An evaluation of sampling and full enumeration strategies for Fisher Jenks classification in big data settings

Large data contexts present a number of challenges to optimal choropleth map classifiers. Application of optimal classifiers to a sample of the attribute space is one proposed solution. The properties of alternative sampling‐based classification methods are examined through a series of Monte Carlo simulations. The impacts of spatial autocorrelation, number of desired classes, and form of sampling are shown to have significant impacts on the accuracy of map classifications. Tradeoffs between improved speed of the sampling approaches and loss of accuracy are also considered. The results suggest the possibility of guiding the choice of classification scheme as a function of the properties of large data sets.     

Change Blindness in Animated Choropleth Maps: An Empirical Study

Animated choropleth maps enable cartographers to visualize time-series data in a way that congruently depicts change over time. However, users have difficulty apprehending information encoded within these displays, and often fail to detect important changes between adjacent scenes. Failures of visual experience, such as change blindness, threaten the effectiveness of dynamic geovisual displays, in which several important changes can occur simultaneously throughout the display. Animated choropleth maps require viewers not only to notice changes but also understand symbolic meanings encoded in rapid transitions between scenes. Graphic interpolation between key frames, also known as “in-betweening” or “tweening”, smoothes transitions and lengthens the duration of the transition between scenes in a dynamic sequence. Previous cartographic literature suggests tweening could be a potential solution for change blindness in the cartographic context. This article examines this issue of change blindness in the cartographic context and reports on a human subjects investigation designed to evaluate the influence of cartographic design variables on map readers' change detection abilities. Our results indicate that 1) map readers have difficulty detecting changes in animated choropleth maps, 2) map readers over-estimate their own change detection abilities, and 3) tweening influences the legibility of change in animated choropleth maps.     

Singly- and Doubly-Constrained Methods of Areal Interpolation for Vector-based GIS

Traditionally, areal interpolation has referred to techniques for transferring attribute values from one partitioning of space to a different partition of space but this is only one of several situations that create the need for estimating unknown data values for areal units. This paper presents a categorization of four areal interpolation problems that includes the "missing" data problem, the traditional "alternative geography" problem, the overlay of a choropelth and an area-class data layer, and the overlay of two choropleth data layers and demonstrates the relationship between the last three problems and general spatial interaction modelling. The "alternative geography" and overlay of choropleth and area-class data layers mirrors a singly constrained spatial interaction model while the overlay of two choropleth layers is analogous to a doubly constrained interaction model. Iterative proportional fitting techniques with and without ancillary data are developed to solve these three classes of problems.     

空间自相关支撑下的地类分布模式一致性评价

空间分布模式是否保持一致是土地利用数据综合质量评价的一项重要内容。针对当前的研究缺少量化分析和位置表达的现状,提出了一种新的空间数据特有的自相关性评价方法。首先利用语义距离建立空间权重矩阵,随后通过莫兰指数（Moran’s I）计算数据处理前后全局和局部自相关度,最后利用莫兰（Moran）散点图和空间关联的局部指标（local indicators of spatial association,LISA）集聚图相结合的方法对综合前后的土地利用分布模式进行可视化对比。相较传统评价方法,所提方法顾及数据语义关系,计算可量化聚集程度,以直观可视化方法对比展示,更好地对土地利用数据在综合前后的全局空间分布模式一致性进行了评价。认知实验结果符合人类认知,表明所提方法切实有效。     

Unclassed Animated Choropleth Maps

Abstract

The potential of unclassed animated choropleth maps as a solution to false patterns of geographic change arising from data classification is investigated. Old concerns about unclassed choropleth maps may be mitigated through map interactivity that offers four advantages over traditional data legends, and previous insights from testing static choropleth maps do not necessarily translate to animated cartography. Data from user testing revealed unclassed animated choropleth maps neither help nor hurt the ability of map readers to understand patterns of geographic change. However, the unclassed map (1) appeared 'less jumpy' to participants and was perceived to run at a slower pace (despite running at the same number of frames per second), and (2) subtle geographic shifts (e.g., seasonal unemployment cycles) were more readily noticed on the unclassed maps. Preliminary results also suggest classed data emphasise stability over time – while their unclassed counterparts improve our ability to see changes. This paper also outlines animated simultaneous contrast as a new perceptual issue in the creation of animated choropleth maps.     

