空间分析

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文件:Snow-cholera-map.jpg
Map by Dr. John Snow of London, showing clusters of cholera cases in the 1854 Broad Street cholera outbreak. This was one of the first uses of map-based spatial analysis. 来自【伦敦】的【约翰·斯诺】博士绘制的地图,显示了【1854年布罗德街霍乱爆发】时的霍乱病例【群】。这是最早基于地图的空间分析案例之一。

Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic data or transcriptomics data.

空间分析Spatial analysis(或空间统计Spatial statistics)包括所有使用实体的拓扑Topological几何Geometric、或地理Geographic属性来研究实体的技术。空间分析囊括了多种技术,其中许多技术仍处于早期发展阶段。空间分析方法应用广泛,可以应用于天文学Astronomy(研究星系在宇宙Cosmos中的位置)、芯片制造工程(使用位置和路线算法Algorithm来构建复杂的布线结构)等多种领域。在更加有限的意义上,空间分析是应用于人类尺度结构的技术,尤其是在地理数据Geographic data转录组学数据Transcriptomics data的分析中。

Complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research. The most fundamental of these is the problem of defining the spatial location of the entities being studied.空间分析中出现了一些复杂的问题,其中许多问题既没有明确定义,也没有完全解决,但却构成了当前研究的基础。其中最基本的问题是界定所研究实体的空间位置。

Classification of the techniques of spatial analysis is difficult because of the large number of different fields of research involved, the different fundamental approaches which can be chosen, and the many forms the data can take.

由于涉及大量不同的研究领域,可以选择的基本方法也不同,以及数据可能具有多种呈现形式,很难对空间分析技术进行分类。

发展历史

Spatial analysis began with early attempts at cartography and surveying. Land surveying goes back to at least 1,400 B.C in Egypt: the dimensions of taxable land plots were measured with measuring ropes and plumb bobs.[1] b. Many fields have contributed to its rise in modern form. Biology contributed through botanical studies of global plant distributions and local plant locations, ethological studies of animal movement, landscape ecological studies of vegetation blocks, ecological studies of spatial population dynamics, and the study of biogeography. Epidemiology contributed with early work on disease mapping, notably John Snow's work of mapping an outbreak of cholera, with research on mapping the spread of disease and with location studies for health care delivery. Statistics has contributed greatly through work in spatial statistics. Economics has contributed notably through spatial econometrics. Geographic information system is currently a major contributor due to the importance of geographic software in the modern analytic toolbox. Remote sensing has contributed extensively in morphometric and clustering analysis. Computer science has contributed extensively through the study of algorithms, notably in computational geometry. Mathematics continues to provide the fundamental tools for analysis and to reveal the complexity of the spatial realm, for example, with recent work on fractals and scale invariance. Scientific modelling provides a useful framework for new approaches.模板:Cn

空间分析始于早期对地图制图学Cartography测量学Surveying的尝试。土地测量至少可以追溯到公元前1400年的埃及: 用测量绳和铅锤测量应税地块的尺寸[1] 。许多学科都为其现代形式的崛起做出了贡献。生物学Biology通过对全球植物分布和当地植物位置的植物学Botanical研究、对动物运动的伦理学Ethological研究、对植被区块的景观生态学Landscape ecological研究、对空间人口动态的生态学Ecological研究以及生物地理学Biogeography研究做出了贡献。流行病学Epidemiology的贡献在于早期的疾病测绘工作,特别是约翰斯诺John Snow对霍乱疫情的测绘工作,以及对疾病传播的测绘研究和对医疗服务的位置研究。统计学Statistics空间统计学Spatial statistics的发展做出了巨大贡献。经济学Economics空间计量经济学Spatial econometrics的发展具有突出贡献。地理信息系统Geographic information system提供了在现代空间分析中具有重要意义的地理分析软件。遥感Remote sensing在形态学和聚类分析方面有着广泛的应用。计算机科学Computer science通过对算法的研究做出了广泛的贡献,尤其是在计算几何Computational geometry方面。数学Mathematics继续为分析和揭示空间领域的复杂性提供基础工具,例如,最近关于分形Fractals尺度不变性Scale invariance的工作。科学模型Scientific modelling为新方法提供了有用的框架。

基本问题

Spatial analysis confronts many fundamental issues in the definition of its objects of study, in the construction of the analytic operations to be used, in the use of computers for analysis, in the limitations and particularities of the analyses which are known, and in the presentation of analytic results. Many of these issues are active subjects of modern research.模板:Cn

空间分析在其研究对象的定义、其使用的分析方法的构建、使用计算机进行分析的过程、已知的分析的局限性和特殊性以及分析结果的表述方面面临着许多基本问题。其中许多问题都是现代研究中的热点课题。

Common errors often arise in spatial analysis, some due to the mathematics of space, some due to the particular ways data are presented spatially, some due to the tools which are available. Census data, because it protects individual privacy by aggregating data into local units, raises a number of statistical issues. The fractal nature of coastline makes precise measurements of its length difficult if not impossible. A computer software fitting straight lines to the curve of a coastline, can easily calculate the lengths of the lines which it defines. However these straight lines may have no inherent meaning in the real world, as was shown for the coastline of Britain.模板:Cn

由于空间的数学、数据在空间上的特殊呈现方式或现有的工具的不足,在空间分析中常出现一些典型错误。例如,为了保护个人隐私,人口普查数据常将数据汇总到地方单位,因此会引起一些统计问题。海岸线的分形性质使得对其长度的精确测量变得困难。计算机软件通过将直线拟合到海岸线的曲线上,从而计算出它所定义的线长。然而,这些直线在现实世界中可能没有固有的意义,正如英国海岸线Coastline of Britain所显示的那样。

These problems represent a challenge in spatial analysis because of the power of maps as media of presentation. When results are presented as maps, the presentation combines spatial data which are generally accurate with analytic results which may be inaccurate, leading to an impression that analytic results are more accurate than the data would indicate.[2]

这些问题是空间分析中的难点。当结果以地图形式呈现时,这种呈现方式将大体准确的空间数据与可能不准确的分析结果结合起来,产生了分析结果比数据显示的更准确的印象[2]

Spatial characterization空间特征

文件:Bubonic plague-en.svg
Spread of bubonic plague in medieval Europe.[citation needed] The colors indicate the spatial distribution of plague outbreaks over time. 中世纪欧洲黑死病的传播[citation needed]。颜色显示了随着时间的推移鼠疫爆发的空间分布。

The definition of the spatial presence of an entity constrains the possible analysis which can be applied to that entity and influences the final conclusions that can be reached. While this property is fundamentally true of all analysis, it is particularly important in spatial analysis because the tools to define and study entities favor specific characterizations of the entities being studied. Statistical techniques favor the spatial definition of objects as points because there are very few statistical techniques which operate directly on line, area, or volume elements. Computer tools favor the spatial definition of objects as homogeneous and separate elements because of the limited number of database elements and computational structures available, and the ease with which these primitive structures can be created.模板:Cn

对实体的空间存在的定义限制了可以适用于该实体的可能的分析,并影响到可以得出的最终结论。虽然这一属性从根本上说适用于所有的分析Analysis,但它在空间分析中尤为重要,因为定义和研究实体的工具倾向于表征被研究实体的特定特征。统计技术倾向于将物体在空间中定义为点,因为很少有统计技术能直接对线、面积或体积元素进行操作。计算机工具倾向于将对象定义为同质和独立的元素,因为可用的数据库Database元素和计算结构数量有限,而这些原始结构容易创建。

= = 空间依赖 = =

Spatial dependence is the spatial relationship of variable values (for themes defined over space, such as rainfall) or locations (for themes defined as objects, such as cities). Spatial dependence is measured as the existence of statistical dependence in a collection of random variables, each of which is associated with a different geographical location. Spatial dependence is of importance in applications where it is reasonable to postulate the existence of corresponding set of random variables at locations that have not been included in a sample. Thus rainfall may be measured at a set of rain gauge locations, and such measurements can be considered as outcomes of random variables, but rainfall clearly occurs at other locations and would again be random. Because rainfall exhibits properties of autocorrelation, spatial interpolation techniques can be used to estimate rainfall amounts at locations near measured locations.[3]

