An Alternative Classification Scheme for Uncertain Attribute Mapping

The reality of uncertain data cannot be ignored. Anytime that spatial data are used to assist planning, decision making, or policy generation, it is likely that error or uncertainty in the data will propagate through processing protocols and analytic techniques, potentially leading to biased or incorrect decision making. The ability to directly account for uncertainty in spatial analysis efforts is critically important. This article focuses on addressing data uncertainty in one of the most important and widely used exploratory spatial data analysis (ESDA) techniques—choropleth mapping—and proposes an alternative map classification method for uncertain spatial data. The classification approach maximizes within-class homogeneity under data uncertainty while explicitly integrating spatial characteristics to reduce visual map complexity and to facilitate pattern perception. The method is demonstrated by mapping the 2009 to 2013 American Community Survey estimates of median household income in Salt Lake County, Utah, at the census tract level.     

京津冀都市圈经济增长收敛机制的空间分析

区域经济增长收敛机制研究是近年来区域经济学者关注的热点问题之一。本文采用探索性空间数据分析方法,利用空间自相关模型,从新的视角探讨了京津冀都市圈经济增长的空间依赖关系;基于空间计量经济学方法,通过对传统收敛模型加入空间项构建了空间滞后模型和空间误差模型,进而对京津冀都市圈的区域经济收敛机制进行了实证分析。研究结果表明:京津冀都市圈在1992~2003年经济增长存在收敛趋势,但由于强集聚效应,收敛率较低,内部差异仍很显著。     

A scale-explicit model for checking directional consistency in multi-resolution spatial data

Multi-resolution spatial data always contain the inconsistencies of topological, directional, and metric relations due to measurement methods, data acquisition approaches, and map generalization algorithms. Therefore, checking these inconsistencies is critical for maintaining the integrity of multi-resolution or multi-source spatial data. To date, research has focused on the topological consistency, while the directional consistency at different resolutions has been largely overlooked. In this study we developed computation methods to derive the direction relations between coarse spatial objects from the relations between detailed objects. Then, the consistency of direction relations at different resolutions can be evaluated by checking whether the derived relations are compatible with the relations computed from the coarse objects in multi-resolution spatial data. The methods in this study modeled explicitly the scale effects of direction relations induced by the map generalization operator – merging, thus they are efficient for evaluating consistency. The directional consistency is an essential complement to topological and object-based consistencies.     

Spatial autocorrelation and data uncertainty in the American Community Survey: a critique

ABSTRACT

We argue that the use of American Community Survey (ACS) data in spatial autocorrelation statistics without considering error margins is critically problematic. Public health and geographical research has been slow to recognize high data uncertainty of ACS estimates, even though ACS data are widely accepted data sources in neighborhood health studies and health policies. Detecting spatial autocorrelation patterns of health indicators on ACS data can be distorted to the point that scholars may have difficulty in perceiving the true pattern. We examine the statistical properties of spatial autocorrelation statistics of areal incidence rates based on ACS data. In a case study of teen birth rates in Mecklenburg County, North Carolina, in 2010, Global and Local Moran’s I statistics estimated on 5-year ACS estimates (2006–2010) are compared to ground truth rate estimates on actual counts of births certificate records and decennial-census data (2010). Detected spatial autocorrelation patterns are found to be significantly different between the two data sources so that actual spatial structures are misrepresented. We warn of the possibility of misjudgment of the reality and of policy failure and argue for new spatially explicit methods that mitigate the biasedness of statistical estimations imposed by the uncertainty of ACS data.     

