Weight matrices and spatial autocorrelation statistics using a topological vector data model

Abstract

This paper reports on software to construct alternative weight matrices and to compute spatial autocorrelation statistics, namely the Moran coefficient and the Geary coefficient using Arc/Info’s data structure. As such it is an addition to recent efforts in linking GIS with exploratory spatial data analysis. The software is interfaced with Arc/Info via the Arc Macro Language (AML) so that it can be run in the ARC environment. This allows the user to perform exploratory analysis within GIS which may provide insights in subsequent spatial analysis and modelling.     

基于空间自相关的东莞市主体功能区划分

中国“十一五”规划纲要明确提出,根据资源环境承载能力、现有开发密度和发展潜力,统筹考虑未来中国人口分布、经济布局、国土利用和城镇化格局,将国土空间划分为优化开发、重点开发、限制开发和禁止开发四类主体功能区。至今已有不少学者开展主体功能区划分研究,但所用方法工作量大,或带有一定的主观性,且未考虑同类功能区集聚或分散程度。因此提出利用遗传算法改进传统聚类方法,自动划分主体功能区,在划分过程中考虑区域的全局空间自相关特性,使同类功能区在空间上呈集聚分布的格局。以近年来城市快速扩张的东莞市为例,验证了此方法的可行性,能简单有效地进行主体功能区划分。与常用的K-means聚类方法相比,新方法划分结果更符合实际情况,能进一步推广应用到其它地区的主体功能区划分。     

基于空间自相关的东莞市主体功能区划分简

中国“十一五”规划纲要明确提出,根据资源环境承载能力、现有开发密度和发展潜力,统筹考虑未来中国人口分布、经济布局、国土利用和城镇化格局,将国土空间划分为优化开发、重点开发、限制开发和禁止开发四类主体功能区。至今已有不少学者开展主体功能区划分研究,但所用方法工作量大,或带有一定的主观性,且未考虑同类功能区集聚或分散程度。因此提出利用遗传算法改进传统聚类方法,自动划分主体功能区,在划分过程中考虑区域的全局空间自相关特性,使同类功能区在空间上呈集聚分布的格局。以近年来城市快速扩张的东莞市为例,验证了此方法的可行性,能简单有效地进行主体功能区划分。与常用的K-means聚类方法相比,新方法划分结果更符合实际情况,能进一步推广应用到其它地区的主体功能区划分。     

A local scale-sensitive indicator of spatial autocorrelation for assessing high- and low-value clusters in multiscale datasets

Georeferenced user-generated datasets like those extracted from Twitter are increasingly gaining the interest of spatial analysts. Such datasets oftentimes reflect a wide array of real-world phenomena. However, each of these phenomena takes place at a certain spatial scale. Therefore, user-generated datasets are of multiscale nature. Such datasets cannot be properly dealt with using the most common analysis methods, because these are typically designed for single-scale datasets where all observations are expected to reflect one single phenomenon (e.g., crime incidents). In this paper, we focus on the popular local G statistics. We propose a modified scale-sensitive version of a local G statistic. Furthermore, our approach comprises an alternative neighbourhood definition that enables to extract certain scales of interest. We compared our method with the original one on a real-world Twitter dataset. Our experiments show that our approach is able to better detect spatial autocorrelation at specific scales, as opposed to the original method. Based on the findings of our research, we identified a number of scale-related issues that our approach is able to overcome. Thus, we demonstrate the multiscale suitability of the proposed solution.     

Detecting negative spatial autocorrelation in georeferenced random variables

Negative spatial autocorrelation refers to a geographic distribution of values, or a map pattern, in which the neighbors of locations with large values have small values, the neighbors of locations with intermediate values have intermediate values, and the neighbors of locations with small values have large values. Little is known about negative spatial autocorrelation and its consequences in statistical inference in general, and regression-based inference in particular, with spatial researchers to date concentrating mostly on understanding the much more frequently encountered case of positive spatial autocorrelation. What are the spatial contexts within which negative spatial autocorrelation should be readily found? What are its inferential consequences for regression models? This paper presents selected empirical examples of negative spatial autocorrelation, adding to the slowly growing literature about this phenomenon.     

Estimating the spatial pattern of human-caused forest fires using a generalized linear mixed model with spatial autocorrelation in South Korea

Most forest fires in Korea are spatially concentrated in certain areas and are highly related to human activities. These site-specific characteristics of forest fires are analyzed by spatial regression analysis using the R-module generalized linear mixed model (GLMM), which can consider spatial autocorrelation. We examined the quantitative effect of topology, human accessibility, and forest cover without and with spatial autocorrelation. Under the assumption that slope, elevation, aspect, population density, distance from road, and forest cover are related to forest fire occurrence, the explanatory variables of each of these factors were prepared using a Geographic Information System-based process. First, we tried to test the influence of fixed effects on the occurrence of forest fires using a generalized linear model (GLM) with Poisson distribution. In addition, the overdispersion of the response data was also detected, and variogram analysis was performed using the standardized residuals of GLM. Second, GLMM was applied to consider the obvious residual autocorrelation structure. The fitted models were validated and compared using the multiple correlation and root mean square error (RMSE). Results showed that slope, elevation, aspect index, population density, and distance from road were significant factors capable of explaining the forest fire occurrence. Positive spatial autocorrelation was estimated up to a distance of 32 km. The kriging predictions based on GLMM were smoother than those of the GLM. Finally, a forest fire occurrence map was prepared using the results from both models. The fire risk decreases with increasing distance to areas with high population densities, and increasing elevation showed a suppressing effect on fire occurrence. Both variables are in accordance with the significance tests.     

