Global and local spatial autocorrelation in bounded regular tessellations

This paper systematically investigates spatially autocorrelated patterns and the behaviour of their associated test statistic Moran's I in three bounded regular tessellations. These regular tessellations consist of triangles, squares, and hexagons, each of increasing size (n=64; 256; 1024). These tesselations can be downloaded at http://geo-www.sbs.ohio-state.edu/faculty/tiefelsdorf/regspastruc/ in several GIS formats. The selection of squares is particularly motivated by their use in raster based GIS and remote sensing. In contrast, because of topological correspondences, the hexagons serve as excellent proxy tessellations for empirical maps in vector based GIS. For all three tessellations, the distributional characteristics and the feasibility of the normal approximation are examined for global Moran's I, Moran's I ^(k) associated with higher order spatial lags, and local Moran's I _i. A set of eigenvectors can be generated for each tessellation and their spatial patterns can be mapped. These eigenvectors can be used as proxy variables to overcome spatial autocorrelation in regression models. The particularities and similarities in the spatial patterns of these eigenvectors are discussed. The results indicate that [i] the normal approximation for Moran's I is not always feasible; [ii] the three tessellations induce different distributional characteristics of Moran's I, and [iii] different spatial patterns of eigenvectors are associated with the three tessellations. Received: 2 July 1999 / Accepted: 9 November 1999     

Decomposing Malaria Mosquito Aquatic Habitat Data into Spatial Autocorrelation Eigenvectors in a SAS/GIS® Module

We present a geostatistical approach that accounts for spatial autocorrelation in malaria mosquito aquatic habitats in two East African urban environments. QuickBird 0.61 m data, encompassing visible bands and the near infra‐red (NIR) bands, were selected to synthesize images of Anopheles gambiae s.l. aquatic habitats in Kisumu and Malindi, Kenya. Field sampled data of An. gambiae s.l. aquatic habitats were used to determine which ecological covariates were associated with An. gambiae s.l. larval habitat development. A SAS/GIS^® spatial database was used to calculate univariate statistics, correlations and perform Poisson regression analyses on the An. gambiae s.l. aquatic habitat datasets. Semivariograms and global autocorrelation statistics were generated in ArcGIS^®. The spatially dependent models indicate the distribution of An. gambiae s.l. aquatic habitats exhibits weak positive autocorrelation in both study sites, with aquatic habitats of similar log‐larval counts tending to cluster in space. Individual anopheline habitats were further evaluated in terms of their covariations with spatial autocorrelation by regressing them on candidate spatial filter eigenvectors. This involved the decomposition of Moran's I statistic into orthogonal and uncorrelated map pattern components using a negative binomial regression. The procedure generated synthetic map patterns of latent spatial correlation representing the geographic configuration of An. gambiae s.l. aquatic habitat locations in each study site. The Gaussian approximation spatial filter models accounted for approximately 13% to 32% redundant locational information in the ecological datasets. Spatial statistics generated in a SAS/GIS^® module can capture spatial dependency effects on the mean response term of a Poisson regression analysis of field and remotely sampled An. gambiae s.l. aquatic habitat data.     

Modeling network autocorrelation within migration flows by eigenvector spatial filtering

Although the assumption of independence among interaction flows frequently is engaged in spatial interaction modeling, in many circumstances it leads to misspecified models and incorrect inferences. An informed approach is to explicitly incorporate an assumed relationship structure among the interaction flows, and to explicitly model the network autocorrelation. This paper illustrates such an approach in the context of U.S. interstate migration flows. Behavioral assumptions, similar to those of the intervening opportunities or the competing destinations concepts, exemplify how to specify network flows that are related to particular origin–destination combinations. The stepwise incorporation of eigenvectors, which are extracted from a network link matrix, captures the network autocorrelation in a Poisson regression model specification context. Spatial autocorrelation in Poisson regression is measured by the test statistic of Jacqmin-Gadda et al. (Stat Med 16(11):1283–1297, 1997). Results show that estimated regression parameters in the spatial filtering interaction model become more intuitively interpretable.