空间依赖性Spatial dependence是指变量(对于定义为空间的主题,如降雨Rainfall)或位置(对于定义为物体的主题,如城市)的空间关系。空间依赖性被衡量为随机变量Random variables集合中存在的统计相关性Statistical dependence,每个随机变量都与不同的地理位置Geographical location相关。空间依赖性在应用中非常重要,因为在这些应用中,可以合理地假设在未被纳入样本的地点存在相应的随机变量集。因此,降雨Rainfall可能是在一组雨量计所在的位置测量的,这种测量可以被认为是随机测量的结果,而降雨也会随机发生在其他位置。由于降雨Rainfall表现出自相关Autocorrelation的特性,空间插值技术可以用来估计测量地点附近的降雨Rainfall[3]

As with other types of statistical dependence, the presence of spatial dependence generally leads to estimates of an average value from a sample being less accurate than had the samples been independent, although if negative dependence exists a sample average can be better than in the independent case. A different problem than that of estimating an overall average is that of spatial interpolation: here the problem is to estimate the unobserved random outcomes of variables at locations intermediate to places where measurements are made, on that there is spatial dependence between the observed and unobserved random variables.模板:Cn

与其他类型的统计相关性一样,空间依赖性的存在通常会导致对样本平均值的估计不如样本独立时准确,尽管如果存在负的相关性,样本平均值可能比独立情况下更好。与估计总体平均值不同的问题是空间插值Spatial interpolation的问题:空间插值是估计变量在测量地点中未被观测到的随机结果,而空间依赖存在于观测到的和未观测到的随机变量之间。

Tools for exploring spatial dependence include: spatial correlation, spatial covariance functions and semivariograms. Methods for spatial interpolation include Kriging, which is a type of best linear unbiased prediction. The topic of spatial dependence is of importance to geostatistics and spatial analysis.模板:Cn

探索空间相关性的工具包括: 空间相关性Spatial correlation空间协方差函数Spatial covariance function半变异函数Semivariogram。空间插值的方法包括克里金插值法Kriging,这是一种最佳的线性无偏预测Best linear unbiased prediction方法。空间依赖性是地统计学Geostatistics和空间分析中的重要课题。

Spatial auto-correlation空间自相关

Spatial dependency is the co-variation of properties within geographic space: characteristics at proximal locations appear to be correlated, either positively or negatively. Spatial dependency leads to the spatial autocorrelation problem in statistics since, like temporal autocorrelation, this violates standard statistical techniques that assume independence among observations. For example, regression analyses that do not compensate for spatial dependency can have unstable parameter estimates and yield unreliable significance tests. Spatial regression models (see below) capture these relationships and do not suffer from these weaknesses. It is also appropriate to view spatial dependency as a source of information rather than something to be corrected.[4]

= = = = 空间自相关 = = = = 空间依赖性是指地理空间内属性的共同变化:近处的特征似乎是相关的,或正或负。空间依赖性导致了统计学中的空间自相关Spatial autocorrelation问题,因为和时间自相关一样,这违反了假设观察值之间独立的标准统计技术。例如,不对空间依赖性进行补偿的回归Regression分析会有不稳定的参数估计,并产生不可靠的显著性检验。空间回归模型(见下文)可以捕捉到这些关系,并且不存在这些弱点。将空间依赖性视为信息的来源而不是需要纠正的特性也是合适的[4]

Locational effects also manifest as spatial heterogeneity, or the apparent variation in a process with respect to location in geographic space. Unless a space is uniform and boundless, every location will have some degree of uniqueness relative to the other locations. This affects the spatial dependency relations and therefore the spatial process. Spatial heterogeneity means that overall parameters estimated for the entire system may not adequately describe the process at any given location.模板:Cn

位置效应也表现为空间异质性heterogeneity,或一个过程在地理空间中的明显位置变化。除非一个空间是统一的和无界的,否则每个位置相对于其他位置都会有某种程度的独特性。这影响了空间依赖关系,从而也影响了空间过程。空间异质性意味着对整个系统估计出的总体参数可能无法充分描述特定地点的演化过程。

Spatial association空间关联

模板:Further

Spatial association is the degree to which things are similarly arranged in space. Analysis of the distribution patterns of two phenomena is done by map overlay. If the distributions are similar, then the spatial association is strong, and vice versa.[5] In a Geographic Information System, the analysis can be done quantitatively. For example, a set of observations (as points or extracted from raster cells) at matching locations can be intersected and examined by regression analysis.

空间关联Spatial association是指事物在空间中具有相似排列的程度。可以利用地图叠加技术对两种现象的分布模式进行分析。如果分布相似,那么空间关联性就很强,反之亦然[5]。在地理信息系统Geographic Information System中,可以进行定量分析。例如,可以用相交或者回归检查位于匹配位置的一组观察值(点或者从栅格中提取)。

Like spatial autocorrelation, this can be a useful tool for spatial prediction. In spatial modeling, the concept of spatial association allows the use of covariates in a regression equation to predict the geographic field and thus produce a map.

空间自相关Spatial autocorrelation一样,这可以成为空间预测的有用工具。在空间建模中,空间关联的概念允许使用回归方程中的协变量来预测地理场,从而生成地图。

Scaling尺度

Spatial measurement scale is a persistent issue in spatial analysis; more detail is available at the modifiable areal unit problem (MAUP) topic entry. Landscape ecologists developed a series of scale invariant metrics for aspects of ecology that are fractal in nature.[6] In more general terms, no scale independent method of analysis is widely agreed upon for spatial statistics.模板:Cn

= = = 尺度 = = = 空间测量Measurement尺度是空间分析中长期存在的问题,更多的细节可以在可塑性面积单元问题Modifiable areal unit problem的词条中找到。景观生态学家为自然界中的分形Fractal制定了一系列尺度不变Scale invariant的量度[6]。从更普遍的意义上讲,对于空间统计来说,没有一种独立于尺度的分析Analysis方法被广泛认同。

Sampling抽样

Spatial sampling involves determining a limited number of locations in geographic space for faithfully measuring phenomena that are subject to dependency and heterogeneity.[citation needed] Dependency suggests that since one location can predict the value of another location, we do not need observations in both places. But heterogeneity suggests that this relation can change across space, and therefore we cannot trust an observed degree of dependency beyond a region that may be small. Basic spatial sampling schemes include random, clustered and systematic. These basic schemes can be applied at multiple levels in a designated spatial hierarchy (e.g., urban area, city, neighborhood). It is also possible to exploit ancillary data, for example, using property values as a guide in a spatial sampling scheme to measure educational attainment and income. Spatial models such as autocorrelation statistics, regression and interpolation (see below) can also dictate sample design.[citation needed]

= = = 抽样 = = = 空间抽样Sampling是指在地理空间中确定有限的地点,以忠实地测量受依赖性和异质性影响的现象[citation needed]。依赖性表明,由于一个地方可以预测另一个地方的价值,我们不需要在两个地方都进行观察。但异质性表明,这种关系可以在不同的空间发生变化,因此我们不能相信在一个可能很小的区域之外观察到的相关程度。基本的空间抽样方法包括随机抽样、整群抽样和系统抽样。这些基本方法可以在指定的空间层级中的多种级别上应用(例如,城市地区、城市、邻里)。也可以利用辅助数据抽样,例如,在空间抽样中使用财产价值作为标准,以衡量教育程度和收入。空间模型,如自相关统计、回归和插值(见下文)也可以决定抽样设计[citation needed]

Common errors in spatial analysis空间分析中的常见错误

The fundamental issues in spatial analysis lead to numerous problems in analysis including bias, distortion and outright errors in the conclusions reached. These issues are often interlinked but various attempts have been made to separate out particular issues from each other.[7]

= = 空间分析中的常见错误 = = 空间分析中的基本问题导致分析中会产生许多问题,包括所得结论的偏差、扭曲和彻底错误。这些问题往往是相互关联的,但人们已经做出各种尝试,将特定的问题相互分离出来[7]

Length长度

In discussing the coastline of Britain, Benoit Mandelbrot showed that certain spatial concepts are inherently nonsensical despite presumption of their validity. Lengths in ecology depend directly on the scale at which they are measured and experienced. So while surveyors commonly measure the length of a river, this length only has meaning in the context of the relevance of the measuring technique to the question under study.模板:CN

在讨论英国的海岸线Coastline of Britain时,本华·曼德博表明,某些空间概念本质上是无意义的,尽管它们的有效性得到了推定。生态学的长度直接取决于它们被测量的尺度。因此,虽然测量员能够测量河流的长度,但这个长度只有在测量技术与所研究问题相关的背景下才有意义。