The scale effects of the spatial autocorrelation measurement: aggregation level and spatial resolution

The scale effects of the spatial autocorrelation (SA) measurement has been explored for decades. However, the effects of the data aggregation levels and spatial resolution on the SA measurement are often confused. Whether the two types of scale effects are the same is still unclear and requires further investigation. We retrieved the land surface temperature (LST) from Landsat 8 images in 30 capital cities of China. By aggregating the LST images, we observed a decrease in the SA of the LST as the data aggregation level increased; this relationship can be fitted well with a negative logarithmic function. We derived an indicator to measure the scale effects intensity of SA, which was negatively correlated with the spatial complexity of LST. Both aggregating images and the increasing spatial resolution induce weaker SA, but the effect of the former was stronger. The aggregating images negatively affected the SA degree regardless of the spatial resolutions of the original images. The SA degrees of the aggregated images were far below those of the real-life images. This study suggests that the scale effects caused by aggregation levels and spatial resolutions are different, and cautions should be taken when applying relevant conclusions derived from aggregating images.     

基于Moran统计量的空间自相关理论发展和方法改进

本文旨在发展基于Moran指数的空间自相关分析理论和方法。首先,利用线性代数知识对基于Moran统计量的空间自相关过程的数学表示进行规范化整理;其次,基于变换中的不变性思想给出Moran指数的理论解释;第三,对空间权重矩阵的数理性质、建设方法和应用范围提出新的见解。总结并发展了Moran指数的三种计算方法——三步求值法、矩阵标度法和回归分析法,将空间权重矩阵划分为四种基本类型——局域关联型、准局域关联型、准长程关联型和长程关联型。以河南省鹤壁市乡镇体系为实证对象,以本文改进的理论和方法为依据,提供了一个空间自相关分析的简明案例。     

Testing spatial heterogeneity in geographically weighted principal components analysis

We propose a method to evaluate the existence of spatial variability in the covariance structure in a geographically weighted principal components analysis (GWPCA). The method, that is extensive to locally weighted principal components analysis, is based on performing a statistical hypothesis test using the eigenvectors of the PCA scores covariance matrix. The application of the method to simulated data shows that it has a greater statistical power than the current statistical test that uses the eigenvalues of the raw data covariance matrix. Finally, the method was applied to a real problem whose objective is to find spatial distribution patterns in a set of soil pollutants. The results show the utility of GWPCA versus PCA.     

基于社会属性的北京市居民群体空间自相关分析

以北京市各街道居民为调查研究对象,利用问卷调查数据,使用因子生态分析和空间自相关分析技术,将被调查人群综合性地分为五类,即低潜力差现状型人群、高潜力差现状型人群、高潜力中现状型人群、中潜力中现状型人群和高潜力优现状型人群。通过对不同类人群的总体和局部空间自相关分析,得出结论:居民群体空间聚集现象明显。其中低潜力差现状型人群在通州、黑庄户等街道聚集,高潜力差现状型人群在以东直门街道为圆心的一个扇形区域聚集,中潜力中现状型人群多居住于中心城区,高潜力中现状型人群多在天通苑、四季青一带和南苑街道附近聚集,高潜力优现状型人群主要聚集在四季青至永定路街道的区域。     

柴达木盆地植被覆盖度的分析与模拟——空间自相关方法的运用(英文)

Relationship between vegetation and environmental factors has always been a major topic in ecology, but it has also been an important way to reveal vegetation’s dynamic response to and feedback effects on climate change. For the special geographical location and climatic characteristics of the Qaidam Basin, with the support of traditional and remote sensing data, in this paper a vegetation coverage model was established. The quantitative prediction of vegetation coverage by five environmental factors was initially realized through multiple stepwise regression (MSR) models. However, there is significant multicollinearity among these five environmental factors, which reduces the performance of the MSR model. Then through the introduction of the Moran Index, an indicator that reflects the spatial auto-correlation of vegetation distribution, only two variables of average annual rainfall and local Moran Index were used in the final establishment of the vegetation coverage model. The results show that there is significant spatial autocorrelation in the distribution of vegetation. The role of spatial autocorrelation in the establishment of vegetation coverage model has not only improved the model fitting R2 from 0.608 to 0.656, but also removed the multicollinearity among independents.     

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.     

