利用主成分分析法及地理加权回归模型分析AOD数据

针对采用地理加权回归模型（GWR）进行预测时输入变量较多导致计算复杂度高,而输入变量较少引起预测精度降低这一问题,提出了一种基于主成分分析的地理加权回归方法（PCA-GWR）。首先,该方法检验了气溶胶光学厚度（AOD）影响因素之间的共线性;然后,通过非线性主成分分析法（NLPCA）对影响AOD值的若干相关变量进行处理,既消除了相关变量彼此之间的多重共线性,又可以起到降维的作用;最后,利用非线性主成分分析得到较少的几个综合指标,通过地理加权回归模型对AOD值进行分析预测。为验证该方法的有效性,采用京津冀地区的AOD、高程、风速、气温、湿度、气压、坡度、坡向数据,利用Pearson相关系数法选取与AOD浓度具有较高相关性的影响因素作为常规的GWR模型的输入变量,在变量个数相同的前提下,与本文方法进行对比。研究结果表明：应用非线性主成分分析法对相关变量进行预处理后,有效地解决了变量之间的共线性,保留了原始影响因素主要信息,提高了运算效率,且该方法所得的MAE、RMSE、AIC及其拟合优度R²均优于常规的GWR模型。     

The pyrogeography of sub-Saharan Africa: a study of the spatial non-stationarity of fire–environment relationships using GWR

This study analyses the relationship between fire incidence and some environmental factors, exploring the spatial non-stationarity of the phenomenon in sub-Saharan Africa. Geographically weighted regression (GWR) was used to study the above relationship. Environment covariates comprise land cover, anthropogenic and climatic variables. GWR was compared to ordinary least squares, and the hypothesis that GWR represents no improvement over the global model was tested. Local regression coefficients were mapped, interpreted and related with fire incidence. GWR revealed local patterns in parameter estimates and also reduced the spatial autocorrelation of model residuals. All the covariates were non-stationary and in terms of goodness of fit, the model replicates the data very well (R ² = 87%). Vegetation has the most significant relationship with fire incidence, with climate variables being more important than anthropogenic variables in explaining variability of the response. Some coefficient estimates exhibit locally different signs, which would have gone undetected by a global approach. This study provides an improved understanding of spatial fire–environment relationships and shows that GWR is a valuable complement to global spatial analysis methods. When studying fire regimes, effects of spatial non-stationarity need to be incorporated in vegetation-fire modules to have better estimates of burned areas and to improve continental estimates of biomass burning and atmospheric emissions derived from vegetation fires.     

一种顾及空间关系的遥感影像阴影检测算法

以城市区域内高大建筑阴影为研究对象,针对现有的阴影检测算法在复杂地物环境下检测精度和可靠性不高的问题,提出了一种结合颜色空间特征和空间关系的遥感影像阴影检测方法。首先,采用SLIC超像素算法对影像进行分割;然后基于Lab和HSI颜色空间构建初步检测条件,将阴影划分为阴影主体区域和待检测区域;最后,借助Canny边缘检测信息合并待判别区域内的超像素块,并利用阴影区域与造成干扰区域间的空间位置关系构建的检测条件进行判别。实验结果表明,该方法可以有效提高复杂地物环境下遥感影像阴影的检测精度和算法可靠性。     

Mapping local regression for spatial object-pairs

Local regression methods such as geographically weighted regression (GWR) can provide specific information about individual locations (or places) in spatial analysis that is useful for mapping nonstationary covariate relationships. However, the distance-based weighting schemes used in GWR are only adaptable for spatial objects that are point or area features. In particular, spatial object-pairs pose a challenge for local analysis because they have a linear dimensionality rather than a point dimensionality. This paper proposes using an alternative local regression model – quantile regression (QR) – for investigating the stationarity of regression parameters with respect to these linear features as well as facilitating the visualization of the results. An empirical example of a gravity model analysis of trade patterns within Europe is used to illustrate the utility of the proposed method.     

