify four main methodologies, which we define as (1) PCA applied to spatial objects, (2) PCA applied to raster data, (3) atmospheric science PCA, and (4) PCA on flows. In the second approach, we look at PCA adapted for effects in geographical space by looking at PCA methods adapted for first-order nonstationary effects (spatial heterogeneity) and second-order stationary effects (spatial autocorrelation). We also describe how PCA can be...

Spectral–Spatial Classification of Hyperspectral Data Using Loopy Belief Propagation and Active Learning

Abstract: In this paper, we propose a new framework for spectral-spatial classification of hyperspectral image data. The proposed approach serves as an engine in the context of which active learning algorithms can exploit both spatial and spectral information simultaneously. An important contribution of our paper is the fact that we exploit the marginal probability distribution which uses the whole information in the hyperspectral data. We learn such distributions from both the spectral and spatial information contained in the original hyperspectral data using loopy belief propagation. The adopted probabilistic model is a discriminative random field in which the association potential is a multinomial logistic regression classifier and the interaction potential is a Markov random field multilevel logistic prior. Our experimental results with hyperspectral data sets collected using the National Aeronautics and Space Administration's Airborne Visible Infrared Imaging Spectrometer and the Reflective Optics System Imaging Spectrometer system indicate that the proposed framework provides state-of-the-art performance when compared to other similar developments.

Dimension reduction and alleviation of confounding for spatial generalized linear mixed models

Abstract: Summary. Non-Gaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model offers a very popular and flexible approach to modelling such data, but this model suffers from two major shortcomings: variance inflation due to spatial confounding and high dimensional spatial random effects that make fully Bayesian inference for such models computationally challenging. We propose a new parameterization of the spatial generalized linear mixed model that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects. We illustrate the application of our approach to simulated binary, count and Gaussian spatial data sets, and to a large infant mortality data set.

New Approaches for Calculating Moran’s Index of Spatial Autocorrelation

Abstract: Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran’s index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran’s index. Moran’s scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran’s index and Geary’s coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran’s index and Geary’s coefficient will be clarified and defined. One of theoretical findings is that Moran’s index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.

Handbook of Spatial Point-Pattern Analysis in Ecology

Abstract: Application of Spatial Statistics in Ecology Analysis of Spatial Patterns Fundamentals of Point-Pattern Analysis Fundamental Steps of Point-Pattern Analyses Data Summary Statistics Null Models and Point-Process Models Methods to Compare Data and Point-Process Models Dealing with Heterogeneous Patterns Estimators and Toolbox Estimators of Summary Statistics Replicate Patterns Superposition of Point Processes Toolbox Examples Analysis of Univariate Patterns Analysis of Bivariate Patterns Analysis of Multivariate Patterns Analysis of Qualitatively Marked Patterns Analysis of Quantitatively Marked Patterns Analysis of Objects with Finite Size A Course Outline Based on the Book Introduction Analysis of Univariate Patterns Analysis of Bivariate Patterns Analysis of Qualitatively Marked Patterns Analysis of Quantitatively Marked Patterns Analysis of Objects of Finite Size and Real Shape Frequently Used Symbols Glossary References Index

CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors

Abstract: Conditional autoregressive models are commonly used to represent spatial autocorrelation in data relating to a set of non-overlapping areal units, which arise in a wide variety of applications including agriculture, education, epidemiology and image analysis. Such models are typically specified in a hierarchical Bayesian framework, with inference based on Markov chain Monte Carlo (MCMC) simulation. The most widely used software to fit such models is WinBUGS or OpenBUGS, but in this paper we introduce the R package CARBayes. The main advantage of CARBayes compared with the BUGS software is its ease of use, because: (1) the spatial adjacency information is easy to specify as a binary neighbourhood matrix; and (2) given the neighbourhood matrix the models can be implemented by a single function call in R. This paper outlines the general class of Bayesian hierarchical models that can be implemented in the CARBayes software, describes their implementation via MCMC simulation techniques, and illustrates their use with two worked examples in the fields of house price analysis and disease mapping.

