一种协同时空地理加权回归PM2.5浓度估算方法

针对PM2.5浓度估算中时空特征考虑不足和样本量较少的问题,该文将协同训练和时空地理加权回归相结合,提出了协同时空地理加权回归。采用两个不同参数的时空地理加权回归模型作为回归器,利用一个回归器训练另一个回归器的未标注样本,选择最优结果作为标注样本加入标注样本,通过不断学习扩大标注样本量提升模型的回归性能。以京津冀地区2015年3-7月的PM2.5浓度数据为实验数据,利用气溶胶光学厚度产品、温度、风速和相对湿度进行建模,采用不同核函数的时空地理加权回归作为对比方法进行实验。结果显示,协同时空地理加权回归性能比基于Gauss核函数时空地理加权回归提升了10%,比基于bi-square核函数时空地理加权回归提升了6.25%,证明该文方法能够提升时空样本数量不足时的PM2.5浓度估算精度。     

贪心算法的地理加权回归特征变量选择方法

针对建立地理加权回归(GWR)模型时,无法直接应用普通线性回归(OLR)常用的特征变量选择方法,且计算过程较复杂的问题,该文基于贪心算法原理,通过引入Akaike信息法则,设计了适用于GWR的特征变量选择方法:逐个引入或删除特征变量,判断该变量对模型置信水平影响程度,根据评价准则决定该变量的取舍,最终实现模型外没有关系强的变量、模型内没有关系弱的变量。实验结果表明,比较基于OLR的逐步回归、向前引入法和向后删除法3种方法选择变量建立模型,向前引入法优于向后剔除法,两者都优于基于OLR的逐步回归法,更适用于GWR分析。     

融合地理探测器和地理加权回归的太原市建设用地变化因素研究

准确地识别城市化进程中建设用地的变化情况及其背后的驱动力,对城市后续的可持续发展具有重要意义。本文首先以2000—2020年遥感影像为基础,对太原市建设用地空间分布变化进行研究,然后结合地理探测器模型和地理加权回归模型,对研究区建设用地的空间分布影响驱动力因子进行研究,得到以下结论:除政策因素外,现有的城市建设用地空间分布变化还受到高程、交通、GDP、人口等因素的显著作用。太原市城市建设用地变化的布局不单是GDP变化、人口变化、海拔高度、公路网密度4个显著性因子均匀、独立、直接作用的结果,而是具有空间异质性的各因子两两交互作用后增效的产物。本文成果有望为城市建设用地驱动力研究提供一种新思路。     

Exploring relation of land surface temperature with selected variables using geographically weighted regression and ordinary least square methods in Manipur State,India

In the present study, relationship between Land surface temperature and selected indices, vegetation index (VARI), built-up index (BUI) and elevation (DEM) is investigated. Ordinary least square method and geographically weighted regression are used to analyse the spatial correlation between the indices with surface temperature. Subsequently, temporal trends (2001–2015) in surface temperature and vegetation are explored after every two years of interval. LANDSAT image and ASTER DEM are used to extract LST and additional indices. The selected variables (Built-up, vegetation and topography) explain 69% of the variation in surface temperature. The OLS and GWR revealed that topography and vegetation are the significant factor of LST in Manipur State. Topography being a constant parameter, its effect is constant over time. The changing scenario of vegetation is significantly contributing to LST. The surface temperature over a period of 15 years show increasing trend and is negatively and strongly correlated to vegetation cover.     

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.     

Analysing regional industrialisation in Jiangsu province using geographically weighted regression

 Industry is the most important sector in the Chinese economy. To identify the spatial interaction between the level of regional industrialisation and various factors, this paper takes Jiangsu province of China as a case study. To unravel the existence of spatial nonstationarity, geographically weighted regression (GWR) is employed in this article. Conventional regression analysis can only produce `average' and `global' parameter estimates rather than `local' parameter estimates which vary over space in some spatial systems. Geographically weighted regression (GWR), on the other hand, is a relatively simple, but useful new technique for the analysis of spatial nonstationarity. Using the GWR technique to study regional industrialisation in Jiangsu province, it is found that there is a significant difference between the ordinary linear regression (OLR) and GWR models. The relationships between the level of regional industrialisation and various factors show considerable spatial variability. Received: 4 April 2001 / Accepted: 17 November 2001     

混合地理加权回归模型算法研究

以迭代算法为基础，推导出混合地理加权回归模型的常系数（全局参数）和变系数（局域参数）的计算方法，并以上海市住宅小区楼盘销售平均价格为例进行验证。结果表明，混合地理加权回归模型的计算量略大于地理加权回归模型，但对样本数据的拟合更好，局域参数估计更稳健。     

Understanding demographic and socioeconomic biases of geotagged Twitter users at the county level