Image:britain-fractal-coastline-200km.png|Britain measured using a 200km linear measurement Image:britain-fractal-coastline-100km.png|Britain measured using a 100km linear measurement Image:britain-fractal-coastline-50km.png|Britain measured using a 50km linear measurement

图像: 英国-分形-海岸线-200公里.png | 采用200公里的线性测量法测量的英国海岸线 图像: 英国-分形-海岸线-100公里.png |采用100公里的线性测量法测量的英国海岸线 图像: 英国-分形-海岸线-50公里.png|采用50公里的线性测量法测量的英国海岸线

Locational fallacy位置谬误

The locational fallacy refers to error due to the particular spatial characterization chosen for the elements of study, in particular choice of placement for the spatial presence of the element.模板:Cn

位置谬误是指由于为研究元素选择了特定空间特征而导致的错误,特别是对元素空间存在的位置选择。

Spatial characterizations may be simplistic or even wrong. Studies of humans often reduce the spatial existence of humans to a single point, for instance their home address. This can easily lead to poor analysis, for example, when considering disease transmission which can happen at work or at school and therefore far from the home.模板:Cn

空间描述可能过于简单,甚至是错误的。对人类的研究常常将人类的空间存在缩小到一个点,例如他们的家庭住址,这很容易导致分析不足。例如,疾病传播可能发生在工作或学校这些远离家庭的区域。

The spatial characterization may implicitly limit the subject of study. For example, the spatial analysis of crime data has recently become popular but these studies can only describe the particular kinds of crime which can be described spatially. This leads to many maps of assault but not to any maps of embezzlement with political consequences in the conceptualization of crime and the design of policies to address the issue.[8]

空间特征可能隐含着对研究对象的限制。例如,对犯罪数据的空间分析最近变得很流行,但这些研究只能描述可以在空间上表征的特定种类的犯罪。这导致了许多袭击地图的出现,但没有出现任何在犯罪概念化和设计解决这一问题的政策方面具有政治后果的贪污地图[8]

Atomic fallacy原子谬误

This describes errors due to treating elements as separate 'atoms' outside of their spatial context. The fallacy is about transferring individual conclusions to spatial units.[9]

原子谬误是指由于将元素作为其空间背景之外的独立 "原子 "而产生的错误。该谬误将个别结论转移到了空间单元[9]

Ecological fallacy区群谬误

The ecological fallacy describes errors due to performing analyses on aggregate data when trying to reach conclusions on the individual units.[10] Errors occur in part from spatial aggregation. For example, a pixel represents the average surface temperatures within an area. Ecological fallacy would be to assume that all points within the area have the same temperature.

= = = = 区群谬误 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =区群谬误Ecological fallacy是指通过分析聚合数据,得出对个体的结论时出现的错误[10]。错误的发生部分来自于空间聚合。例如,一个像元Pixel代表一个区域内的平均表面温度,而区群谬误假设该区域内的所有点都有相同的温度。

= Solutions to the fundamental issues基本问题的解决方案 =

Geographic space地理空间

文件:Manhattan distance.svg
Manhattan distance versus Euclidean distance: The red, blue, and yellow lines have the same length (12) in both Euclidean and taxicab geometry. In Euclidean geometry, the green line has length 6×模板:Radic ≈ 8.48, and is the unique shortest path. In taxicab geometry, the green line's length is still 12, making it no shorter than any other path shown. 曼哈顿距离与欧几里德距离。红、蓝、黄三条线在欧几里得和曼哈顿几何中都有相同的长度(12)。在欧氏几何中,绿线的长度为6×模板:Radic≈8.48,是唯一的最短路径。在曼哈顿几何学中,绿线的长度仍然是12,这使得它不比其他路径短。


A mathematical space exists whenever we have a set of observations and quantitative measures of their attributes. For example, we can represent individuals' incomes or years of education within a coordinate system where the location of each individual can be specified with respect to both dimensions. The distance between individuals within this space is a quantitative measure of their differences with respect to income and education. However, in spatial analysis, we are concerned with specific types of mathematical spaces, namely, geographic space. In geographic space, the observations correspond to locations in a spatial measurement framework that capture their proximity in the real world. The locations in a spatial measurement framework often represent locations on the surface of the Earth, but this is not strictly necessary. A spatial measurement framework can also capture proximity with respect to, say, interstellar space or within a biological entity such as a liver. The fundamental tenet is Tobler's First Law of Geography: if the interrelation between entities increases with proximity in the real world, then representation in geographic space and assessment using spatial analysis techniques are appropriate.

= = = = = 地理空间 = = = 只要我们有一组观察值和对其属性的定量测量,就存在一个数学空间。例如,我们可以在坐标系中表示个人的收入或受教育年限,在这个坐标系中,每个人的位置都可以用这两个维度指定。在这个空间内,个人之间的距离是对他们在收入和教育方面的差异的定量衡量。然而,在空间分析中,我们关注的是特定类型的数学空间,即地理空间。在地理空间中,观察值对应于空间测量框架中的位置,这些位置反映了它们在现实世界中的临近性。空间测量框架中的位置通常代表地球表面的位置,但这并不是严格的必要条件。空间测量框架也可以捕捉到星际空间或生物实体(如肝脏)之间的临近性。基本原则是托布勒的地理学第一定律Tobler's First Law of Geography:如果实体之间的相互关系随其在现实世界中的临近性的增加而增加,那么可以在地理空间表示它们,并使用空间分析技术对它们进行评估。

The Euclidean distance between locations often represents their proximity, although this is only one possibility. There are an infinite number of distances in addition to Euclidean that can support quantitative analysis. For example, "Manhattan" (or "Taxicab") distances where movement is restricted to paths parallel to the axes can be more meaningful than Euclidean distances in urban settings. In addition to distances, other geographic relationships such as connectivity (e.g., the existence or degree of shared borders) and direction can also influence the relationships among entities. It is also possible to compute minimal cost paths across a cost surface; for example, this can represent proximity among locations when travel must occur across rugged terrain.

欧几里得距离Euclidean distance通常代表位置间的接近程度,尽管这只是一种可能的表示方式。除了欧氏距离外,还有无限多的距离可以支持定量分析。例如,"曼哈顿"(或 "出租车Taxicab")距离:在城市环境中,移动被限制在与轴线平行的路径上。在城市中,曼哈顿距离可能比欧几里得距离更有意义。除了距离之外,其他地理关系,如连通性(例如,共享边界的存在或程度The existence or degree of shared borders)和方向Direction也可以影响实体之间的关系。也有可能计算出跨越成本面的最小成本路径;例如,当必须跨越崎岖的地形旅行时,最小成本路径可以代表地点之间的接近性。

Types 种类

Spatial data comes in many varieties and it is not easy to arrive at a system of classification that is simultaneously exclusive, exhaustive, imaginative, and satisfying. -- G. Upton & B. Fingelton[11]


= = = = 空间数据有许多种类,要同时达到排他性、详尽性、想象性和令人满意的分类系统是不容易的。 --G. 厄普顿和B. 芬格尔顿[11]

Spatial data analysis空间数据分析

Urban and Regional Studies deal with large tables of spatial data obtained from censuses and surveys. It is necessary to simplify the huge amount of detailed information in order to extract the main trends. Multivariable analysis (or Factor analysis, FA) allows a change of variables, transforming the many variables of the census, usually correlated between themselves, into fewer independent "Factors" or "Principal Components" which are, actually, the eigenvectors of the data correlation matrix weighted by the inverse of their eigenvalues. This change of variables has two main advantages:

  1. Since information is concentrated on the first new factors, it is possible to keep only a few of them while losing only a small amount of information; mapping them produces fewer and more significant maps
  2. The factors, actually the eigenvectors, are orthogonal by construction, i.e. not correlated. In most cases, the dominant factor (with the largest eigenvalue) is the Social Component, separating rich and poor in the city. Since factors are not-correlated, other smaller processes than social status, which would have remained hidden otherwise, appear on the second, third, ... factors.