Land-Cover Mapping by Markov Modeling of Spatial–Contextual Information in Very-High-Resolution Remote Sensing Images

Abstract: Markov models represent a wide and general family of stochastic models for the temporal and spatial dependence properties associated to 1-D and multidimensional random sequences or random fields. Their applications range over a wide variety of subareas of the information and communication technology (ICT) field, including networking, automation, speech processing, genomic-sequence analysis, or image processing. Focusing on the applicative problem of land-cover mapping from very-high-resolution (VHR) remote sensing images, which is a relevant problem in many applications of environmental monitoring and natural resource exploitation, Markov models convey a great potential, thanks to their capability to effectively describe and incorporate the spatial information associated with image data into an image-classification process. In this framework, the main ideas and previous work about Markov modeling for VHR image classification will be recalled in this paper and processing results obtained through recent methods proposed by the authors will be discussed.

A demonstration of SpatialHadoop: an efficient mapreduce framework for spatial data

Abstract: This demo presents SpatialHadoop as the first full-fledged MapReduce framework with native support for spatial data. SpatialHadoop is a comprehensive extension to Hadoop that pushes spatial data inside the core functionality of Hadoop. SpatialHadoop runs existing Hadoop programs as is, yet, it achieves order(s) of magnitude better performance than Hadoop when dealing with spatial data. SpatialHadoop employs a simple spatial high level language, a two-level spatial index structure, basic spatial components built inside the MapReduce layer, and three basic spatial operations: range queries, k-NN queries, and spatial join. Other spatial operations can be similarly deployed in SpatialHadoop. We demonstrate a real system prototype of SpatialHadoop running on an Amazon EC2 cluster against two sets of real spatial data obtained from Tiger Files and OpenStreetMap with sizes 60GB and 300GB, respectively.

Spatial turn in health research

Abstract: Spatial analysis using maps to associate geographic information with disease can be traced as far back as the 17th century. Currently, the widespread diffusion of geospatial data acquisition technologies is enabling creation of highly accurate spatial (and temporal) data relevant to health research. New approaches in geography and related fields, capitalizing on advances in technologies such as geographic information systems (GIS), the Global Positioning System (GPS), satellite remote sensing, and computer cartography, are often referred to collectively as geographic information science (1, 2). GPS and related systems make it possible to integrate highly accurate geographic location and time with virtually any observation. GIS provides the means to store, share, analyze, and visualize real-time and archived spatial data. It also permits the integration of multiple layers of interdisciplinary spatial data, such as health, environmental, genomic, social, or demographic data, for interactive spatial analysis and modeling. Spatial and spatiotemporal statistical methods (3), such as multilevel analysis, spatial data mining, and agent-based modeling, provide ways of relating health and disease to specific genetic, epigenetic, and environmental factors (4). The density, accuracy, and specificity of current geospatial data also facilitate sophisticated spatial and spatiotemporal analysis and the modeling of complex spatial health processes at the level of the individual rather than the aggregate (5, 6) (see the figure). Research based on data-intensive real-time GPS/GIS methods with miniaturized “wearable” environmental and biomedical monitors is generating advances in exposure assessment, as well as in mobility and obesity studies (7). In addition to individual interventions, this research can lead to outcomes such as the design of healthier environments which enhance access to parks and quality foods, and better treatment programs for a wide range of health conditions, from asthma to diabetes. Figure Exposure assessment with GPS/GIS data of individuals GIS visualization and analytical tools also enable researchers to identify spatial patterns and to model specific processes of disease diffusion or contagion, such as of pandemic influenza viruses, or evolving genetic strains of hepatitis or tuberculosis. Researchers have integrated patient demographics, daily activities, and HIV viral concentrations to map and model changing spatial patterns of HIV infections and their relationships to health care treatment programs (8), or to social risk factors (9). Researchers have also used GIS data, spatial statistics, and interactive mapping to identify HIV concentration hotspots near the Mexico–U.S. border (10). This kind of GIS-based analysis enables proactive and timely delivery of tailored prevention and treatment strategies, such as HIV testing, antiretroviral therapy intervention, and education to the affected communities. Geospatial data on health and social environments have also been used to provide information about health disparities. Using GIS-based ethnic density measures and spatial data on mothers’ residential locations, a recent study of infant health inequalities among Bangladeshi immigrant women in New York City found that their infants were most vulnerable to poor health outcomes, such as low birth weight, when living either in very isolated settings or in areas of the highest ethnic density (11). With real-time interactive GPS/GIS functionality (12) now increasingly embedded in cell phones and low-cost navigation and other mobile devices, individual citizens also are contributing to the flow of health-related geospatial data. These activities are variously referred to as participatory GIS, crowd-sourcing, or volunteered geographic information (x). Despite unresolved issues of privacy and quality assurance, the ability to access georeferenced data from millions of people could be transformative. For example, by analyzing data from 15 million mobile-phone subscribers, Wesolowski et al. (13) could examine the complex interactions between human and animal movements and the spread of malaria in Kenya. From Japan to California, volunteers with GPS-enabled real-time air-quality monitoring systems are assessing exposures to air pollution and radiation at spatial resolution levels and data densities not previously feasible (14). Better institutional and educational models for successfully integrating the spatial dimension into health research and practice are needed to achieve the full benefits of these new capabilities in a timely manner (15, 16). There is also an urgent need for the creation of distributed, interoperable spatial data infrastructures to integrate health research data across and within disparate health research programs. In addition to fostering standards and scientific access, such large-scale spatial data infrastructures are themselves powerful new resources for generating and testing hypotheses, detecting spatial patterns, and responding to health threats. Ongoing collaborations between the NIH and the Association of American Geographers are addressing key technical and institutional challenges (e.g., standards, interoperability, common terminology, data confidentiality) to facilitate the generation, coordination, and use of the rapidly growing body of geospatial health data (17). Research agendas that systematically incorporate spatial data and analysis into global health research hold extraordinary potential for creating new discovery pathways in science (18).