ABSTRACT

Massive social media data produced from microblog platforms provide a new data source for studying human dynamics at an unprecedented scale. Meanwhile, population bias in geotagged Twitter users is widely recognized. Understanding the demographic and socioeconomic biases of Twitter users is critical for making reliable inferences on the attitudes and behaviors of the population. However, the existing global models cannot capture the regional variations of the demographic and socioeconomic biases. To bridge the gap, we modeled the relationships between different demographic/socioeconomic factors and geotagged Twitter users for the whole contiguous United States, aiming to understand how the demographic and socioeconomic factors relate to the number of Twitter users at county level. To effectively identify the local Twitter users for each county of the United States, we integrate three commonly used methods and develop a query approach in a high-performance computing environment. The results demonstrate that we can not only identify how the demographic and socioeconomic factors relate to the number of Twitter users, but can also measure and map how the influence of these factors vary across counties.     

Geographically weighted regression‐based determinants of malaria incidences in northern China

Geographically weighted regression (GWR) is an important local method to explore spatial non‐stationarity in data relationships. It has been repeatedly used to examine spatially varying relationships between epidemic diseases and predictors. Malaria, a serious parasitic disease around the world, shows spatial clustering in areas at risk. In this article, we used GWR to explore the local determinants of malaria incidences over a 7‐year period in northern China, a typical mid‐latitude, high‐risk malaria area. Normalized difference vegetation index (NDVI), land surface temperature (LST), temperature difference, elevation, water density index (WDI) and gross domestic product (GDP) were selected as predictors. Results showed that both positively and negatively local effects on malaria incidences appeared for all predictors except for WDI and GDP. The GWR model calibrations successfully depicted spatial variations in the effect sizes and levels of parameters, and also showed substantially improvements in terms of goodness of fits in contrast to the corresponding non‐spatial ordinary least squares (OLS) model fits. For example, the diagnostic information of the OLS fit for the 7‐year average case is R² = 0.243 and AICc = 837.99, while significant improvement has been made by the GWR calibration with R² = 0.800 and AICc = 618.54.     

Incorporating spatial variation in housing attribute prices: a comparison of geographically weighted regression and the spatial expansion method

Hedonic house price models typically impose a constant price structure on housing characteristics throughout an entire market area. However, there is increasing evidence that the marginal prices of many important attributes vary over space, especially within large markets. In this paper, we compare two approaches to examine spatial heterogeneity in housing attribute prices within the Tucson, Arizona housing market: the spatial expansion method and geographically weighted regression (GWR). Our results provide strong evidence that the marginal price of key housing characteristics varies over space. GWR outperforms the spatial expansion method in terms of explanatory power and predictive accuracy.

SuperMap GIS地理加权回归模型研究与实现

地理加权回归分析是对普通线性回归模型的扩展,将空间数据的地理位置嵌入线性回归参数之中,以此来研究空间关系的空间异质性或空间非平稳性,属于局部空间分析模型.通过地理加权回归分析可以确定两种或两种以上变量间相互依赖的定量关系,局部区域的参数估计可以得到地理空间存在的不同空间关系,核函数的选取规则和带宽参数的验证方法也是本文研究的内容.     

GIS-based analysis of obesity and the built environment in the US

This paper examines the statewide relationship between built environment and obesity at the county scale by using the Geographically Weighted Regression (GWR) method. The independent variables include three built environment factors – street connectivity, walk score, fast-food/full-service restaurants ratio – and two sociodemographic variables, race heterogeneity and poverty rate. The urban influence is considered as a covariate in the analysis. Through the regression model we found that walk score and street connectivity are negatively related to obesity, poverty rate and metro are positively related, and the fast-food/full-service restaurants ratio is not significant. A regionalization method is used to group US counties to regions based on their GWR coefficients. Qualitative inferences of policies are made available to facilitate better understanding of the obesity problem associated with the built environment in these regions.     

一种基于半监督学习的地理加权回归方法

地理加权回归方法在小样本数据下回归分析精度往往不高。半监督学习是一种利用未标记样本参与训练的机器学习方法,可以有效地提升少量有标记样本的学习性能。基于此本文提出了一种基于半监督学习的地理加权回归方法,其核心思想是利用有标记样本建立回归模型来训练未标记样本,再选择置信度高的结果扩充有标记样本,不断训练,以提高回归性能。本文采用模拟数据和真实数据进行试验,以均方误差提升百分比作为性能评价指标,将SSLGWR与GWR、COREG对比分析。模拟数据试验中,SSLGWR在3种不同配置下性能分别提升了39.66%、11.92%和0.94%。真实数据试验中,SSLGWR在3种不同配置下性能分别提升了8.94%、3.36%和5.87%。SSLGWR结果均显著优于GWR和COGWR。试验证明,半监督学习方法能利用未标记数据提升地理加权回归模型的性能,特别是在有标记样本数量较少时作用显著。     

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.     