Multicollinearity and correlation among local regression coefficients in geographically weighted regression

Present methodological research on geographically weighted regression (GWR) focuses primarily on extensions of the basic GWR model, while ignoring well-established diagnostics tests commonly used in standard global regression analysis. This paper investigates multicollinearity issues surrounding the local GWR coefficients at a single location and the overall correlation between GWR coefficients associated with two different exogenous variables. Results indicate that the local regression coefficients are potentially collinear even if the underlying exogenous variables in the data generating process are uncorrelated. Based on these findings, applied GWR research should practice caution in substantively interpreting the spatial patterns of local GWR coefficients. An empirical disease-mapping example is used to motivate the GWR multicollinearity problem. Controlled experiments are performed to systematically explore coefficient dependency issues in GWR. These experiments specify global models that use eigenvectors from a spatial link matrix as exogenous variables.This study was supported by grant number 1 R1 CA95982-01, Geographic-Based Research in Cancer Control and Epidermiology, from the National Cancer Institute. The author thank the anonymous reviewers and the editor for their helpful comments.     

Comparison of Geographically Weighted Regression and Regression Kriging for Estimating the Spatial Distribution of Soil Organic Matter

Soil organic matter (SOM) is an important component of soils, and knowing the spatial distribution and variation of SOM is the premise for sustainably utilizing soils. The objective of this study was to compare geographically weighted regression (GWR) with regression kriging (RK) for estimating the spatial distribution of SOM using field-sample data in SOM and auxiliary data in correlated environmental variables (e.g., elevation, slope, ferrous minerals index, and Normalized Difference Vegetation Index). Results showed that GWR was a relatively better method and could provide promising results for SOM prediction in comparison with RK. The map interpolated by GWR showed similar spatial patterns influenced by environmental variables and the nonapparent effect of data outliers, but with higher accuracies, compared to that interpolated by RK.     

Geographically weighted regression and multicollinearity: dispelling the myth

Geographically weighted regression (GWR) extends the familiar regression framework by estimating a set of parameters for any number of locations within a study area, rather than producing a single parameter estimate for each relationship specified in the model. Recent literature has suggested that GWR is highly susceptible to the effects of multicollinearity between explanatory variables and has proposed a series of local measures of multicollinearity as an indicator of potential problems. In this paper, we employ a controlled simulation to demonstrate that GWR is in fact very robust to the effects of multicollinearity. Consequently, the contention that GWR is highly susceptible to multicollinearity issues needs rethinking.     

Grid-enabling Geographically Weighted Regression: A Case Study of Participation in Higher Education in England

Geographically Weighted Regression (GWR) is a method of spatial statistical analysis used to explore geographical differences in the effect of one or more predictor variables upon a response variable. However, as a form of local analysis, it does not scale well to (especially) large data sets because of the repeated processes of fitting and then comparing multiple regression surfaces. A solution is to make use of developing grid infrastructures, such as that provided by the National Grid Service (NGS) in the UK, treating GWR as an "embarrassing parallel" problem and building on existing software platforms to provide a bridge between an open source implementation of GWR (in R) and the grid system. To demonstrate the approach, we apply it to a case study of participation in Higher Education, using GWR to detect spatial variation in social, cultural and demographic indicators of participation.     

Exploring the Impact of Non-normality on Spatial Non-stationarity in Geographically Weighted Regression Analyses: Tobacco Outlet Density in New Jersey