Occupancy Grids: A Stochastic Spatial Representation for Active Robot Perception

Abstract: In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a multi-dimensional random field model that maintains probabilistic estimates of the occupancy state of each cell in a spatial lattice. Bayesian estimation mechanisms employing stochastic sensor models allow incremental updating of the Occupancy Grid using multi-view, multi-sensor data, composition of multiple maps, decision-making, and incorporation of robot and sensor position uncertainty. We present the underlying stochastic formulation of the Occupancy Grid framework, and discuss its application to a variety of robotic tusks. These include range-based mapping, multi-sensor integration, path-planning and obstacle avoidance, handling of robot position uncertainty, incorporation of pre-compiled maps, recovery of geometric representations, and other related problems. The experimental results show that the Occupancy Grid approach generates dense world models, is robust under sensor uncertainty and errors, and allows explicit handling of uncertainty. It supports the development of robust and agile sensor interpretation methods, incremental discovery procedures, and composition of information from multiple sources. Furthermore, the results illustrate that robotic tasks can be addressed through operations performed di- rectly on the Occupancy Grid, and that these operations have strong parallels to operations performed in the image processing domain.

Modelling dendritic ecological networks in space: an integrated network perspective

Abstract: Dendritic ecological networks (DENs) are a unique form of ecological networks that exhibit a dendritic network topology (e.g. stream and cave networks or plant architecture). DENs have a dual spatial representation; as points within the network and as points in geographical space. Consequently, some analytical methods used to quantify relationships in other types of ecological networks, or in 2-D space, may be inadequate for studying the influence of structure and connectivity on ecological processes within DENs. We propose a conceptual taxonomy of network analysis methods that account for DEN characteristics to varying degrees and provide a synthesis of the different approaches within the context of stream ecology. Within this context, we summarise the key innovations of a new family of spatial statistical models that describe spatial relationships in DENs. Finally, we discuss how different network analyses may be combined to address more complex and novel research questions. While our main focus is streams, the taxonomy of network analyses is also relevant anywhere spatial patterns in both network and 2-D space can be used to explore the influence of multi-scale processes on biota and their habitat (e.g. plant morphology and pest infestation, or preferential migration along stream or road corridors).

Maximum Likelihood and Generalized Spatial Two-Stage Least-Squares Estimators for a Spatial-Autoregressive Model with Spatial-Autoregressive Disturbances:

Abstract: We describe the spreg command, which implements a maximum likelihood estimator and a generalized spatial two-stage least-squares estimator for the parameters of a linear cross-sectional spatial-autoregressive model with spatial-autoregressive disturbances.

Creating and managing spatial-weighting matrices with the spmat command

Abstract: We present the spmat command for creating, managing, and storing spatial-weighting matrices, which are used to model interactions between spatial or more generally cross-sectional units. spmat can store spatial-weighting matrices in a general and banded form. We illustrate the use of the spmat command and discuss some of the underlying issues by using United States county and postal-code-level data.

Comparison of four spatial interpolation methods for estimating soil moisture in a complex terrain catchment.