= = = 空间数据分析 = = = 城市和区域研究要处理从人口普查和调查中获得的大量包含空间数据表格。有必要简化大量的详细信息,以提取主要趋势。多变量分析(或因子分析Factor analysis,FA)允许改变变量,将人口普查中通常相互关联的许多变量转化为较少的独立 "因子 "或 "主成分"。这实际上是数据相关矩阵的特征向量Eigenvectors,以其特征值的逆值加权。这种变量的变化有两个主要优点。

  1. 由于信息集中在第一个新的因子上,因此可以只保留其中的几个因子,而只损失少量的信息;对它们的映射产生更少、更重要的地图.
  2. 因子实际上是特征向量,其在构造上是正交的,即不相关的。在大多数情况下,主导因素(具有最大的特征值)是社会组成,它将城市中的富人和穷人分开。由于因素是不相关的,其他比社会地位更小的过程,要么被隐藏起来,要么出现在第二、第三、......因素上。

Factor analysis depends on measuring distances between observations : the choice of a significant metric is crucial. The Euclidean metric (Principal Component Analysis), the Chi-Square distance (Correspondence Analysis) or the Generalized Mahalanobis distance (Discriminant Analysis) are among the more widely used.[12] More complicated models, using communalities or rotations have been proposed.[13]

因子分析依赖于测量观测值之间的距离:选择一个重要的度量标准是至关重要的。欧氏距离(主成分分析)、卡方距离(对应分析)或广义马氏距离(判别分析)是比较广泛使用的[12]。还提出了使用共同性或旋转的复杂模型[13]

Using multivariate methods in spatial analysis began really in the 1950s (although some examples go back to the beginning of the century) and culminated in the 1970s, with the increasing power and accessibility of computers. Already in 1948, in a seminal publication, two sociologists, Wendell Bell and Eshref Shevky,[14] had shown that most city populations in the US and in the world could be represented with three independent factors : 1- the « socio-economic status » opposing rich and poor districts and distributed in sectors running along highways from the city center, 2- the « life cycle », i.e. the age structure of households, distributed in concentric circles, and 3- « race and ethnicity », identifying patches of migrants located within the city. In 1961, in a groundbreaking study, British geographers used FA to classify British towns.[15] Brian J Berry, at the University of Chicago, and his students made a wide use of the method,[16] applying it to most important cities in the world and exhibiting common social structures.[17] The use of Factor Analysis in Geography, made so easy by modern computers, has been very wide but not always very wise.[18]

使用多变量方法进行空间分析真正开始于20世纪50年代(尽管有些例子可以追溯到本世纪初),并随着计算机的算力提升和不断普及在20世纪70年代达到顶峰。早在1948年,两位社会学家温德·贝尔Wendell Bell和埃什里夫·舍夫斯基[14]在一份开创性的出版物中表明,美国和世界上大多数城市的人口可以用三个独立的因素来表示:1-"社会经济地位",将富人区和穷人区对立起来,并沿着市中心的高速公路分布;2-"生命周期",即家庭的年龄结构,呈同心圆分布;3-"种族和民族",确定城市内的移民斑块。1961年,在一项开创性的研究中,英国地理学家使用FA对英国城镇进行分类[15]。芝加哥大学的布赖恩·贝利和他的学生广泛地使用了这种方法[16],他们将这种方法应用于世界上最重要的城市,并展示了共同的社会结构[17]。现代计算机使人们能够轻易地在地理学中使用因子分析,因子分析的使用非常广泛,但并不总是明智的[18]

Since the vectors extracted are determined by the data matrix, it is not possible to compare factors obtained from different censuses. A solution consists in fusing together several census matrices in a unique table which, then, may be analyzed. This, however, assumes that the definition of the variables has not changed over time and produces very large tables, difficult to manage. A better solution, proposed by psychometricians,[19] groups the data in a « cubic matrix », with three entries (for instance, locations, variables, time periods). A Three-Way Factor Analysis produces then three groups of factors related by a small cubic « core matrix ».[20] This method, which exhibits data evolution over time, has not been widely used in geography.[21] In Los Angeles,[22] however, it has exhibited the role, traditionally ignored, of Downtown as an organizing center for the whole city during several decades.

由于提取的向量是由数据矩阵决定的,所以不能比较从不同普查中获得的因素。一个解决方案是将几个普查矩阵融合在一个独特的表格中,然后可以对其进行分析。然而,这假设变量的定义没有随着时间的推移而改变,并且难以管理非常大的表格。心理测量学家提出了一个更好的解决方案[19],根据"立方矩阵"中的三个条目(例如,地点、变量、时间段)划分数据。三向因子分析产生了由立方体 "核心矩阵 "关联的三组因素[20]。这种方法展示了数据随时间的演变,但在地理学中还没有被广泛使用[21]。然而,在洛杉矶[22],它显示了市中心作为整个城市的组织中心在数十年间所发挥的作用,这一作用在传统上被忽视了。

Spatial autocorrelation空间自相关

Spatial autocorrelation statistics measure and analyze the degree of dependency among observations in a geographic space. Classic spatial autocorrelation statistics include Moran's [math]\displaystyle{ I }[/math], Geary's [math]\displaystyle{ C }[/math], Getis's [math]\displaystyle{ G }[/math] and the standard deviational ellipse. These statistics require measuring a spatial weights matrix that reflects the intensity of the geographic relationship between observations in a neighborhood, e.g., the distances between neighbors, the lengths of shared border, or whether they fall into a specified directional class such as "west". Classic spatial autocorrelation statistics compare the spatial weights to the covariance relationship at pairs of locations. Spatial autocorrelation that is more positive than expected from random indicate the clustering of similar values across geographic space, while significant negative spatial autocorrelation indicates that neighboring values are more dissimilar than expected by chance, suggesting a spatial pattern similar to a chess board.

= = = 空间自相关 = = = 空间自相关Autocorrelation统计、衡量和分析地理空间中观测值之间的依赖程度。经典的空间自相关统计包括莫兰指数Moran's I,Geary's C指数, Getis's G指数标准差椭圆Standard deviational ellipse。这些统计需要测量一个空间权重矩阵,该矩阵反映了邻里之间观测值的地理关系强度,例如,邻里之间的距离、共同边界的长度,或者它们是否属于一个特定的方向类别,如 "西"。经典的空间自相关统计将空间权重与成对位置的协方差关系进行比较。空间自相关比随机的预期值更为正,表明地理空间中相似值的聚集,而显著的负空间自相关表明相邻值比偶然的预期值更为不相似,表明一种类似于棋盘的空间模式。

Spatial autocorrelation statistics such as Moran's [math]\displaystyle{ I }[/math] and Geary's [math]\displaystyle{ C }[/math] are global in the sense that they estimate the overall degree of spatial autocorrelation for a dataset. The possibility of spatial heterogeneity suggests that the estimated degree of autocorrelation may vary significantly across geographic space. Local spatial autocorrelation statistics provide estimates disaggregated to the level of the spatial analysis units, allowing assessment of the dependency relationships across space. [math]\displaystyle{ G }[/math] statistics compare neighborhoods to a global average and identify local regions of strong autocorrelation. Local versions of the [math]\displaystyle{ I }[/math] and [math]\displaystyle{ C }[/math] statistics are also available.

Moran's I和Geary's C等空间自相关统计指标是全局性的,因为它们估计了数据集的总体空间自相关程度。空间异质性的可能性表明,估计的自相关程度在不同的地理空间可能有很大的不同。局部空间自相关统计Local spatial autocorrelation statistics提供了分解到空间分析单元水平的估计,允许评估跨空间的依赖关系。G统计量将邻域与全局平均数进行比较,并确定局部强自相关区域,也可以使用局部I和C统计量实现这一过程。

Spatial heterogeneity空间异质性

模板:Excerpt


Spatial heterogeneity is a property generally ascribed to a landscape or to a population. It refers to the uneven distribution of various concentrations of each species within an area. A landscape with spatial heterogeneity has a mix of concentrations of multiple species of plants or animals (biological), or of terrain formations (geological), or environmental characteristics (e.g. rainfall, temperature, wind) filling its area. A population showing spatial heterogeneity is one where various concentrations of individuals of this species are unevenly distributed across an area; nearly synonymous with "patchily distributed."

空间异质性Spatial heterogeneity景观Landscape种群Population中普遍存在的属性。它指的是物种Species在区域内的不均匀分布。具有空间异质性的景观具有多种植物或动物物种(生物)、或地形Terrain构造(地质)、或环境特征(如降雨量、温度、风)。呈现空间异质性的种群是指该物种的个体不均匀地分布在一个地区;几乎与 "零星分布 "同义。

Spatial interpolation空间插值

Spatial interpolation methods estimate the variables at unobserved locations in geographic space based on the values at observed locations. Basic methods include inverse distance weighting: this attenuates the variable with decreasing proximity from the observed location. Kriging is a more sophisticated method that interpolates across space according to a spatial lag relationship that has both systematic and random components. This can accommodate a wide range of spatial relationships for the hidden values between observed locations. Kriging provides optimal estimates given the hypothesized lag relationship, and error estimates can be mapped to determine if spatial patterns exist.