The principal rationale for applying geographically weighted regression (GWR) techniques is to investigate the potential spatial non-stationarity of the relationship between the dependent and independent variables—i.e., that the same stimulus would provoke different responses in different locations. The calibration of GWR employs a geographically weighted local least squares regression approach. To obtain meaningful inference, it assumes that the regression residual follows a normal or asymptotically normal distribution. In many classical econometric analyses, the assumption of normality is often readily relaxed, although it has been observed that such relaxation might lead to unreliable inference of the estimated coefficients' statistical significance. No studies, however, have examined the behavior of residual non-normality and its consequences for the modeled relationships in GWR. This study attempts to address this issue for the first time by examining a set of tobacco-outlet-density and demographic variables (i.e., percent African American residents, percent Hispanic residents, and median household income) at the census tract level in New Jersey in a GWR analysis. The regression residual using the raw data is apparently non-normal. When GWR is estimated using the raw data, we find that there is no significant spatial variation of the coefficients between tobacco outlet density and percentage of African American and Hispanics. After transforming the dependent variable and making the residual asymptotically normal, all coefficients exhibit significant variation across space. This finding suggests that relaxation of the normality assumption could potentially conceal the spatial non-stationarity of the modeled relationships in GWR. The empirical evidence of the current study implies that researchers should verify the normality assumption prior to applying GWR techniques in analyses of spatial non-stationarity.     

城市建成环境存量的空间计算：进展及展望

城市建成环境是人类赖以生存的人造环境,城市建成环境存量是指城市中建筑物和基础设施的材料质量。反演城市建成环境存量的空间分布,是数字城市建设的新方向,它能够帮助我们了解城市发展模式,更加有效管理城市资源和废弃物等,对发展城市循环经济、实现城市的可持续发展有着十分重要的意义。本文详细介绍了城市建成环境存量空间计算的3种方法（自上而下、自下而上和遥感计算方法）的理论基础和发展现状,总结了目前的几中方法都存在着过度依赖统计数据、无法兼顾研究区域大尺度和高空间分辨率等问题。在地理大数据时代,更多的数据源为存量的计算带来了新的研究方向。本文总结了新数据源的优势,并展望了结合地理大数据和机器学习方法的存量计算方法,为城市建成环境存量的空间计算提供了一种新的思路。     

利用搜索引擎数据模拟疾病空间分布

互联网记录了人们的日常生活,对带有位置信息的搜索引擎数据进行分析和挖掘可以获得隐藏于其中的地理信息。本文通过分析中国各省流感月度发病数与相关关键词百度搜索指数之间的相关性,选取相关性较高关键词的百度指数作为解释变量,发病数作为因变量,在采用主成分分析法消除变量共线性后,分别使用普通最小二乘回归（OLS）、地理加权回归（GWR）及时空地理加权回归（GTWR）构建流感发病数的空间分布模型。模型的拟合度能够从OLS的0.737、GWR的0.915提高到GTWR的0.959,赤池信息准则（AIC）也表明,GTWR模型明显优于OLS与GWR模型。验证结果显示,GTWR模型能准确识别流感高发地区,将该方法与搜索引擎数据结合能较好地模拟流感空间分布,为空间流行病学的研究提供预测模型和统计解释。     

Alleviating the effect of collinearity in geographically weighted regression

Geographically weighted regression (GWR) is a popular technique to deal with spatially varying relationships between a response variable and predictors. Problems, however, have been pointed out (see Wheeler and Tiefelsdorf in J Geogr Syst 7(2):161–187, 2005), which appear to be related to locally poor designs, with severe impact on the estimation of coefficients. Different remedies have been proposed. We propose two regularization methods. The first one is generalized ridge regression, which can also be seen as an empirical Bayes method. We show that it can be implemented using ordinary GWR software with an appropriate choice of the weights. The second one augments the local sample as needed while running GWR. We illustrate both methods along with ordinary GWR on an example of housing prices in the city of Bilbao (Spain) and using simulations.     

Using Contextualized Geographically Weighted Regression to Model the Spatial Heterogeneity of Land Prices in Beijing,China

Geographically Weighted Regression (GWR) is a method of spatial statistical analysis allowing the modeled relationship between a response variable and a set of covariates to vary geographically across a study region. Its use of geographical weighting arises from the expectation that observations close together by distance are likely to share similar characteristics. In practice, however, two points can be geographically close but socially distant because the contexts (or neighborhoods) within which they are situated are not alike. Drawing on a previous study of geographically and temporally weighted regression, in this article we develop what we describe as contextualized Geographically Weighted Regression (CGWR), applying it to the field of hedonic house price modeling to examine spatial heterogeneity in the land parcel prices of Beijing, China. Contextual variables are incorporated into the analysis by adjusting the geographical weights matrix to measure proximity not only by distance but also with respect to an attribute space defined by measures of each observation's neighborhood. Comparing CGWR with GWR suggests that adding the contextual information improves the model fit.     