Spatial association detector (SPADE)

The geographical detector model can be applied to either spatial or non-spatial data for discovering associations between a dependent variable and potential discrete controlling factors. It can also be applied to continuous factors after they are discretized. However, the power of determinant (PD), measuring data association based on the variance of the dependent variable within zones of a potential controlling factor, does not explicitly consider the spatial characteristics of the data and is also influenced by the number of levels into which each continuous factor is discretized. Here, we propose an improved spatial data association estimator (termed as SPatial Association DEtector, SPADE) to measure the spatial data association by the power of spatial and multilevel discretization determinant (PSMD), which explicitly considers the spatial variance by assigning the weight of the influence based on spatial distribution and also minimizes the influence of the number of levels on PD values by using the multilevel discretization and considering information loss due to discretization. We illustrate our new method by applying it to simulated data with known benchmark association and to dissection density data in the United States to assess its potential controlling factors. Our results show that PSMD is a better measure of association between spatially distributed data than the original PD.     

Quantifying local flow direction uncertainty

Absolute elevation error in digital elevation models (DEMs) can be within acceptable National Map Accuracy standards, but still have dramatic impacts on field-level estimates of surface water flow direction, particularly in level regions. We introduce and evaluate a new method for quantifying uncertainty in flow direction rasters derived from DEMs. The method utilizes flow direction values derived from finer resolution digital elevation data to estimate uncertainty, on a cell-by-cell basis, in flow directions derived from coarser digital elevation data. The result is a quantification and spatial distribution of flow direction uncertainty at both local and regional scales. We present an implementation of the method using a 10-m DEM and a reference 1-m lidar DEM. The method contributes to scientific understanding of DEM uncertainty propagation and modeling and can inform hydrological analyses in engineering, agriculture, and other disciplines that rely on simulations of surface water flow.     

Exploring determinants of the extent of long distance commuting in Australia: accounting for space

Previous research exploring the impacts of long distance commuting (LDC) or, more generally, mining on host regions, struggles to explain the variability of these impacts over time and across space. This article argues that spatial effects should be accounted for explicitly in order to improve the predictive power of contemporary research. We study the extent of LDC in a region in a spatial model disaggregating Australia into 325 subregions. We find evidence that space is an important factor in explaining the extent of LDC in a region, which challenges the validity of studying LDC impacts on host regions in isolation. With regards to the determinants of the extent of LDC, we find that residential attractiveness of a region influences the extent of LDC in a region; the size of the pool of unemployed in a region does not.     

Flexible Spatial Multilevel Modeling of Neighborhood Satisfaction in Beijing

This article develops an innovative and flexible Bayesian spatial multilevel model to examine the sociospatial variations in perceived neighborhood satisfaction, using a large-scale household satisfaction survey in Beijing. In particular, we investigate the impact of a variety of housing tenure types on neighborhood satisfaction, controlling for household and individual sociodemographic attributes and geographical contextual effects. The proposed methodology offers a flexible framework for modeling spatially clustered survey data widely used in social science research by explicitly accounting for spatial dependence and heterogeneity effects. The results show that neighborhood satisfaction is influenced by individual, locational, and contextual factors. Homeowners, except those of resettlement housing, tend to be more satisfied with their neighborhood environment than renters. Moreover, the impacts of housing tenure types on satisfaction vary significantly in different neighborhood contexts and spatial locations.     

空间数据关联规则挖掘的不确定性处理及度量

针对传统空间数据关联规则挖掘缺乏不确定性处理及度量的局限性,将空间数据的不确定性和空间数据挖掘的不确定性有机结合,初步建立了空间数据关联规则挖掘的不确定性处理模型及度量指标,包括空间数据不确定性的Monte Carlo模拟、基于不确定性空间数据的空间自相关度量和关联规则不确定性度量等,并以我国某地区环境调查数据为例进行验证。     

Sample surveying to estimate the mean of a heterogeneous surface: reducing the error variance through zoning

One of the major sources of uncertainty associated with geographical data in GIS arises when they are the outcome of a sampling process. It is well known that when sampling from a spatially autocorrelated homogeneous surface, stratification reduces the error variance of the estimator of the population mean. In this study, we evaluate the efficiency of different spatial sampling strategies when the surface is not homogeneous. When the surface is first-order heterogeneous (the mean of the surface varies across the map), we examine the effects of stratifying it into first-order homogeneous zones prior to the usual stratification for a systematic or stratified random sample. We investigate the effect of this form of spatial heterogeneity on the performance of different methods for estimating the population mean and its error variance. We do so by distinguishing between the real surface to be surveyed (?), the sampling frame (?) including the choice of zoning, and the statistical estimators (Ψ). The study shows that zoning improves estimator efficiency when sampling a heterogeneous surface. Systematic comparison provides rules of thumb for choice of sample design, sample statistics and uncertainty estimation, based on considering different spatial heterogeneities on real surfaces.     