空间插值Spatial interpolation方法根据观测值来估计空间中的未观测值。基本的方法包括反距离加权法Inverse distance weighting:它以插值点与样本点间的距离为权重进行加权平均, 离插值点越近的样本点赋予的权重越大。克里金法Kriging是一种更复杂的方法,它根据具有系统和随机成分的空间滞后关系进行跨空间插值。这一方法能够很好的适应观测值与隐藏值间存在的广泛空间关系。克里金法在假设的滞后关系下提供了最佳的估计值,并且可以对误差估计值进行映射以确定是否存在空间模式。

Spatial regression空间回归


另见:局部回归Local regression克里金回归Regression-Kriging

Spatial regression methods capture spatial dependency in regression analysis, avoiding statistical problems such as unstable parameters and unreliable significance tests, as well as providing information on spatial relationships among the variables involved. Depending on the specific technique, spatial dependency can enter the regression model as relationships between the independent variables and the dependent, between the dependent variables and a spatial lag of itself, or in the error terms. Geographically weighted regression (GWR) is a local version of spatial regression that generates parameters disaggregated by the spatial units of analysis.[23] This allows assessment of the spatial heterogeneity in the estimated relationships between the independent and dependent variables. The use of Bayesian hierarchical modeling[24] in conjunction with Markov chain Monte Carlo (MCMC) methods have recently shown to be effective in modeling complex relationships using Poisson-Gamma-CAR, Poisson-lognormal-SAR, or Overdispersed logit models. Statistical packages for implementing such Bayesian models using MCMC include WinBugs, CrimeStat and many packages available via R programming language.[25]

空间回归方法在回归分析Regression analysis中捕捉到了空间依赖性,避免了不稳定的参数和不可靠的显著性检验等统计问题,同时也提供了相关变量之间的空间关系信息。从技术角度,空间依赖性可以作为自变量和因变量之间的关系、因变量和自身的空间滞后之间的关系,或在误差项中纳入回归模型。地理加权回归Geographically weighted regression(GWR)是一种局部空间回归模型,产生按空间分析单元分类的参数[23]。这允许评估所估计的自变量和因变量关系的空间异质性。最近,结合贝叶斯分层模型Bayesian hierarchical modeling[24]马尔科夫链蒙特卡洛Markov chain Monte Carlo(MCMC)方法的应用表明,泊松-伽马-CAR、泊松-正态-SAR或过度分散logit模型能够有效建模复杂关系。使用MCMC实现这种贝叶斯模型的统计软件包括WinBugsCrimeStat和许多通过R编程语言R programming language编写的软件包[25]

Spatial stochastic processes, such as Gaussian processes are also increasingly being deployed in spatial regression analysis. Model-based versions of GWR, known as spatially varying coefficient models have been applied to conduct Bayesian inference.[24] Spatial stochastic process can become computationally effective and scalable Gaussian process models, such as Gaussian Predictive Processes[26] and Nearest Neighbor Gaussian Processes (NNGP).[27]

空间随机过程,如高斯过程Gaussian processes,也越来越多地被应用在空间回归分析中。基于模型的GWR,即空间变化系数模型,已经被应用于进行贝叶斯推断[24]。空间随机过程可以成为计算有效且可扩展的高斯过程模型,例如高斯预测过程[26]和最近邻高斯过程(NNGP)[27]

Spatial interaction空间交互

Spatial interaction or "gravity models" estimate the flow of people, material or information between locations in geographic space. Factors can include origin propulsive variables such as the number of commuters in residential areas, destination attractiveness variables such as the amount of office space in employment areas, and proximity relationships between the locations measured in terms such as driving distance or travel time. In addition, the topological, or connective, relationships between areas must be identified, particularly considering the often conflicting relationship between distance and topology; for example, two spatially close neighborhoods may not display any significant interaction if they are separated by a highway. After specifying the functional forms of these relationships, the analyst can estimate model parameters using observed flow data and standard estimation techniques such as ordinary least squares or maximum likelihood. Competing destinations versions of spatial interaction models include the proximity among the destinations (or origins) in addition to the origin-destination proximity; this captures the effects of destination (origin) clustering on flows. Computational methods such as artificial neural networks can also estimate spatial interaction relationships among locations and can handle noisy and qualitative data.[citation needed]

空间交互或 "引力模型Gravity model"估计了地理空间中不同地点之间的人员、物质或信息的流动。因子可以包括原点推进变量(如住宅区的通勤者数量),目的地吸引力变量(如就业区的办公空间数量),以及以驾驶距离或旅行时间等衡量的地点之间的邻近关系。此外,必须确定区域之间的拓扑结构或连接Connective关系,特别是考虑距离和拓扑结构之间经常发生冲突的关系;例如,如果两个空间上接近的社区被一条高速公路隔开,它们可能不会显示任何明显的互动。在指定了这些关系的函数形式后,分析人员可以使用观测到的流量数据和标准的估计技术,如最小二乘法或最大似然法来估计模型参数。竞争目的地版本的空间交互模型除了包括原点-目的地的邻近性外,还包括目的地(或原点)之间的邻近性,这可以捕捉到目的地(原点)集群对流量的影响。人工神经网络Artificial neural networks等计算方法也可以估计地点之间的空间交互关系,并可以处理嘈杂和定性的数据[citation needed]

Simulation and modeling仿真和建模

Spatial interaction models are aggregate and top-down: they specify an overall governing relationship for flow between locations. This characteristic is also shared by urban models such as those based on mathematical programming, flows among economic sectors, or bid-rent theory. An alternative modeling perspective is to represent the system at the highest possible level of disaggregation and study the bottom-up emergence of complex patterns and relationships from behavior and interactions at the individual level.[citation needed]

空间交互模型是总体的和自上而下的:它们为地点之间的流动指定一个总体的关系。城市模型也具有这一特点,如基于数学规划、经济部门之间的流动或竞租理论的模型。另一种建模视角是在尽可能高的分解水平上表示系统,并研究在个体层面的行为和互动中出现的自下而上的复杂模式和关系[citation needed]

Complex adaptive systems theory as applied to spatial analysis suggests that simple interactions among proximal entities can lead to intricate, persistent and functional spatial entities at aggregate levels. Two fundamentally spatial simulation methods are cellular automata and agent-based modeling. Cellular automata modeling imposes a fixed spatial framework such as grid cells and specifies rules that dictate the state of a cell based on the states of its neighboring cells. As time progresses, spatial patterns emerge as cells change states based on their neighbors; this alters the conditions for future time periods. For example, cells can represent locations in an urban area and their states can be different types of land use. Patterns that can emerge from the simple interactions of local land uses include office districts and urban sprawl. Agent-based modeling uses software entities (agents) that have purposeful behavior (goals) and can react, interact and modify their environment while seeking their objectives. Unlike the cells in cellular automata, simulysts can allow agents to be mobile with respect to space. For example, one could model traffic flow and dynamics using agents representing individual vehicles that try to minimize travel time between specified origins and destinations. While pursuing minimal travel times, the agents must avoid collisions with other vehicles also seeking to minimize their travel times. Cellular automata and agent-based modeling are complementary modeling strategies. They can be integrated into a common geographic automata system where some agents are fixed while others are mobile.