A Spatial Filtering Specification for an Auto-negative Binomial Model of Anopheles arabiensis Aquatic Habitats

This research accounts for spatial autocorrelation by including latent map pattern components as predictor variables in a malaria mosquito aquatic habitat model specification. The data used to derive the model was from a digitized grid-based algorithm, generated in an ArcInfo database, using QuickBird visible and near-infrared (NIR) data. The Feature Extraction (FX) Module in ENVI 4.4^® was used to categorize individual pixels of field sampled aquatic habitats into separate spectral classes, convert remotely sensed raster layers to vector coverages, and classify output layers to vector format as ESRI shapefiles. These data were used to construct a geographic weights matrix for evaluation of field and remote sampled covariates of Anopheles arabiensis aquatic habitats, a major vector of malaria in East Africa. The principal finding is that synthetic map pattern variables, which are eigenvectors computed for a geographic weights matrix, furnish an alternative way of capturing spatial dependency effects in the mean response term of a regression model. The spatial autocorrelation components suggest the presence of roughly 11 to 28% redundant information in the aquatic habitat larval count samples. The presence of redundant information in the models suggest that the sampling configuration of the An. arabiensis aquatic habitats, in the study sites, may cause field and remote observations of aquatic habitats to be dependent, rather than independent, moving data analysis away from the classical statistical independence model. A Poisson regression model, with a non-constant, gamma-distributed mean, can decompose field and remote sampled An. arabiensis data into positive and negative spatial autocorrelation eigenvectors, which can assess the precision of a malaria mosquito aquatic habitat map and the significance of all factors associated with larval abundance and distribution in a riceland agroecosystem.     

A linear regression solution to the spatial autocorrelation problem

The Moran Coefficient spatial autocorrelation index can be decomposed into orthogonal map pattern components. This decomposition relates it directly to standard linear regression, in which corresponding eigenvectors can be used as predictors. This paper reports comparative results between these linear regressions and their auto-Gaussian counterparts for the following georeferenced data sets: Columbus (Ohio) crime, Ottawa-Hull median family income, Toronto population density, southwest Ohio unemployment, Syracuse pediatric lead poisoning, and Glasgow standard mortality rates, and a small remotely sensed image of the High Peak district. This methodology is extended to auto-logistic and auto-Poisson situations, with selected data analyses including percentage of urban population across Puerto Rico, and the frequency of SIDs cases across North Carolina. These data analytic results suggest that this approach to georeferenced data analysis offers considerable promise. Received: 18 February 1999/Accepted: 17 September 1999     

利用地标空间关系约束的点实体匹配方法

针对传统的点实体匹配方法的不足,提出了利用地标空间关系约束的点实体匹配方法。该方法以参考点实体、候选匹配点实体与其邻域内的同名地标之间的空间关系为基础构造距离特征向量和方向特征向量,基于距离特征向量和方向特征向量计算点实体的相似度,进而确定点同名实体。实验结果表明,该方法在点同名实体空间位置偏差较大的情况下依然能够取得很好的效果,验证了该方法的有效性。     

基于ArcObjects的空间权重矩阵的建立与实现

空间自相关度量的基础是空间权重矩阵的生成,而人工建立空间权重矩阵是一项耗时且计算量大的工作,因此需要解决空间权重矩阵的自动生成问题。本文以ArcObjects为空间目标的管理工具,利用VB可视化编程环境,研究了空间权重矩阵的自动建立方法。实验结果表明,该程序具有较好的健壮性和可执行性,可以成功的应用于空间统计分析模块的计算中。     

A computationally efficient method for delineating irregularly shaped spatial clusters

In this paper, we present an efficiency improvement for the algorithm called AMOEBA, A Multidirectional Optimum Ecotope-Based Algorithm, devised by Aldstadt and Getis (Geogr Anal 38(4):327?C343, 2006). AMOEBA embeds a local spatial autocorrelation statistic in an iterative procedure in order to identify spatial clusters (ecotopes) of related spatial units. We provide an analysis of the computational complexity of the original AMOEBA and develop an alternative formulation that reduces computational time without losing optimality. Empirical evidence is provided using georeferenced socio-demographic data in Accra, Ghana.     

A criterion matrix for the second order design of control networks

This paper proposes an original method of constructing a criterion matrix for the optimal design of control networks by means of the contraction of the eigenvalues and the rotation of the eigenvectors of a covariance matrix. The rotation of the eigenvectors is carried out by two different methods, that is through independent rotations of the pairs of the eigenvector matrix components and through a procrustean transfomation of the same matrix. The required criterion is that the “essential eigenvector components” must be as orthogonal as possible to the predicted direction of deformation. A Second Order Design problem is then resolved, that is the optimization of the precision of the observations of a local free distance network to be constructed for the study of recent crustal movements in the seismogenetic area of Friuli (Italy). The results obtained show a high degree of correspondence for the two proposed methods of rotation if limited rotations of the eigenvectors are considered.     