Evaluating the uncertainty caused by Post Office Box addresses in environmental health studies: A restricted Monte Carlo approach

A Monte Carlo approach is used to evaluate the uncertainty caused by incorporating Post Office Box (PO Box) addresses in point‐cluster detection for an environmental‐health study. Placing PO Box addresses at the centroids of postcode polygons in conventional geocoding can introduce significant error into a cluster analysis of the point data generated from them. In the restricted Monte Carlo method I presented in this paper, an address that cannot be matched to a precise location is assigned a random location within the smallest polygon believed to contain that address. These random locations are then combined with the locations of precisely matched addresses, and the resulting dataset is used for performing cluster analysis. After repeating this randomization‐and‐analysis process many times, one can use the variance in the calculated cluster evaluation statistics to estimate the uncertainty caused by the addresses that cannot be precisely matched. This method maximizes the use of the available spatial information, while also providing a quantitative estimate of the uncertainty in that utilization. The method is applied to lung‐cancer data from Grafton County, New Hampshire, USA, in which the PO Box addresses account for more than half of the address dataset. The results show that less than 50% of the detected cluster area can be considered to have high certainty.     

Incorporating spatial association into statistical classifiers: local pattern-based prior tuning

ABSTRACT

This paper proposes a new classification method for spatial data by adjusting prior class probabilities according to local spatial patterns. First, the proposed method uses a classical statistical classifier to model training data. Second, the prior class probabilities are estimated according to the local spatial pattern and the classifier for each unseen object is adapted using the estimated prior probability. Finally, each unseen object is classified using its adapted classifier. Because the new method can be coupled with both generative and discriminant statistical classifiers, it performs generally more accurately than other methods for a variety of different spatial datasets. Experimental results show that this method has a lower prediction error than statistical classifiers that take no spatial information into account. Moreover, in the experiments, the new method also outperforms spatial auto-logistic regression and Markov random field-based methods when an appropriate estimate of local prior class distribution is used.     

土壤粒径空间预测方法研究综述

土壤粒径（砂粒、粉粒和黏粒）是各种陆表过程和生态系统服务评估等模型的关键参数。作为一种土壤成分数据,土壤粒径的空间预测方法有和为1（或100%）等特殊要求,其空间分布精度受预测方法影响较大。本文针对土壤粒径相较于其他土壤属性的特殊性,提出了土壤粒径空间预测方法框架,综述了土壤粒径数据变换、空间插值和精度验证等系列方法,总结了提升土壤粒径空间预测精度的各种途径,包括通过有效的数据变换改善数据分布、结合数据分布特点选择合适的预测方法、结合辅助变量提升制图精度和分布合理性、使用混合模型提升插值精度、使用多成分联合模拟模型提升预测的系统性等。最后,提出了今后土壤粒径空间预测方法研究的未来方向,包括从考虑数据变换原理和机制角度改善数据分布、发展多成分联合模拟模型和高精度曲面建模方法,以及引入土壤粒径函数曲线并与随机模拟结合等。     