应用于空间分析的复杂自适应系统Complex adaptive systems理论表明,邻近实体之间的简单交互作用可以在总体水平上导致复杂的、持久的和功能性的空间实体。两个基本的空间模拟方法是元胞自动机和基于主体的建模。元胞自动机Cellular automata建模规定了一个固定的空间框架,如网格单元,并指定了规则,根据其邻近单元的状态来决定一个单元的状态。随着时间的推移,单元根据其邻居改变状态而出现空间模式;这些改变了未来时间段的条件。例如,元胞可以代表城区的位置,它们的状态可以是不同类型的土地使用。从土地利用的简单交互作用中可以出现包括办公区和城市扩张Urban sprawl等模式。基于主体的建模Agent-based model使用带有目的行为(目标)的软件实体(主体),这些实体能在寻求其目标的同时反应、互动和修改其环境。与元胞自动机中的元胞不同,模拟系统可以允许主体在空间中移动。例如,我们可以用代表车辆的主体来模拟交通流和动态,这些车辆试图在指定的出发地和目的地之间最小化旅行时间。在追求最小旅行时间的同时,主体必须避免与其他也在寻求最小旅行时间的车辆发生碰撞。元胞自动机和基于主体的建模是互补的建模策略。它们可以被整合到一个共同的地理自动机系统中,其中一些主体是固定的,而另一些是移动的。

Calibration plays a pivotal role in both CA and ABM simulation and modelling approaches. Initial approaches to CA proposed robust calibration approaches based on stochastic, Monte Carlo methods.[28][29] ABM approaches rely on agents' decision rules (in many cases extracted from qualitative research base methods such as questionnaires).[30] Recent Machine Learning Algorithms calibrate using training sets, for instance in order to understand the qualities of the built environment.[31]

校准在CA和ABM模拟和建模方法中都起着关键作用。最初的CA方法提出了基于随机、蒙特卡洛方法的稳健校准方法[28][29]。ABM方法依赖于主体的决策规则(在许多情况下,从问卷调查等定性的基础研究方法中获取[30])。最近的机器学习算法使用训练集进行校准,例如,使用机器学习算法理解建筑环境的质量[31]

Multiple-point geostatistics (MPS)多点地统计学

Spatial analysis of a conceptual geological model is the main purpose of any MPS algorithm. The method analyzes the spatial statistics of the geological model, called the training image, and generates realizations of the phenomena that honor those input multiple-point statistics.

= = = = 多点地统计学(MPS) = = = 对概念地质模型进行空间分析是任何 MPS 算法的主要目的。该方法分析地质模型的空间统计量,称为训练图像,并生成符合输入多点统计量的现象的实现。

A recent MPS algorithm used to accomplish this task is the pattern-based method by Honarkhah.[32] In this method, a distance-based approach is employed to analyze the patterns in the training image. This allows the reproduction of the multiple-point statistics, and the complex geometrical features of the training image. Each output of the MPS algorithm is a realization that represents a random field. Together, several realizations may be used to quantify spatial uncertainty.

最近 Honarkhah 提出了基于模式的MPS 算法[32]。该方法采用基于距离的方法对训练图像中的模式进行分析。这样就可以重现多点统计信息和训练图像中复杂的几何特征。MPS 算法的每个输出都是一个表示随机场的实现。总之,几个实现可以用来量化空间的不确定性。

One of the recent methods is presented by Tahmasebi et al.[33] uses a cross-correlation function to improve the spatial pattern reproduction. They call their MPS simulation method as the CCSIM algorithm. This method is able to quantify the spatial connectivity, variability and uncertainty. Furthermore, the method is not sensitive to any type of data and is able to simulate both categorical and continuous scenarios. CCSIM algorithm is able to be used for any stationary, non-stationary and multivariate systems and it can provide high quality visual appeal model.,[34][35]

Tahmasebi 等人提出了CCSIM 算法,该方法使用互相关函数来改善空间模式再现[33]。该方法能够量化空间连通性、变异性和不确定性。此外,该方法对任何类型的数据都不敏感,能够同时模拟分类和连续的场景。CCSIM 算法适用于任何平稳、非平稳和多变量系统,能够提供高质量的视觉吸引力模型[34][35]

Geospatial and hydrospatial analysis地理空间和水文空间分析

模板:Cleanup merge Geospatial and hydrospatial analysis, or just spatial analysis,[36] is an approach to applying statistical analysis and other analytic techniques to data which has a geographical or spatial aspect. Such analysis would typically employ software capable of rendering maps processing spatial data, and applying analytical methods to terrestrial or geographic datasets, including the use of geographic information systems and geomatics.[37][38][39]

= = 地理空间和水文空间分析 = = 地理空间和水文空间分析Geospatial and hydrospatial analysis,或空间分析Spatial analysis[36],是一种将统计分析Statistical analysis和其他分析技术应用于具有地理或空间方面的数据的方法。这种分析通常会使用能够渲染地图的软件来处理空间数据,并将分析Analytical方法应用于陆地或地理Geographic数据集,包括地理信息系统Geographic information system地球空间信息学Geomatics的应用[37][38][39]

Geographical information system usage地理信息系统应用

Geographic information systems (GIS) — a large domain that provides a variety of capabilities designed to capture, store, manipulate, analyze, manage, and present all types of geographical data — utilizes geospatial and hydrospatial analysis in a variety of contexts, operations and applications.

地理信息系统Geographic information system(GIS)ーー一个提供各种能力的大领域,旨在捕获、存储、操作、分析、管理和展示所有类型的地理数据--其在各种背景、操作和应用中利用地理空间和水文空间分析。

Basic applications基本应用

Geospatial and Hydrospatial analysis, using GIS, was developed for problems in the environmental and life sciences, in particular ecology, geology and epidemiology. It has extended to almost all industries including defense, intelligence, utilities, Natural Resources (i.e. Oil and Gas, Forestry ... etc.), social sciences, medicine and Public Safety (i.e. emergency management and criminology), disaster risk reduction and management (DRRM), and climate change adaptation (CCA). Spatial statistics typically result primarily from observation rather than experimentation. Hydrospatial is particularly used for the aquatic side and the members related to the water surface, column, bottom, sub-bottom and the coastal zones.

基于地理信息系统GIS的地理空间和水文空间分析最初是为环境和生命科学中遇到的问题而开发的,特别是生态学Ecology地质学Geology流行病学Epidemiology。它已经扩展到几乎所有行业,包括国防、情报、公用事业、自然资源(即石油和天然气、林业......等)、社会科学、医学和公共安全Public Safety(即应急管理和犯罪学)、灾害风险减少和管理(DRRM)以及气候变化适应Climate change adaptation(CCA)。空间统计通常主要来自于观测而不是实验。水文空间学特别用于水生方面和与水面、水柱、水底、水底下和沿海地区有关的组成。

Basic operations基本操作

Vector-based GIS is typically related to operations such as map overlay (combining two or more maps or map layers according to predefined rules), simple buffering (identifying regions of a map within a specified distance of one or more features, such as towns, roads or rivers) and similar basic operations. This reflects (and is reflected in) the use of the term spatial analysis within the Open Geospatial Consortium (OGC) “simple feature specifications”. For raster-based GIS, widely used in the environmental sciences and remote sensing, this typically means a range of actions applied to the grid cells of one or more maps (or images) often involving filtering and/or algebraic operations (map algebra). These techniques involve processing one or more raster layers according to simple rules resulting in a new map layer, for example replacing each cell value with some combination of its neighbours’ values, or computing the sum or difference of specific attribute values for each grid cell in two matching raster datasets. Descriptive statistics, such as cell counts, means, variances, maxima, minima, cumulative values, frequencies and a number of other measures and distance computations are also often included in this generic term spatial analysis. Spatial analysis includes a large variety of statistical techniques (descriptive, exploratory, and explanatory statistics) that apply to data that vary spatially and which can vary over time. Some more advanced statistical techniques include Getis-ord Gi* or Anselin Local Moran's I which are used to determine clustering patterns of spatially referenced data.

基于矢量的地理信息系统GIS通常与地图叠加(根据预定的规则合并两个或更多的地图或地图层),简单的缓冲区分析(识别地图上一个或多个特征的特定距离内的区域,如城镇、道路或河流)和类似的基本操作有关。这反映了(也体现在)空间分析这一术语在开放地理空间联盟Open Geospatial Consortium(OGC)"简单特征规范 "中的使用。对于广泛用于环境科学和遥感的基于栅格的GIS来说,这通常意味着对一张或多张地图(或图像)的网格单元进行一系列操作,通常涉及过滤和/或代数操作(地图代数)。这些技术根据简单的规则处理一个或多个栅格图层,从而形成一个新的地图层,例如用其邻近值的某些组合替换单元值,或计算两个匹配的栅格数据集中每个网格单元的特定属性值的和或差。在空间分析这个通用术语中,经常也包括描述性统计,如单元计数、平均值、方差、最大值、最小值、累积值、频率和其他一些度量和距离计算。空间分析包括大量的统计技术(描述性、探索性Exploratory和解释性统计Statistics),这些技术适用于在空间上有变化的数据,而且这些数据可以随时间变化。一些更高级的统计技术包括Getis-ord Gi*或Anselin Local Moran's I,它们被用来确定空间参考数据的聚类模式。

Advanced operations 高级操作

Geospatial and Hydrospatial analysis goes beyond 2D and 3D mapping operations and spatial statistics. It is multi-dimensional and also temporal and includes:

  • Surface analysis — in particular analysing the properties of physical surfaces, such as gradient, aspect and visibility, and analysing surface-like data “fields”;
  • Network analysis — examining the properties of natural and man-made networks in order to understand the behaviour of flows within and around such networks; and locational analysis. GIS-based network analysis may be used to address a wide range of practical problems such as route selection and facility location (core topics in the field of operations research), and problems involving flows such as those found in Hydrospatial and hydrology and transportation research. In many instances location problems relate to networks and as such are addressed with tools designed for this purpose, but in others existing networks may have little or no relevance or may be impractical to incorporate within the modeling process. Problems that are not specifically network constrained, such as new road or pipeline routing, regional warehouse location, mobile phone mast positioning or the selection of rural community health care sites, may be effectively analysed (at least initially) without reference to existing physical networks. Locational analysis "in the plane" is also applicable where suitable network datasets are not available, or are too large or expensive to be utilised, or where the location algorithm is very complex or involves the examination or simulation of a very large number of alternative configurations.
  • Geovisualization — the creation and manipulation of images, maps, diagrams, charts, 3D views and their associated tabular datasets. GIS packages increasingly provide a range of such tools, providing static or rotating views, draping images over 2.5D surface representations, providing animations and fly-throughs, dynamic linking and brushing and spatio-temporal visualisations. This latter class of tools is the least developed, reflecting in part the limited range of suitable compatible datasets and the limited set of analytical methods available, although this picture is changing rapidly. All these facilities augment the core tools utilised in spatial analysis throughout the analytical process (exploration of data, identification of patterns and relationships, construction of models, and communication of results)

地理空间和水文空间分析超越了二维和三维制图操作和空间统计。它是多维的,也是具有时序特性的,包括。

  • 表面分析ー特别是分析物理表面的属性,如梯度Gradient坡向Aspect可见度Visibility,也用于分析"场"等类似表面的数据。
  • 网络分析ー研究自然和人工网络的属性,以了解这些网络内和周围流的行为;以及定位分析。基于GIS的网络分析可用于解决广泛的实际问题,如路线选择和设施定位(运筹学Operations research领域的核心课题),以及如水文空间分析和水文Hydrology与交通研究等涉及流的问题。在许多情况下,位置问题与网络有关,因此可以用为此目的而设计的工具来解决。但在其他情况下,现有网络可能几乎没有相关性,或者可能无法纳入建模过程。对于那些不受网络限制的问题,如新的道路或管道选址、区域仓库选址、移动基站定位或农村社区卫生保健地点的选择,可以在不参考现有物理网络的情况下进行有效分析(至少在最初)。如果没有合适的网络数据集,或者数据集太大、太昂贵而无法利用,或者定位算法非常复杂,或者涉及对大量替代配置的检查或模拟,"平面 "定位分析也是适用的。
  • 地理数据可视化Geovisualizationー创建和操作图像、地图、图表、三维视图及其相关的表格数据集。GIS软件包越来越多地提供一系列此类工具,包括提供静态或旋转视图,将图像覆盖在2.5D表面上,提供动画和飞越,动态链接和刷新以及时空可视化。后一类工具是最不发达的,部分反映了合适的兼容数据集范围有限,可用的分析方法有限,尽管这种情况正在迅速改变。在整个分析过程中(数据探索、模式和关系识别、模型构建和结果交流),所有这些设施都增强了空间分析中使用的核心工具。

Mobile geospatial and hydrospatial Computing移动地理空间和水文空间计算

Traditionally geospatial and hydrospatial computing has been performed primarily on personal computers (PCs) or servers. Due to the increasing capabilities of mobile devices, however, geospatial computing in mobile devices is a fast-growing trend.[40] The portable nature of these devices, as well as the presence of useful sensors, such as Global Navigation Satellite System (GNSS) receivers and barometric pressure sensors, make them useful for capturing and processing geospatial and hydrospatial information in the field. In addition to the local processing of geospatial information on mobile devices, another growing trend is cloud-based geospatial computing. In this architecture, data can be collected in the field using mobile devices and then transmitted to cloud-based servers for further processing and ultimate storage. In a similar manner, geospatial and hydrospatial information can be made available to connected mobile devices via the cloud, allowing access to vast databases of geospatial and hydrospatial information anywhere where a wireless data connection is available.

传统上,地理空间和水文空间计算主要在个人电脑(PC)或服务器上进行。然而,由于移动设备的功能不断增加,移动设备中的地理空间计算呈快速增长的趋势[40]。便携的设备及有用的传感器的出现,如全球导航卫星系统(GNSS)接收器和气压传感器的存在,使用户可以在野外获取和处理地理空间和水文空间信息。除了在移动设备上对地理空间信息进行本地处理外,另一个增长的趋势是基于云的地理空间计算。在这种架构中,在野外使用移动设备收集数据后,可以传输到基于云的服务器中进行进一步处理和最终存储。类似的,地理空间和水文空间信息可以通过云计算提供给连接的移动设备,允许在任何有无线数据连接的地方访问庞大的地理空间和水文空间信息数据库。

Geographic information science and spatial analysis地理信息科学与空间分析 模板:Anchor

模板:Further

文件:Minard.png
This flow map of Napoleon's ill-fated march on Moscow is an early and celebrated example of geovisualization. It shows the army's direction as it traveled, the places the troops passed through, the size of the army as troops died from hunger and wounds, and the freezing temperatures they experienced. 这幅拿破仑在莫斯科行军的流型图是早期地理可视化的著名例子。它显示了军队行进的方向,军队经过的地方,军队因饥饿和受伤而死亡的规模,以及他们所经历的严寒。


Geographic information systems (GIS) and the underlying geographic information science that advances these technologies have a strong influence on spatial analysis. The increasing ability to capture and handle geographic data means that spatial analysis is occurring within increasingly data-rich environments. Geographic data capture systems include remotely sensed imagery, environmental monitoring systems such as intelligent transportation systems, and location-aware technologies such as mobile devices that can report location in near-real time. GIS provide platforms for managing these data, computing spatial relationships such as distance, connectivity and directional relationships between spatial units, and visualizing both the raw data and spatial analytic results within a cartographic context. Subtypes include:

地理信息系统Geographic information system(GIS)和推动这些技术的基础地理信息科学Geographic information science对空间分析有很大影响。随着数据获取与处理的能力不断增强,空间分析逐渐应用于多源大数据处理中。地理数据采集系统包括遥感图像采集系统、环境监测系统,如智能交通系统,及如移动设备等可以近实时报告位置的位置感知技术。GIS提供了管理这些数据,计算数据间的空间关系(如空间单位之间的距离、连通性和方向关系),并将原始数据和空间分析结果可视化到在地图内的平台。子类型包括:

  • Geovisualization (GVis) combines scientific visualization with digital cartography to support the exploration and analysis of geographic data and information, including the results of spatial analysis or simulation. GVis leverages the human orientation towards visual information processing in the exploration, analysis and communication of geographic data and information. In contrast with traditional cartography, GVis is typically three- or four-dimensional (the latter including time) and user-interactive.
  • Geographic knowledge discovery (GKD) is the human-centered process of applying efficient computational tools for exploring massive spatial databases. GKD includes geographic data mining, but also encompasses related activities such as data selection, data cleaning and pre-processing, and interpretation of results. GVis can also serve a central role in the GKD process. GKD is based on the premise that massive databases contain interesting (valid, novel, useful and understandable) patterns that standard analytical techniques cannot find. GKD can serve as a hypothesis-generating process for spatial analysis, producing tentative patterns and relationships that should be confirmed using spatial analytical techniques.
  • Spatial decision support systems (SDSS) take existing spatial data and use a variety of mathematical models to make projections into the future. This allows urban and regional planners to test intervention decisions prior to implementation.[41]
  • 地理可视化Geovisualization(GVis)将科学可视化与数字制图Digital cartography相结合,以支持对包括空间分析与模拟的结果在内的地理信息数据的探索和分析。GVis利用了人类对视觉信息处理的取向来探索、分析和交流地理数据和信息。与传统的地图学相比,GVis通常是三维或四维的(后者包括时间),并且是交互式的。
  • 地理知识发现Geographic knowledge discovery(GKD)是以人为中心,利用高效的计算工具探索海量空间数据库Spatial database的过程。GKD包括地理数据挖掘Data mining、数据选择、数据清理和预处理以及结果解释等相关活动。GVis也可以在GKD过程中起到核心作用。GKD的前提是大规模的数据库包含标准分析技术无法发现的有趣(有效、新颖、有用和可理解)的模式。GKD可以作为空间分析的假设生成过程,产生暂定的模式和关系,应使用空间分析技术加以确认。
  • 空间决策支持系统Spatial decision support system(SDSS)利用现有的空间数据,使用各种数学模型对未来进行预测。该系统使城市和区域规划者能够在实施前测试干预决策[41]