空间自相关在区域经济统计分析中的应用

利用了空间自相关分析方法,分析了海南省区域经济的空间分布模式研究,结果表明其能很好地检测区域经济之间的空间关联模式。     

Map Generalization with a Triangulated Data Structure

Automation of map generalization requires facilities to monitor the spatial relationships and interactions among multiple map objects. An experimental map generalization system has been developed which addresses this issue by representing spatial objects within a simplicial data structure (SDS) based on constrained Delaunay triangulation of the source data. Geometric generalization operators that have been implemented include object exaggeration, collapse, amalgamation, boundary reduction and displacement. The generalization operators exploit a set of primitive SDS functions to determine topological and proximal relationships, measure map objects, apply transformations, and detect and resolve spatial conflicts. Proximal search functions are used for efficient analysis of the structure and dimensions of the intervening spaces between map objects. Because geometric generalization takes place within a fully triangulated representation of the map surface, the presence of overlap conflicts, resulting from individual operators, can be detected due to the introduction of singularities in the triangulation, the structure of which is used to generate displacement vectors to resolve the conflict. Examples of the application of the implemented operators are described and illustrated using large scale topographic map data.     

Frequency Histogram Legend in the Choropleth Map: A Substitute to Traditional Legends

This article presents the use of the frequency histogram legend (FHL) as a substitute to traditional legends in both classed and unclassed choropleth maps. Great variation in the size of mapping units can hinder readers' ability to comprehend statistical distributions from a choropleth map. Replacing conventional legends with FHL can aid readers in their understanding of spatial as well as statistical distributions of the mapped data simultaneously. A customized mapping application was designed in ArcInfo 9.0 to test the use of FHL in both classed and unclassed choropleth maps. Frequency histogram legends were tested on different types of statistical distributions. Although the comparison of the results shows that the FHL works best for a Gaussian or close to a Gaussian distribution for eight or fewer classes, the customized application permits users to generate choropleth maps with frequency histogram legends for any type of statistical distribution with any number of classes. The analysis reveals that readers' background in statistics helped them to effectively utilize and interpret frequency histogram legends in the choropleth maps.     

矢量曲线的视觉清晰度及在网络地图综合中的应用

互联网用户参与的地图制图容易出现视觉冲突、压盖、拥挤等地图表达问题,需要引入地图自动综合协助解决。网络地图中由于原图比例尺和综合后比例尺均难以准确量化,常规地图自动综合基于“原图比例尺-综合后比例尺”判断是否需要综合的方法已不再适用。矢量数据在可视化后会产生视觉粘连,视觉粘连越明显,地图表达效果越差,综合的需求也越强烈。基于此规律,本文提出对视觉粘连进行定量描述并据此判断是否需要综合。首先,从人类视觉感受出发,结合栅格化思想设计了矢量曲线视觉粘连的量化指标——视觉清晰度。然后,基于“金字塔式”的尺度空间计算曲线在多个比例尺表达的清晰度,并拟合了清晰度的变化函数。最后,将该函数应用于众源地理数据的网络地图综合决策。试验结果表明,本文方法可准确判断每条矢量曲线是否需要综合,能有效解决地理数据尺度异质性带来的可视化难题。同时,清晰度变化函数将曲线的尺度描述由静态数值扩展到连续函数,有望更好地支持多尺度空间数据处理及网络地图综合等问题。     

Mapping the Results of Geographically Weighted Regression

Abstract

Geographically weighted regression (GWR) is a local spatial statistical technique for exploring spatial nonstationarity. Previous approaches to mapping the results of GWR have primarily employed an equal step classification and sequential no-hue colour scheme for choropleth mapping of parameter estimates. This cartographic approach may hinder the exploration of spatial nonstationarity by inadequately illustrating the spatial distribution of the sign, magnitude, and significance of the influence of each explanatory variable on the dependent variable. Approaches for improving mapping of the results of GWR are illustrated using a case study analysis of population density–median home value relationships in Philadelphia, Pennsylvania, USA. These approaches employ data classification schemes informed by the (nonspatial) data distribution, diverging colour schemes, and bivariate choropleth mapping.     