Abstract: Many spatial interpolation methods perform well for gentle terrains when producing spatially continuous surfaces based on ground point data. However, few interpolation methods perform satisfactorily for complex terrains. Our objective in the present study was to analyze the suitability of several popular interpolation methods for complex terrains and propose an optimal method. A data set of 153 soil water profiles (1 m) from the semiarid hilly gully Loess Plateau of China was used, generated under a wide range of land use types, vegetation types and topographic positions. Four spatial interpolation methods, including ordinary kriging, inverse distance weighting, linear regression and regression kriging were used for modeling, randomly partitioning the data set into 2/3 for model fit and 1/3 for independent testing. The performance of each method was assessed quantitatively in terms of mean-absolute-percentage-error, root-mean-square-error, and goodness-of-prediction statistic. The results showed that the prediction accuracy differed significantly between each method in complex terrain. The ordinary kriging and inverse distance weighted methods performed poorly due to the poor spatial autocorrelation of soil moisture at small catchment scale with complex terrain, where the environmental impact factors were discontinuous in space. The linear regression model was much more suitable to the complex terrain than the former two distance-based methods, but the predicted soil moisture changed too sharply near the boundary of the land use types and junction of the sunny (southern) and shady (northern) slopes, which was inconsistent with reality because soil moisture should change gradually in short distance due to its mobility in soil. The most optimal interpolation method in this study for the complex terrain was the hybrid regression kriging, which produced a detailed, reasonable prediction map with better accuracy and prediction effectiveness.

Mapping provisioning ecosystem services at the local scale using data of varying spatial and temporal resolution

Abstract: Spatial data on land use and land cover (LULC) are broadly available on different scales and are used widely for mapping ecosystem services as LULC and their changes impact on the provision of multiple ecosystem services. Here four spatial data sets were compared for their practicability as input data for the LULC based assessment method in the Bornhoved Lakes study area. The results for this 60 km² study area are that more detailed land use information (ATKIS and a combined ATKIS/InVeKoS/Landsat data set) is preferred to CORINE land cover data due to the possibility of including spatial details (e.g. number of LULC classes and crop information) in the assessment of provisioning ecosystem services. The CORINE data set overestimated the supply of the two analyzed provisioning services crops and fodder in comparison to the combined data set which revealed information on the specific crops, making quantification with statistical information on yields easier. Spatial input data quality has an effect on the resulting provisioning service maps and quantifications of ecosystem services in the study area due to the identification/omission of ecosystem services, their extent and change. Consequently they also influence decision-making and the development of the ecosystem services concept in the future.

Spatial fixed effects and spatial dependence in a single cross-section†

Abstract: We investigate the common conjecture in applied econometric work that the inclusion of spatial fixed effects in a regression specification for a single cross-sectional data set removes spatial dependence. We demonstrate analytically and by means of a series of simulation experiments how evidence of the removal of spatial autocorrelation by spatial fixed effects may be spurious when the true data generating processes (DGP) takes the form of a spatial lag or spatial error dependence. In addition, we also show that spatial fixed effects correctly remove spatial correlation only in the special case where the dependence is group-wise, with all observations in the same group as neighbours of each other.

Spatial occupancy models for large data sets

Abstract: Since its development, occupancy modeling has become a popular and useful tool for ecologists wishing to learn about the dynamics of species occurrence over time and space. Such models require presence–absence data to be collected at spatially indexed survey units. However, only recently have researchers recognized the need to correct for spatially induced overdisperison by explicitly accounting for spatial autocorrelation in occupancy probability. Previous efforts to incorporate such autocorrelation have largely focused on logit-normal formulations for occupancy, with spatial autocorrelation induced by a random effect within a hierarchical modeling framework. Although useful, computational time generally limits such an approach to relatively small data sets, and there are often problems with algorithm instability, yielding unsatisfactory results. Further, recent research has revealed a hidden form of multicollinearity in such applications, which may lead to parameter bias if not explicitly addressed. Com...

Spatial spline regression models

Abstract: Summary We describe a model for the analysis of data distributed over irregularly shaped spatial domains with complex boundaries, strong concavities and interior holes Adopting an approach that is typical of functional data analysis, we propose a spatial spline regression model that is computationally efficient, allows for spatially distributed covariate information and can impose various conditions over the boundaries of the domain Accurate surface estimation is achieved by the use of piecewise linear and quadratic finite elements

Efficient Gaussian process regression for large datasets

Abstract: Gaussian processes are widely used in nonparametric regression, classification and spatiotemporal modelling, facilitated in part by a rich literature on their theoretical properties. However, one of their practical limitations is expensive computation, typically on the order of n3 where n is the number of data points, in performing the necessary matrix inversions. For large datasets, storage and processing also lead to computational bottlenecks, and numerical stability of the estimates and predicted values degrades with increasing n. Various methods have been proposed to address these problems, including predictive processes in spatial data analysis and the subset-of-regressors technique in machine learning. The idea underlying these approaches is to use a subset of the data, but this raises questions concerning sensitivity to the choice of subset and limitations in estimating fine-scale structure in regions that are not well covered by the subset. Motivated by the literature on compressive sensing, we propose an alternative approach that involves linear projection of all the data points onto a lower-dimensional subspace. We demonstrate the superiority of this approach from a theoretical perspective and through simulated and real data examples.

