空间数据统计分析的思想起源与应用演化

系统总结了空间数据统计分析的发展历程,并分为五个时期：① 早期孕育（计量革命之前）,其重要思想是19世纪初德国的区位论;② 计量革命（1950-1960年代）,主要是经典统计学的应用和理论探索;③ 空间统计学（1970-1980年代）,重点是空间点数据、面数据和空间连续性数据的分析;④ 成熟与扩散（1990-2000年代）,空间数据统计分析发展成熟并快速向其他领域扩散;⑤ 时空大数据（2010年以后）。换句话说,计量革命开始后的空间数据统计分析大约每20年有重要的新技术或方法出现,到现在已经具有成熟、系统化的方法和显著的社会效益。而在当前的时空大数据时期,其发展需要计算机科学家、统计学家和地理学家等不同学科领域人员的共同努力。     

空间关联规则挖掘研究进展

随着空间数据获取技术的进步, 空间数据量日益增大, 已超出人们的分析能力。传统的空 间数据分析方法只能进行简单的数据分析, 无法满足人们获取知识的需要。空间关联规则是空间 数据挖掘一个基本的任务, 是从具有海量、多维、多尺度、不确定性边界等特性的空间数据中进行 知识发现的重要方法。本文从基本概念、分类、挖掘过程、挖掘方法、目前研究成果等方面对其进 行综述, 重点阐述了空间关联规则挖掘效率的改进策略、基于不确定空间信息的挖掘方法、挖掘 过程及结果的可视化、弱空间关联规则的挖掘方法等。通过对现有空间关联规则研究成果和存在 问题的深入剖析, 指出了其未来主要的发展方向。     

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.     

Estimating the prediction performance of spatial models via spatial k-fold cross validation

In machine learning, one often assumes the data are independent when evaluating model performance. However, this rarely holds in practice. Geographic information datasets are an example where the data points have stronger dependencies among each other the closer they are geographically. This phenomenon known as spatial autocorrelation (SAC) causes the standard cross validation (CV) methods to produce optimistically biased prediction performance estimates for spatial models, which can result in increased costs and accidents in practical applications. To overcome this problem, we propose a modified version of the CV method called spatial k-fold cross validation (SKCV), which provides a useful estimate for model prediction performance without optimistic bias due to SAC. We test SKCV with three real-world cases involving open natural data showing that the estimates produced by the ordinary CV are up to 40% more optimistic than those of SKCV. Both regression and classification cases are considered in our experiments. In addition, we will show how the SKCV method can be applied as a criterion for selecting data sampling density for new research area.     

空间数据挖掘的地理案例推理方法及试验

从空间数据挖掘的角度谈地理案例推理方法,认为地理案例推理是面向问题的一种空间数据挖掘方法。针对这一思想进行了基于地理案例的空间数据挖掘具体算法介绍。首先在明确地理案例具体定义的基础上,给出了面向问题的空间数据挖掘地理案例界定和组织方法;其次,鉴于地理空间的自然地带性和区域分异性规律的影响,深入探讨了地理案例自身或其间所可能存在的相互依赖和相互制约关系,并给出了采用粗糙集方法进行地理案例内蕴空间关系的定量挖掘方法;第三,针对地理案例表达时考虑的空间特征和空间关系的不同,给出了三种状况下的空间相似性计算模型;最后,以土地利用这一典型的地学现象为例,给出具体实例,一方面进行土地利用问题的定量分析与推测;另一方面,通过实例展示地理案例推理方法在地学问题求解以及空间数据定量分析上的特点和优势。     

Using rough set theory to identify villages affected by birth defects: the example of Heshun,Shanxi, China

This article uses rough set theory to explore spatial decision rules in neural-tube birth defects and searches for novel spatial factors related to the disease. The whole rule induction process includes data transformation, searching for attribute reducts, rule generation, prediction or classification, and accuracy assessment. We use Heshun as an example, where neural-tube birth defects are prevalent, to validate the approach. About 50% of the villages in Heshun are used as the sample data, from which all of the rules are extracted. Meanwhile, the other villages are used as reference data. The rules extracted from the training data are then applied to the reference data. The result shows that the rules' generalization is reasonably good. Moreover, a novel relationship between the spatial attributes and the neural-tube birth defects was discovered. That is, the villages that lie in Watershed 9 of this district and that are also associated with a gradient of between 16° and 25° are vulnerable to neural-tube birth defects. This result paves the road for predicting where high rates of neural-tube birth defects will occur and can be used as a preliminary step in finding a direct cause for the disease.     