降雨信息空间插值的不确定性分析

文章以潮白河流域为样区,根据58个雨量站1990年的降雨观测数据,采用反距离权重法、克立格法、样条函数法、趋势面法等插值方法,分析了站点数量变化、时间尺度变化、栅格像元的尺度变化、插值方法的差异对降雨数据空间插值结果的影响,剖析降雨插值中的不确定性。结果表明：（1）插值站点数量越大,区域降雨插值的不确定性越小;（2）像元尺度在50m~1000m间变化对降雨插值的不确定性只有微弱的影响;（3）对应于时间尺度由年到月到日的变化,降雨插值的不确定性随时间尺度的减小而显著增大;（4）不同插值方法影响到降雨空间插值的不确定性水平。为了减少降雨信息空间插值的不确定性,根本途径是要引入第三方相关变量,并将其整合到现有的插值算法中。高相关性变量的选取及其与插值模型的整合方式将成为降雨插值研究的主导方向。     

Special Issue on parallel processing in GIS

This paper explores three theoretical approaches for estimating the degree of correctness to which the accuracy figures of a gridded Digital Elevation Model (DEM) have been estimated depending on the number of checkpoints involved in the assessment process. The widely used average‐error statistic Mean Square Error (MSE) was selected for measuring the DEM accuracy. The work was focused on DEM uncertainty assessment using approximate confidence intervals. Those confidence intervals were constructed both from classical methods which assume a normal distribution of the error and from a new method based on a non‐parametric approach. The first two approaches studied, called Chi‐squared and Asymptotic Student t, consider a normal distribution of the residuals. That is especially true in the first case. The second case, due to the asymptotic properties of the t distribution, can perform reasonably well with even slightly non‐normal residuals if the sample size is large enough. The third approach developed in this article is a new method based on the theory of estimating functions which could be considered much more general than the previous two cases. It is based on a non‐parametric approach where no particular distribution is assumed. Thus, we can avoid the strong assumption of distribution normality accepted in previous work and in the majority of current standards of positional accuracy. The three approaches were tested using Monte Carlo simulation for several populations of residuals generated from originally sampled data. Those original grid DEMs, considered as ground data, were collected by means of digital photogrammetric methods from seven areas displaying differing morphology employing a 2 by 2 m sampling interval. The original grid DEMs were subsampled to generate new lower‐resolution DEMs. Each of these new DEMs was then interpolated to retrieve its original resolution using two different procedures. Height differences between original and interpolated grid DEMs were calculated to obtain residual populations. One interpolation procedure resulted in slightly non‐normal residual populations, whereas the other produced very non‐normal residuals with frequent outliers. Monte Carlo simulations allow us to report that the estimating function approach was the most robust and general of those tested. In fact, the other two approaches, especially the Chi‐squared method, were clearly affected by the degree of normality of the residual population distribution, producing less reliable results than the estimating functions approach. This last method shows good results when applied to the different datasets, even in the case of more leptokurtic populations. In the worst cases, no more than 64–128 checkpoints were required to construct an estimate of the global error of the DEM with 95% confidence. The approach therefore is an important step towards saving time and money in the evaluation of DEM accuracy using a single average‐error statistic. Nevertheless, we must take into account that MSE is essentially a single global measure of deviations, and thus incapable of characterizing the spatial variations of errors over the interpolated surface.     

Multi-criteria spatial screening and uncertainty analysis applied to direct-use geothermal projects

ABSTRACT

The focus of this work is general methods for prioritization or screening of project sites based on the favorability of multiple spatial criteria. We present a threshold-based transformation of each underlying spatial favorability factor into a continuous scale with a common favorability interpretation across all criteria. We compare several methods of computing site favorability and propagating uncertainty from the data to the favorability metrics. Including uncertainty allows decision makers to determine if seeming differences among sites are significant. We address uncertainty using Taylor series approximations and analytical distributions, which are compared to computationally intensive Monte Carlo simulations. Our methods are applied to siting direct-use geothermal energy projects in the Appalachian Basin, where our knowledge about any particular site is limited, yet sufficient data exist to estimate favorability. We consider four factors that contribute to site favorability: the thermal resource described by the depth to 80°C rock, natural reservoir productivity described by rock permeability and thickness, potential for induced seismicity, and the estimated cost of surface infrastructure for heat distribution. Those factors are combined in three ways. We develop favorability uncertainty propagation and sensitivity analysis methods. All methods are general and can be applied to other multi-criteria spatial screening problems.     