城镇地价的空间相关性研究

空间自相关(spatial autocorrelation)是指变量在空间上表现出一定的规律性,空间回归是考虑了空间相关性的回归技术。本文将空间自相关性理论应用于地价样点价格分析,发现地价分布规律,并通过地价样点和地价影响因素建立空间线性回归模型的方法估算土地的价值,改进了传统的回归估价方法,从而提高了地价评估的准确程度。     

A Spatial Entropy-Based Decision Tree for Classification of Geographical Information

A decision tree is a classification algorithm that automatically derives a hierarchy of partition rules with respect to a target attribute of a large dataset. However, spatial autocorrelation makes conventional decision trees underperform for geographical datasets as the spatial distribution is not taken into account. The research presented in this paper introduces the concept of a spatial decision tree based on a spatial diversity coefficient that measures the spatial entropy of a geo‐referenced dataset. The principle of this solution is to take into account the spatial autocorrelation phenomena in the classification process, within a notion of spatial entropy that extends the conventional notion of entropy. Such a spatial entropy‐based decision tree integrates the spatial autocorrelation component and generates a classification process adapted to geographical data. A case study oriented to the classification of an agriculture dataset in China illustrates the potential of the proposed approach.     

Testing spatial autocorrelation in weighted networks: the modes permutation test

In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardized exchange matrix appearing in spectral clustering and generalize to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an accessibility matrix into an exchange matrix with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains.     

显著局部空间同位模式自动探测方法

局部空间同位模式挖掘旨在揭示多类地理事件在异质环境下的共生共存规律。已有的方法一方面需要模式筛选的频繁度阈值参数,另一方面需要区域探测的划分参数或聚类参数,参数的不合理设置会导致挖掘结果不可靠甚至出现错误。因此,提出了一种显著局部空间同位模式自动探测方法。首先,基于空间统计思想,采用非参数模式重建方法对空间同位模式进行显著性判别,将全局非显著空间同位模式作为进一步局部探测的候选模式;然后,借助自适应空间聚类方法提取每个候选模式的热点区域;最后,通过不断生长并测试每个热点区域,界定显著局部空间同位模式的有效边界,即空间影响域。通过实验与比较发现,该方法能够客观且有效判别空间同位模式的显著性,并且自适应地提取局部同位模式的空间分布结构,降低了现有方法参数设置的主观性。     

视频数据的地理信息提取研究

针对视频数据虽然能高效、逼真、详细地展现地理信息,但是因不具备地理框架而不能直接与GIS结合,参与空间分析的问题,该文通过多次真实环境条件下的尝试性实验,探索出一种从视频中提取地理信息的方案:采用运动目标检测技术自动识别出视频帧中实体的轮廓;通过半自动的处理清除提取数据的干扰轮廓;借助数据变换技术为视频帧及其提取的数据赋予准确的地理框架。基于真实环境的实验结果表明:该方案不仅可以有效地提取视频中的地理信息参与空间分析,还能够实现其空间分析结果的多视角可视化。本研究针对视频与GIS结合问题做出初步探索,为视频GIS的深层次研究提供帮助。     

基于ArcGIS的空间自相关分析模块的开发与应用

针对目前GIS的空间分析能力,利用ArcObjects开发了空间自相关分析模块。模块包括空间权值矩阵建立、全局空间自相关分析、局部空间自相关分析三方面的功能,并可以嵌入到ArcGIS系统中。论文介绍了空间自相关分析的基本概念、空间自相关分析模块的设计与开发,并演示了模块的应用。     

城市扩展极限学习机模型

城市空间结构及其扩展的模拟是城市科学管理与规划的重要前提,本文基于极限学习机提出了顾及不同非城市用地转化为城市用地差异与强度的城市扩展元胞自动机模型（ELM-CA）。模型验证表明：①ELM-CA模型的模拟精度达到70.30%,相比于逻辑回归和神经网络分别提高了2.21%和1.54%,FoM系数分别提高了0.025 9和0.017 9,Kappa系数分别提高了0.024 7和0.016 9,且Moran I指数接近于实际值,说明极限学习机模型较逻辑回归和神经网络能更有效模拟城市扩展的空间形态及其变化;②ELM模型的训练时间仅为神经网络的1/3左右,体现了ELM学习速度的优势;③在小样本情况下,逻辑回归和神经网络都受到明显的影响,而极限学习机还能保持良好的性能,这个特点使其在样本难以获取的情况下具有明显的优势。两个时相的城市扩展模拟与真实数据的比较表明：基于极限学习机的城市扩展元胞自动机模型（ELM-CA）,简化了CA模型的复杂度,并在小样本情况下能有效提高模拟精度,适合于复杂土地利用条件下城市扩展模拟与预测。     

The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce “spurious correlation” that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.     

Part 4 Technology and the future of GIS and spatial analysis

Geographical Information Science is essentially computational geography and has its own research program, namely all aspects of formal models for spatial natural processes and the interaction of humans with the environment in space and time. This is not a question of technology and technology-related research; but technology influences what questions can be researched effectively. Collection of data in the field and the simulation of field experience through Virtual Reality are just two questions of how spatial reality and human experience are linked. The focus on human spatial cognition is similarly found in software engineering for interoperable Geographic Information Systems.