A New Indicator for Evaluating Spatial Concentration Based on Local Spatial Decompositions of the Gini Coefficient

Measuring spatial concentration is a key problem when studying geographical phenomena in many areas, including economic activities, atmospheric pollution, animal habitats, and so on. Two important aspects related to the measurement of spatial concentration are data variability and spatial autocorrelation. Rather than combining different indicators for each of these characteristics, this article proposes a new indicator based on the reconstruction of local spatial decompositions of the classical Gini coefficient. A Monte Carlo simulation study is conducted to evaluate the properties of the new indicator, and the results demonstrate that the indicator is highly linearly correlated with both spatial autocorrelation and data dispersion. Moreover, its elasticities to either the spatial autocorrelation or data dispersion are extremely close to 1 under various experimental circumstances. These findings indicate that the new indicator can reflect not only the absolute level of but also the change in spatial concentration effectively. Applying the indicator to the per capita gross domestic product data set for the middle reach of the Yangtze River, we also demonstrate that the new indicator and its local components are easy to implement and are useful in local spatial association analyses.     

Topology revisited: representing spatial relations

Topology is a central, defining feature of geographical information systems (GIS). The advantages of topological data structures are that data storage for polygons is reduced because boundaries between adjacent polygons are not stored twice, explicit adjacency relations are maintained, and data entry and map production is improved by providing a rigorous, automated method to handle artifacts of digitizing. However, what explains the resurgence of non-topological data structures and why do contemporary desktop GIS packages support them? The historical development of geographical data structures is examined to provide a context for identifying the advantages and disadvantages of topological and non-topological data structures. Although explicit storage of adjacent features increases performance of adjacency analyses, it is not required to conduct these operations. Non-topological data structures can represent features that conform to planar graph theory (i.e. non-overlapping, space-filling polygons). A data structure that can represent proximal and directional spatial relations, in addition to topological relationships is described. This extension allows a broader set of functional relationships and connections between geographical features to be explicitly represented.     

Metadata and provenance for spatial analysis: the case of spatial weights

Within a CyberGIS environment, the development of effective mechanisms to encode metadata for spatial analytical methods and to track the provenance of operations is a key requirement. Spatial weights are a fundamental element in a wide range of spatial analysis methods that deal with testing for and estimating models with spatial autocorrelation. They form the link between the data structure in a GIS and the spatial analysis methods. Over time, the number of formats for spatial weights implemented in software has proliferated, without any standard or easy interoperability. In this paper, we propose a flexible format that provides a way to ensure interoperability within a cyberinfrastructure environment. We illustrate the format with an application of a spatial weights web service, which is part of an evolving spatial analytical workbench. We describe an approach to embed provenance in spatial weights structures and illustrate the performance of the web service by means of a number of small experiments.     

A rough set approach to the discovery of classification rules in spatial data

This paper proposes a novel rough set approach to discover classification rules in real‐valued spatial data in general and remotely sensed data in particular. A knowledge induction process is formulated to select optimal decision rules with a minimal set of features necessary and sufficient for a remote sensing classification task. The approach first converts a real‐valued or integer‐valued decision system into an interval‐valued information system. A knowledge induction procedure is then formulated to discover all classification rules hidden in the information system. Two real‐life applications are made to verify and substantiate the conceptual arguments. It demonstrates that the proposed approach can effectively discover in remotely sensed data the optimal spectral bands and optimal rule set for a classification task. It is also capable of unraveling critical spectral band(s) discerning certain classes. The framework paves the road for data mining in mixed spatial databases consisting of qualitative and quantitative data.     

基于粗糙集理论的地学空间关系规则分析及其应用——以珠江三角洲为例

Spatial relations,reflecting the complex association between geographical phenomena and environments,are very important in the solution of geographical issues. Different spatial relations can be expressed by indicators which are useful for the analysis of geographical issues. Urbanization,an important geographical issue,is considered in this paper. The spatial relationship indicators concerning urbanization are expressed with a decision table. Thereafter,the spatial relationship indicator rules are extracted based on the application of rough set theory. The extraction process of spatial relationship indicator rules is illustrated with data from the urban and rural areas of Shenzhen and Hong Kong,located in the Pearl River Delta. Land use vector data of 1995 and 2000 are used. The extracted spatial relationship indicator rules of 1995 are used to identify the urban and rural areas in Zhongshan,Zhuhai and Macao. The identification accuracy is approximately 96.3%. Similar procedures are used to extract the spatial relationship indicator rules of 2000 for the urban and rural areas in Zhongshan,Zhuhai and Macao. An identification accuracy of about 83.6% is obtained.     

Application of rough set-based analysis to extract spatial relationship indicator rules: An example of land use in Pearl River Delta

Spatial relations, reflecting the complex association between geographical phenomena and environments, are very important in the solution of geographical issues. Different spatial relations can be expressed by indicators which are useful for the analysis of geographical issues. Urbanization, an important geographical issue, is considered in this paper. The spatial relationship indicators concerning urbanization are expressed with a decision table. Thereafter, the spatial relationship indicator rules are extracted based on the application of rough set theory. The extraction process of spatial relationship indicator rules is illustrated with data from the urban and rural areas of Shenzhen and Hong Kong, located in the Pearl River Delta. Land use vector data of 1995 and 2000 are used. The extracted spatial relationship indicator rules of 1995 are used to identify the urban and rural areas in Zhongshan, Zhuhai and Macao. The identification accuracy is approximately 96.3%. Similar procedures are used to extract the spatial relationship indicator rules of 2000 for the urban and rural areas in Zhongshan, Zhuhai and Macao. An identification accuracy of about 83.6% is obtained.     