一种多因子加权平均温度模型的构建方法

针对在地基GNSS水汽反演的过程中,天顶湿延迟转换为大气可降水量时如何建立精确的大气加权平均温度(Tm)模型的问题,该文在建立Tm模型前全面考虑了对Tm有显著影响的变量并选择最优回归子集。但分析发现,最优回归子集中各变量之间存在较强的相关性,这将会导致变量之间存在多重共线性,从而影响模型的稳定性和可靠性。选择2013—2015年相关气象数据作为变量并应用岭回归的方法削弱变量之间的多重共线性,建立稳定的多因子Tm回归模型。并利用该模型分别预测2016年1—12月、2019年1—7月的Tm,均方根误差分别为2.3 K和2.0 K,预测精度较高,这将为高精度的水汽反演奠定较好的数据基础。     

南昌市二手房价格影响因子的空间异质性

以安居客网站爬取的2018年10月894个南昌市住宅小区二手房价格为研究对象,利用地理加权回归模型探讨了建筑特征、邻里特征、区位特征等方面各影响因子对住宅价格的作用差异.研究结果表明:1)地理加权回归(GWR)模型的拟合结果优于OLS模型,将回归系数结果空间可视化发现南昌市二手房价格影响因子具有空间异质性.2)不同因子...     

市域尺度货物运输碳排放时空变化及因素分析

针对货物运输导致碳排放成为温室气体主要来源之一的问题,该文综合货物运输车辆的微观温室气体排放及时空变化,从市域尺度分析货物运输碳排放的时空变化规律。利用微观排放模型计算了2000年、2005年、2010年和2015年全国286个城市货物运输碳排放的空间分布及其变化,并应用地理加权回归模型探究城市化不同层面因素对碳排放时空分布变化的影响。结果表明:货物运输碳排放具有显著的空间集聚特征,且高排放地区的集聚规律更加显著;地理加权回归模型精度明显高于普通线性回归模型,经济变量、人口变量、货运强度变量与货物运输碳排放存在显著正相关关系。该研究可为中国各市级区域制订节能减排政策提供量化的科学依据。     

地形因子与小微地震相关度的空间异质性分析

针对传统最小二乘回归未能顾及数据的空间特性,且无法度量模型自变量与因变量相关性的空间变异特性的问题,本文提出利用地理加权回归方法分析小微地震频次与地形因子相关度的空间异质性。以四川地区的地震监测资料、DEM为实验数据,选取地形复杂度、坡度变率、坡向变率和地面曲率为自变量,地震发生频次为因变量,构建地理加权回归模型,并进行回归系数的空间变异分析。实验分析发现,地震频次与地形因子具有一定的相关性:地形复杂度与地震频次相关性最强;坡度变率、沟壑密度、剖面曲率与地震频次的相关性依次减弱;不同空间位置的地形因子和地震频次的相关性具有较明显的空间异质性。实验结果表明,地理加权回归可以有效地度量分析地震频次与地形因子相关度的空间异质性,研究结果可为地震及次生灾害的分析与预报提供辅助决策参考。     

多中心视角下的武汉市路网与经济活动空间关系分析

探究道路网络与经济活动的空间关系对城市科学规划有促进作用。采用多中心评价模型测度武汉市路网情况,并结合核密度估计法和地理加权回归法探究武汉市路网多中心和经济活动多中心的空间分布情况及其相关关系。研究表明:武汉市路网和经济活动分布整体呈现出多中心分布形态;武汉市路网多中心与经济活动多中心存在较强的关联性,且其相关程度存在空间异质性,建议考虑要素空间差异进行科学规划。     

中国区域加权平均温度的时空分析及模型研究

加权平均温度(T_m)是全球卫星导航系统技术反演大气可降水量的关键参数,影响着水汽反演的精度。针对传统的Bevis模型运用在中国区域精度不高的问题,该文提出新的增加时空参数的T_m多元线性回归模型。根据2013—2015年中国86个探空站点的探空资料,分析了T_m的时空特征;然后根据2013年站点资料,利用线性回归建模方法建立了中国区域的T_m单因子回归模型和增加了时空参数的T_m多因子回归模型,并利用2014—2015年的探空数据进行验证。T_m单因子回归模型和T_m多因子回归模型的精度分别为3.1 K和2.6 K,比Bevis模型(精度3.3 K)分别提高了约6.0%和21.2%。考虑到季节对T_m的影响,将T_m多因子回归模型按季节分段,得到按季节分段的T_m多因子回归模型,其精度与T_m多因子回归模型大致相当,但能更细致表达出不同季节T_m的精度情况。结果表明增加了时空参数的T_m多因子回归模型更加适合中国区域的加权平均温度T_m的计算。