Uncertainty in the effects of the modifiable areal unit problem under different levels of spatial autocorrelation: a simulation study

ABSTRACT

The objective of this paper is to investigate uncertainties surrounding relationships between spatial autocorrelation (SA) and the modifiable areal unit problem (MAUP) with an extensive simulation experiment. Especially, this paper aims to explore how differently the MAUP behaves for the level of SA focusing on how the initial level of SA at the finest spatial scale makes a significant difference to the MAUP effects on the sample statistics such as means, variances, and Moran coefficients (MCs). The simulation experiment utilizes a random spatial aggregation (RSA) procedure and adopts Moran spatial eigenvectors to simulate different SA levels. The main findings are as follows. First, there are no substantive MAUP effects for means. However, the initial level of SA plays a role for the zoning effect, especially when extreme positive SA is present. Second, there is a clear and strong scale effect for the variances. However, the initial SA level plays a non-negligible role in how this scale effect deploys. Third, the initial SA level plays a crucial role in the nature and extent of the MAUP effects on MCs. A regression analysis confirms that the initial SA level makes a substantial difference to the variability of the MAUP effects.     

A new approach to quantifying spatial contiguity using graph theory and spatial interaction

Spatial contiguity is an important and fundamental landscape property in land allocation, habitat design, and forest management. The agreed upon notion of contiguity in the literature suggests shapelessness. However, existing approaches for measuring/promoting contiguity use proxies that either favour a particular shape or ignore inter‐patch relationships in fragmented landscapes. We propose an unbiased relative measure of contiguity ranging from zero to one based on graph theory and spatial interaction. The new measure reflects intra‐patch and inter‐patch relationships by quantifying contiguity within patches and potential contiguity among patches. Empirical analysis suggests that this measure of contiguity is reliable, consistent, and insensitive to sub‐region shape.     

Seismic reflection studies using local earthquake sources

Summary. A method is presented for processing three-component digital recordings of micro-earthquakes to obtain near-vertical reflection profiles in regions of shallow seismicity. The processing includes magnitude and focal-depth normalization and event stacking, where stacking is by small localized groups, with ray theoretical time and distance corrections applied to compensate for varying focal depths. In areas with high seismicity, this procedure allows earthquakes to be treated as "controlled" sources to probe layered structures of the deep crust and upper mantle. The validity of our approach is demonstrated using S-waves from aftershocks of the Borah Peak, Idaho, earthquake (Ms = 7.3) of 1983.     

Testing for similarity in area-based spatial patterns: A nonparametric Monte Carlo approach

The proliferation of geographic information systems and point data has made the analysis of spatial point patterns of increasing interest in a variety of disciplines. Though early forms of spatial point pattern analysis were limited in their scope, current forms have been developed that provide significant insight into underlying data generating processes. This paper builds on the spatial point pattern analysis literature through the development of a nonparametric Monte Carlo spatial point pattern test (and corresponding index) to measure the degree of similarity between two spatial point patterns. The applicability of this new test is then shown using crime data.     

地方自治背景下印度尼西亚空间规划面临的挑战

空间规划通过协调区域活动,合理地利用空间,辅助国家政治、经济和社会等事务的治理。印尼的空间规划由总统制定、落实,它体现着国家政治层面的发展愿景和任务。当国家治理结构改变时,各区域的空间规划及其具体的实施过程也随之改变。分权化和地方自治是2001年以来印尼政府体制的重大变革。通过相关规划法律条文和文献分析,发现空间规划开始面临一系列问题,主要表现为资金和专业人员的缺乏、政策交叉现象和空间规划违规行为等。此外,印尼的地方自治制度对空间规划产生了一定的积极影响：首先,在地方自治的背景下,地方政府通过系统的管理增加了区域收入,以支持空间规划的实施;其次,地方政府开始优先聘用空间规划的专业人员,制定更加有效的空间规划政策;最后,各地区加强了对空间规划违规者的执法力度,增强了区域间团结意识,从而促进地区繁荣发展。目前中央与地方之间在权力和利益分配上仍存在着大量的博弈和冲突,应加强上下级政府之间的沟通与合作,保障地方对地方相关事务决策时的参与权,建立地方利益表达与平衡的机制,提高中央决策的科学化和民主化水平。     

Exploring spatiotemporal heterogeneity in online travel searches: a local spatial model approach

ABSTRACT

Online travel searches are important forms of travel virtual spaces. Previous studies have neglected to analyze the spatial features of the travel searches themselves, and the spatial heterogeneity of their influencing factors. In this study, a travel search index based on the Baidu index was established for analyzing travel searches. Meanwhile, a local spatial model was created for the linear features in order to discuss the spatiotemporal heterogeneity of the influencing factors. The results of this study indicated that travel searches have obvious spatial inequality, and economically developed regions had displayed advantages in the travel search network. The fitting results of the local model were found to be superior to global model. The number of attractions and the GDP of the origin were found to have promoting effects on the travel searches, whereas distances had shown inhibiting effects. These effects presented significant spatiotemporal heterogeneity. It was also found that within the travel search virtual space, the distance effects still existed, but the intensity was weaker than in the real space. The local spatial model for the linear features provided a new spatial analysis method for understanding the travel search network, as well as other types of networks (flow patterns).