地形信息的LoD建模及精度分析

对细节层次模型(LoD模型)不同层次之间的精度进行研究.提出用于分层的简化比率概念,建立表示LoD不同层次精度的分辨率误差模型,选取5种典型地貌区域进行实验,得到不同地貌区域的误差拟合公式.根据这些公式,可内插得到各种分辨率比率的误差.同时,利用逆公式,又能由误差确定相应的分辨率比率.最后,对不同地貌类型不同化简算法的模型化简误差进行分析研究.研究成果为评价LoD模型精度提供新的方法,也为简化DEM模型时选择适宜的分辨率提供科学依据.     

Modeling Urban Growth Using GIS and Remote Sensing

Based on remote sensing and GIS, this study models the spatial variations of urban growth patterns with a logistic geographically weighted regression (GWR) technique. Through a case study of Springfield, Missouri, the research employs both global and local logistic regression to model the probability of urban land expansion against a set of spatial and socioeconomic variables. The logistic GWR model significantly improves the global logistic regression model in three ways: (1) the local model has higher PCP (percentage correctly predicted) than the global model; (2) the local model has a smaller residual than the global model; and (3) residuals of the local model have less spatial dependence. More importantly, the local estimates of parameters enable us to investigate spatial variations in the influences of driving factors on urban growth. Based on parameter estimates of logistic GWR and using the inverse distance weighted (IDW) interpolation method, we generate a set of parameter surfaces to reveal the spatial variations of urban land expansion. The geographically weighted local analysis correctly reveals that urban growth in Springfield, Missouri is more a result of infrastructure construction, and an urban sprawl trend is observed from 1992 to 2005.     

Using Landsat Imagery and Census Data for Urban Population Density Modeling in Port-au-Prince,Haiti

This research uses the most recent (2003) census data and a Landsat ETM+ image to build a population estimation model for Port-au-Prince, Haiti. The purpose of the study is to establish the linkage of population density with remotely sensed surface reflectance signals of an urban area, and use that to estimate population when census data are not available in a timely fashion. The research begins with deriving subpixel vegetation-impervious surface-soil (VIS) fractions derived from the Landsat ETM+ multispectral bands, and then uses the geographically weighted regression (GWR) model to examine how the variation of population density can be explained by the VIS variables and their derivatives. With comparison to the ordinary least square (OLS) model, the GWR model accounts for spatial non-stationarity in the relationship between population patterns and land characteristics in the study area. The study reveals that three VIS variables are significant in explaining population density: the mean value of houses fraction image, the mean value of vegetation fraction image, and the standard deviation of vegetation fraction image.     

一种支持城市路网交通关系自动化的智能模型

针对车载导航、地图网站等应用中路网要素之间交通关系维护的难题,提出一种支持路网要素交通关系自动化的智能过程模型,将路网要素交通关系自动化过程理解为由路网要素间的空间和语义关系、规则集和控制系统组成的产生式系统.该产生式系统可在路网要素空间和语义信息基础上,通过定义可扩展的交通关系规则集,自动化地生成符合应用需求的路网要素间的交通关系.此外,在该产生式系统中引入触发器概念监控和响应几何网络及其交通关系规则集的变更,实时更新逻辑网络中的连通关系信息,实现几何网络、规则集和逻辑网络三者的一致性.同时,提出路网要素交通关系处理的控制策略和关键流程,并对该智能网络模型的有效性进行了验证.