A Novel Technique for Optimal Feature Selection in Attribute Profiles Based on Genetic Algorithms

Abstract: Morphological and attribute profiles have been proven to be effective tools to fuse spectral and spatial information for classification of remote sensing data. A wide range of filters (i.e., number of levels in the profiles) is usually necessary in order to properly model the spatial information in a remote sensing scene. A dense sampling of the values of the parameters of the filters generates profiles that have both a very large dimensionality (leading to the Hughes phenomenon in classification) and a high redundancy. In this paper, a novel iterative technique based on genetic algorithms (GAs) is proposed to automatically optimize the selection of the optimal features from the profiles. The selection of the filtered images that compose the profile is performed by dividing them into three classes corresponding to high, medium, and low importance. We propose to measure the importance (modeled in terms of discriminative power in the classification task) using a random forest classifier, which provides a rank for each feature with its model. Only the set of images associated with the highest importance is selected, i.e., preserved for classification. The proposed technique is applied to the features labeled with medium importance, whereas the images with the lowest importance are removed from the profile. This method is employed to classify three hyperspectral data sets achieving significantly high classification accuracy values. A parallel computing implementation has been developed in order to significantly reduce the time required for the run of the GAs.

Spatial Distribution of Tourist Flows to China's Cities

Abstract: This paper investigates the spatial distribution of inbound and domestic tourist flows to cities in China and their growth rates using exploratory spatial data analysis. This method is a set of GIS spatial statistical techniques that are useful in describing and visualizing the spatial distribution, detecting patterns of hot-spots, and suggesting spatial regimes. The global Moran's I statistics for inbound and domestic tourist flows reveal strong positive and significant spatial autocorrelation. Furthermore, the Moran significance maps indicate four significant inbound tourism hot-spot areas in 1999 and 2006 (the Beijing-Tianjin cluster, the Yangtze River Delta cluster, the Fujian coast cluster and the Pearl River Delta cluster), and five significant domestic tourism hot-spot areas in 2002 and 2006 (with the addition of the Chengdu cluster). Based on the results, we show that tourism flows are polarized into clusters and remain very stable over time. As has been seen in other countries, hot-spots...

The GWmodel R package: Further Topics for Exploring Spatial Heterogeneity using Geographically Weighted Models

Abstract: In this study, we present a collection of local models, termed geographically weighted (GW) models, that can be found within the GWmodel R package. A GW model suits situations when spatial data are poorly described by the global form, and for some regions the localised fit provides a better description. The approach uses a moving window weighting technique, where a collection of local models are estimated at target locations. Commonly, model parameters or outputs are mapped so that the nature of spatial heterogeneity can be explored and assessed. In particular, we present case studies using: (i) GW summary statistics and a GW principal components analysis; (ii) advanced GW regression fits and diagnostics; (iii) associated Monte Carlo significance tests for non-stationarity; (iv) a GW discriminant analysis; and (v) enhanced kernel bandwidth selection procedures. General Election data sets from the Republic of Ireland and US are used for demonstration. This study is designed to complement a companion GWmodel study, which focuses on basic and robust GW models.

Assessment of regression kriging for spatial interpolation – comparisons of seven GIS interpolation methods

Abstract: As an important GIS function, spatial interpolation is one of the most often used geographic techniques for spatial query, spatial data visualization, and spatial decision-making processes in GIS and environmental science. However, less attention has been paid on the comparisons of available spatial interpolation methods, although a number of GIS models including inverse distance weighting, spline, radial basis functions, and the typical geostatistical models (i.e. ordinary kriging, universal kriging, and cokriging) are already incorporated in GIS software packages. In this research, the conceptual and methodological aspects of regression kriging and GIS built-in interpolation models and their interpolation performance are compared and evaluated. Regression kriging is the combination of multivariate regression and kriging. It takes into consideration the spatial autocorrelation of the variable of interest, the correlation between the variable of interest and auxiliary variables (e.g., remotely sensed imag...