See also另见

General topics 一般主题
  • 缓冲区分析Buffer analysis
  • 制图Cartography
  • 完全空间随机模型Complete spatial randomness
  • 成本距离分析Cost distance analysis
  • 地理计算GeoComputation
  • 地理空间智能Geospatial intelligence
  • 地理空间预测建模Geospatial predictive modeling
  • 维数扩展的九交集模型Dimensionally Extended nine-Intersection Model(DE-9IM)
  • 地理信息科学Geographic information science
  • 数理统计Mathematical statistics
  • 可塑性面积单元问题Modifiable areal unit problem
  • 点过程Point process
  • 邻近分析Proximity analysis
  • 空间自相关Spatial autocorrelation
  • 空间描述统计学Spatial descriptive statistics
  • 空间关系Spatial relation
  • 地形分析Terrain analysis
  • 空间分析软件列表List of spatial analysis software
Specific applications具体应用


  • 地理信息系统Geographic information systems
  • 地理人口分割Geodemographic segmentation
  • 可视域分析Viewshed analysis
  • 模糊建筑空间分析Fuzzy architectural spatial analysis
  • 适宜性分析Suitability analysis
  • 外推域分析Extrapolation domain analysis
  • 地理信息学Geoinformatics
  • 地理统计学Geostatistics
  • 边界问题(空间分析)Boundary problem (in spatial analysis)
  • 空间流行病学Spatial epidemiology
  • 空间计量学Spatial econometrics

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Further reading拓展阅读

模板:Further reading cleanup

  • Abler, R., J. Adams, and P. Gould (1971) Spatial Organization–The Geographer's View of the World, Englewood Cliffs, NJ: Prentice-Hall.
  • Anselin, L. (1995) "Local indicators of spatial association – LISA". Geographical Analysis, 27, 93–115.
  • Awange, Joseph; Paláncz, Béla (2016). Geospatial Algebraic Computations, Theory and Applications, Third Edition. New York: Springer. ISBN 978-3319254630. 
  • Banerjee, Sudipto; Carlin, Bradley P.; Gelfand, Alan E. (2014), Hierarchical Modeling and Analysis for Spatial Data, Second Edition, Monographs on Statistics and Applied Probability (2nd ed.), Chapman and Hall/CRC, ISBN 9781439819173
  • Benenson, I. and P. M. Torrens. (2004). Geosimulation: Automata-Based Modeling of Urban Phenomena. Wiley.
  • Fotheringham, A. S., C. Brunsdon and M. Charlton (2000) Quantitative Geography: Perspectives on Spatial Data Analysis, Sage.
  • Fotheringham, A. S. and M. E. O'Kelly (1989) Spatial Interaction Models: Formulations and Applications, Kluwer Academic
  • Fotheringham, A. S.; Rogerson, P. A. (1993). "GIS and spatial analytical problems". International Journal of Geographical Information Systems. 7: 3–19. doi:10.1080/02693799308901936.
  • Goodchild, M. F. (1987). "A spatial analytical perspective on geographical information systems". International Journal of Geographical Information Systems. 1 (4): 327–44. doi:10.1080/02693798708927820.
  • MacEachren, A. M. and D. R. F. Taylor (eds.) (1994) Visualization in Modern Cartography, Pergamon.
  • Levine, N. (2010). CrimeStat: A Spatial Statistics Program for the Analysis of Crime Incident Locations. Version 3.3. Ned Levine & Associates, Houston, TX and the National Institute of Justice, Washington, DC. Ch. 1-17 + 2 update chapters
  • Miller, H. J. (2004). "Tobler's First Law and spatial analysis". Annals of the Association of American Geographers. 94 (2): 284–289. doi:10.1111/j.1467-8306.2004.09402005.x. S2CID 19172678.
  • Miller, H. J. and J. Han (eds.) (2001) Geographic Data Mining and Knowledge Discovery, Taylor and Francis.
  • O'Sullivan, D. and D. Unwin (2002) Geographic Information Analysis, Wiley.
  • Parker, D. C.; Manson, S. M.; Janssen, M.A.; Hoffmann, M. J.; Deadman, P. (2003). "Multi-agent systems for the simulation of land-use and land-cover change: A review". Annals of the Association of American Geographers. 93 (2): 314–337. CiteSeerX 10.1.1.109.1825. doi:10.1111/1467-8306.9302004. S2CID 130096094.
  • White, R.; Engelen, G. (1997). "Cellular automata as the basis of integrated dynamic regional modelling". Environment and Planning B: Planning and Design. 24 (2): 235–246. doi:10.1068/b240235. S2CID 62516646.
  • Scheldeman, X.; van Zonneveld, M. (2010). Training Manual on Spatial Analysis of Plant Diversity and Distribution. Bioversity International. http://www.bioversityinternational.org/index.php?id=244&tx_news_pi1%5Bnews%5D=1256&cHash=110ef499ad0d2d17abb48849909f1356. 
  • Fisher MM, Leung Y (2001) Geocomputational Modelling: techniques and applications. Springer Verlag, Berlin
  • Fotheringham, S; Clarke, G; Abrahart, B (1997). "Geocomputation and GIS". Transactions in GIS. 2 (3): 199–200. doi:10.1111/j.1467-9671.1997.tb00010.x.
  • Openshaw S and Abrahart RJ (2000) GeoComputation. CRC Press
  • Diappi Lidia (2004) Evolving Cities: Geocomputation in Territorial Planning. Ashgate, England
  • Longley PA, Brooks SM, McDonnell R, Macmillan B (1998), Geocomputation, a primer. John Wiley and Sons, Chichester
  • Ehlen, J; Caldwell, DR; Harding, S (2002). "GeoComputation: what is it?". Comput Environ and Urban Syst. 26 (4): 257–265. doi:10.1016/s0198-9715(01)00047-3.
  • Gahegan, M (1999). "What is Geocomputation?". Transactions in GIS. 3 (3): 203–206. doi:10.1111/1467-9671.00017.
  • Murgante B., Borruso G., Lapucci A. (2009) "Geocomputation and Urban Planning" Studies in Computational Intelligence, Vol. 176. Springer-Verlag, Berlin.
  • Reis, José P.; Silva, Elisabete A.; Pinho, Paulo (2016). "Spatial metrics to study urban patterns in growing and shrinking cities". Urban Geography. 37 (2): 246–271. doi:10.1080/02723638.2015.1096118. S2CID 62886095.
  • Papadimitriou, F. (2002). "Modelling indicators and indices of landscape complexity: An approach using G.I.S". Ecological Indicators. 2 (1–2): 17–25. doi:10.1016/S1470-160X(02)00052-3.
  • Fischer M., Leung Y. (2010) "GeoComputational Modelling: Techniques and Applications" Advances in Spatial Science. Springer-Verlag, Berlin.
  • Murgante B., Borruso G., Lapucci A. (2011) "Geocomputation, Sustainability and Environmental Planning" Studies in Computational Intelligence, Vol. 348. Springer-Verlag, Berlin.
  • Tahmasebi, P.; Hezarkhani, A.; Sahimi, M. (2012). "Multiple-point geostatistical modeling based on the cross-correlation functions". Computational Geosciences. 16 (3): 779–79742. doi:10.1007/s10596-012-9287-1. S2CID 62710397.
  • Geza, Tóth; Áron, Kincses; Zoltán, Nagy (2014). European Spatial Structure. LAP LAMBERT Academic Publishing. doi:10.13140/2.1.1560.2247. 


External links外部链接

模板:Library resources box 模板:Commons category


  • ICA Commission on Geospatial Analysis and Modeling
  • An educational resource about spatial statistics and geostatistics
  • A comprehensive guide to principles, techniques & software tools
  • Social and Spatial Inequalities
  • National Center for Geographic Information and Analysis (NCGIA)
  • International Cartographic Association (ICA), the world body for mapping and GIScience professionals

= External links外部链接 =

  • ICA 地理空间分析和建模委员会
  • 空间统计和地理统计学教育资源
  • 原则、技术和软件工具综合指南
  • 社会和空间不平等
  • 国家地理信息和分析中心
  • 国际制图协会,世界制图和地理信息系统专业人士组织

模板:Visualization


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