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.     

中国空间格局的规律认知与理论提炼

胡焕庸线、“T”型模式以及双核结构,可归纳为“一线两轴双核”结构,是不同时期中国人文地理学者对于中国空间格局的规律认知和理论提炼。胡焕庸线属于自然地理学地域分异规律在人文地理学中的延伸和拓展,遵循的是均质区域的基本假设;“T”型模式和双核结构则超越了地域分异规律的分析思路,遵循的是功能区域的基本假设。其中,“T”型模式是陆大道提出的点轴系统理论在中国的实践应用。从现象看,双核结构附属于“T”型开发模式,但后继研究实现了由特殊向一般的转化,完成了科学发现、机理分析、数学推导和实践应用的全过程科学研究,成为一个普适性较强的区域空间结构理论。从理论层面而言,分别基于均质区域和功能区域假设的胡焕庸线和“T”型模式属于空间分异规律的分析结果,属于地理学中的个例性理论;双核结构则属于符合一般科学意义上的普适性较强的理论。显然,胡焕庸线、“T”型模式和双核结构三位一体的分析,一方面表明中国是一个非常适合进行区域分析并在此基础上进行地理学规律和理论提炼的国家;另一方面,本文的研究可为区域空间结构规律的总结和人文地理学理论的提炼提供研究思路和方法论角度的启迪。     

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。     

北京宜居城市满意度空间特征

利用近万份的实地调查问卷,采用空间插值、空间相关性分析等空间分析方法,研究了北京市区宜居城市满意度的总体特征和空间自相关特性。结果表明,北京市区宜居城市满意度总体水平尚可,存在明显的空间自相关特性,并且空间自相关性表现出较强的尺度变化特点,而反映满意度的不同子指标的尺度也各有特点。对宜居城市满意度的空间差异性研究表明,满意度总体由城市中心向郊区递减,在交通节点附近存在满意度的"洼地"区域,同时,一些特殊区域的存在,也使北京宜居城市满意度的空间分布更加复杂。     

基于空间扩展模型和地理加权回归模型的城市住房价格空间分异比较

鉴于已有研究主要集中探讨住房价格的空间依赖性,较少涉及空间异质性对住房特征价格的影响,也很少尝试构建不同计量模型来比较模型间刻画住房价格影响因素空间分异的准确性,以长沙市中心城区为研究区,采用空间扩展模型和地理加权回归模型比较分析城市住房价格影响因素的空间分异,结果表明：① 空间扩展模型和地理加权回归模型都表明,长沙市中心城区的住房属性边际价格随着区位的变化而变化,揭示住房价格影响因素具有显著的空间异质性;小区环境、交通条件、教育配套、生活设施等因素对住房价格的影响强度存在明显的空间分异。② 地理加权回归模型和空间扩展模型都能对传统特征价格模型进行改进,但地理加权回归模型在解释能力和精度方面都超过空间扩展模型;对属性系数估计空间模式的分析,地理加权回归模型形成的结果比采用坐标多义扩展的空间扩展模型更为复杂和直观。     

空间信息分析技术

在GIS技术日趋成熟和空间数据极大丰富的今天,通过分析空间数据探索空间过程机理正变得日益迫切。空间信息分析技术至少包括以下六个主要方面:(1)空间数据获取和预处理;(2)属性数据空间化和空间尺度转换;(3)空间信息探索分析;(4)地统计;(5)格数据分析;(6)复杂信息反演和预报。本文提出了解决具体应用问题一般的空间数据分析计算、结果解释和反馈程序。认为空间过程的一般共性和作为共同的研究对象,各种不同的方法技术最终可能导致空间数学(spatialmathematics)的产生,同时发展鲁棒的空间分析软件包对于普及空间数学是必要的。     

Incorporating spatial interaction patterns in classifying and understanding urban land use

Land use classification has benefited from the emerging big data, such as mobile phone records and taxi trajectories. Temporal activity variations derived from these data have been used to interpret and understand the land use of parcels from the perspective of social functions, complementing the outcome of traditional remote sensing methods. However, spatial interaction patterns between parcels, which could depict land uses from a perspective of connections, have rarely been examined and analysed. To leverage spatial interaction information contained in the above-mentioned massive data sets, we propose a novel unsupervised land use classification method with a new type of place signature. Based on the observation that spatial interaction patterns between places of two specific land uses are similar, the new place signature improves land use classification by trading off between aggregated temporal activity variations and detailed spatial interactions among places. The method is validated with a case study using taxi trip data from Shanghai.     

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.