Abstract：

Maintaining the traffic connectivity relations between road features has always been a time consuming task for in-vehicle navigation, map website, and other traveling service related applications. Such a task has been commonly conducted artificially and inevitably inefficient, yet makes data quality control difficult. Considering the intrinsic rules of traffic connectivity formed by the geometrical structures, spatial and semantic relationships between road features in city road networks, an intelligent processing model is set forward in this paper for traffic connectivity automation. It is argued that traffic connectivity automation between road features is fundamentally a production system composed of the spatial and semantic relations between road features, connectivity rules and control system. With the implementation of an extendable connectivity rule set, the traffic connectivity relations between road network features are built automatically based on the spatial and semantic information of road network. The trigger concept is adopted to monitor and respond the changes in geometrical network and connectivity rules, and then dynamically updates the traffic connectivity between road network features in logical network so as to guarantee the consistence between geometrical network, connectivity rules and logical network. A series of control strategies and a conducting engine are developed to maintain the traffic connectivity relations. A case study conducted on a real road network verifies the effects of the proposed intelligent model.     

The development of integrated terrestrial and marine pathways in the Argo-Saronic region,Greece

Least cost path applications can be a powerful tool for understanding connectivity across a landscape. A limitation to this method is its difficulty in integrating terrestrial, marine, and cultural factors – all of which would have been at play in the prehistoric Aegean. This study looks at a method of modeling pathways that integrates major factors (land, sea, and culture) that would be in play while considering medium- to long-distance travel in the Aegean. This test case explores the possible relationships between proposed routes for communication and identified coastal sites with parameters modeled in geographic information system that affect travel in cultural, marine, and terrestrial contexts. The methods presented have significance beyond the Late Bronze Age Aegean. The development of a methodology that incorporates marine, cultural, and terrestrial environments provides a mechanism by which specific hypotheses regarding complex communication routes may be addressed in regions of the world where there is an intensive interplay between terrestrial and marine geographies.     

Dynamic land use change simulation using cellular automata with spatially nonstationary transition rules

The dynamic relationships between land use change and its driving forces vary spatially and can be identified by geographically weighted regression (GWR). We present a novel cellular automata (GWR-CA) model that incorporates GWR-derived spatially varying relationships to simulate land use change. Our GWR-CA model is characterized by spatially nonstationary transition rules that fully address local interactions in land use change. More importantly, each driving factor in our GWR model contains effects that both promote and resist land use change. We applied GWR-CA to simulate rapid land use change in Suzhou City on the Yangtze River Delta from 2000 to 2015. The GWR coefficients were visualized to highlight their spatial patterns and local variation, which are closely associated with their effects on land use change. The transition rules indicate low land conversion potential in the city’s center and outer suburbs, but higher land conversion potential in the inner near suburbs along the belt expressway. Residual statistics show that GWR fits the input data better than logistic regression (LR). Compared with an LR-based CA model, GWR-CA improves overall accuracy by 4.1% and captures 5.5% more urban growth, suggesting that GWR-CA may be superior in modeling land use change. Our results demonstrate that the GWR-CA model is effective in capturing spatially varying land transition rules to produce more realistic results, and is suitable for simulating land use change and urban expansion in rapidly urbanizing regions.     

GBGWR模型在降水量空间分布模拟中的应用

近年来,我国大部分地区屡遭洪涝与干旱两种自然灾害侵袭,对重洪涝干旱区域进行空间插值具有重要的意义。针对传统地理加权回归（GWR）模型建模过程中模型识别和参数估计易受观测值异常点影响的问题,本文提出了一种基于吉布斯采样的贝叶斯地理加权回归（GBGWR）方法。运用基于吉布斯采样的马尔可夫链蒙特卡罗贝叶斯方法,估计地理加权回归模型参数,通过平滑函数降低观测值中异常点位数据,最后对湖南省1985-2015年35个观测站点的降水观测数据进行了空间分布模拟。试验结果表明,本文提出的方法相较于GWR模型性能提高了19.8%,相较于BGWR模型性能提高了8.2%,该方法可以有效降低异常值和"弱数据"对回归结果的影响,能够更加真实地模拟湖南省降水量的空间分布。