基于场所的GIS中的不确定性问题及分类框架

基于场所的GIS直接表达人类地理空间知识的管理和加工过程,而不确定性是人类智能的基本特点,因此GIS的智能化需要研究其中的不确定性问题。与传统的GIS相比,基于场所的GIS中的不确定性问题更为丰富,既包括随机性,也包括含糊性,而不确定性的主体既可以是地理要素、场所和空间关系,也包括命题和规则。该文介绍该领域相关的研究成果,基于不确定性主体、类型、表达手段及相关的活动4个视角,建立了基于场所的GIS中所涉及的不确定性框架,从而为相关的不确定性建模提供指导。     

Contextual neural gas for spatial clustering and analysis

This study aims to introduce contextual Neural Gas (CNG), a variant of the Neural Gas algorithm, which explicitly accounts for spatial dependencies within spatial data. The main idea of the CNG is to map spatially close observations to neurons, which are close with respect to their rank distance. Thus, spatial dependency is incorporated independently from the attribute values of the data. To discuss and compare the performance of the CNG and GeoSOM, this study draws from a series of experiments, which are based on two artificial and one real-world dataset. The experimental results of the artificial datasets show that the CNG produces more homogenous clusters, a better ratio of positional accuracy, and a lower quantization error than the GeoSOM. The results of the real-world dataset illustrate that the resulting patterns of the CNG are theoretically more sound and coherent than that of the GeoSOM, which emphasizes its applicability for geographic analysis tasks.     

基于贝叶斯最大熵的甘肃省多年平均降水空间化研究

 贝叶斯最大熵方法可以对具有一定不确定性的“软数据”和认为没有误差的“硬数据”进行插值。对甘肃省1961—1990年52个气象站点的多年平均降水数据进行空间化研究。通过比较普通克里格、共协克里格、三元回归建模后残差插值以及基于贝叶斯最大熵的3种不同软硬数据参与情况下的插值结果,发现考虑降水30 a时间序列不完整性以及辅助变量经验模型不确定性的插值结果的MAE和RMSE,比直接使用多年平均降水数据直接插值的MAE和RMSE小,表明贝叶斯最大熵方法通过对不确定性的考虑可以有效降低预测结果的绝对误差。从降水的空间分布来看,考虑辅助变量DEM的插值结果能相对较好的体现高程对降水的地形影响,尤其分区将辅助变量转换为软数据可以有效体现不同区域高程对降水的不同影响问题。综合误差评价以及降水插值结果的空间分布,认为BME插值过程中可以考虑数据本身以及辅助数据利用的不确定性,使降水空间化的结果更加真实客观,同时为合理利用辅助信息提供了一个新思路。     

农田景观空间异质性分析及遥感监测最优尺度选择——以三江平原为例

农情遥感监测需要高时间分辨率的遥感数据,目前这些数据大都为中低空间分辨率影像。在这些尺度下,像元内部往往是异质的,从而影响农情参数反演精度。因此分析和表达农田景观空间异质性和最优尺度选择对遥感农情监测质量的提高具有重要的应用价值。选取建三江农垦区四种典型农田景观为研究点,Landsat/TM NDVI为实验数据,利用实验变异函数对四种景观类型的各向空间异质性进行了分析, 而后通过变异函数模型拟合,定量分析了各个研究点的整体空间异质性,并在此基础上进行了研究区遥感监测最优尺度选择。研究表明:(1) 基于实验变异函数的结构分析方法,可定性地认识空间异质性的大小和方向,进而挖掘出其背后的自然和人为驱动因素。(2) 对实验变异函数进行拟合分析,可定量地刻画不同景观格局各自的空间异质性特性。此外,基于变异函数对空间异质性的定量表达,讨论了利用积分变程A结合Nyquist-Shannon采样定理进行最优尺度选择的方法。