基于GIS的应急预案过程动态推演模拟技术研究

采用图形标绘的方法表达应急预案中的相关要素,并为标绘的图形符号添加各种动画来模拟预案要素随时间的动态变化;采用预案态势演播工具播放预案.     

基于电子地图的超媒体数据模型研究

从电子地图的超媒体数据模型出发，研究基于电子地图的多媒体信息之间关系的非线性存储、组织、管理和浏览信息的表达技术和数据的组织形式。在分析电子地图和超媒体技术特点的基础上，以实例来阐述这种模型建立的基本思路。试验表明，基于电子地图的超媒体数据模型能够很好地组织和表达多媒体数据，并取得了较好的效果。     

Measures of spatio-temporal accuracy for time series land cover data

Remote sensing is a useful tool for monitoring changes in land cover over time. The accuracy of such time-series analyses has hitherto only been assessed using confusion matrices. The matrix allows global measures of user, producer and overall accuracies to be generated, but lacks consideration of any spatial aspects of accuracy. It is well known that land cover errors are typically spatially auto-correlated and can have a distinct spatial distribution. As yet little work has considered the temporal dimension and investigated the persistence or errors in both geographic and temporal dimensions. Spatio-temporal errors can have a profound impact on both change detection and on environmental monitoring and modelling activities using land cover data. This study investigated methods for describing the spatio-temporal characteristics of classification accuracy. Annual thematic maps were created using a random forest classification of MODIS data over the Jakarta metropolitan areas for the period of 2001–2013. A logistic geographically weighted model was used to estimate annual spatial measures of user, producer and overall accuracies. A principal component analysis was then used to extract summaries of the multi-temporal accuracy. The results showed how the spatial distribution of user and producer accuracy varied over space and time, and overall spatial variance was confirmed by the principal component analysis. The results indicated that areas of homogeneous land cover were mapped with relatively high accuracy and low variability, and areas of mixed land cover with the opposite characteristics. A multi-temporal spatial approach to accuracy is shown to provide more informative measures of accuracy, allowing map producers and users to evaluate time series thematic maps more comprehensively than a standard confusion matrix approach. The need to identify suitable properties for a temporal kernel are discussed.     

移动GIS中可视化技术研究

针对移动设备硬件特点,提出移动GIS中3D可视化简化模型,并设计简化的三维投影变换算法,描述根据已有的2D矢量数据创建3D地图的过程。接着针对移动设备有限的软硬件资源条件,提出了空间数据组织和处理原则。为了逼真地展现地理场景的立体视觉效果,给出了3D可视化预处理措施,并采取了必要的3D场景增强技术,以较少的时间和空间代价,完成3D变换。最后,通过实验,在移动G IS系统中实施了基于2D矢量空间数据的3D可视化技术,生成直观、逼真、实时的3D地图,同时给出了实验测试数据。     

Animated Maps of Aggregate Data: Conceptual and Practical Problems

Predictions of the 1960s about the computer's potential to change cartography are finally being fulfilled. Dynamic maps for vehicle navigation, interactive cartographic/statistical tools, and map animation are being investigated actively. As these new environments for mapping become available, we must reevaluate past questions about transformations from reality to data and data to map. In this paper, we consider these transformation questions in the context of statistical map animation. The issues discussed were raised in producing a “map movie” depicting the spread of acquired immune deficiency syndrome (AIDS) over time. Jenks' data model concept is used as the basis for a typology of data models representing phenomena typically depicted by enumeration unit data. The typology is then used to evaluate symbolization decisions for AIDS incidence maps. Implications for symbol selection imposed by dynamic rather than static maps are considered, as are technical issues involved in producing the animation on a microcomputer platform. A hybrid symbolization method that we have termed the “chorodot” is suggested as a way to meet the constraints on symbolization imposed by animation and to represent the appropriate data model for AIDS incidence.     

Dynamic spatial panels: models, methods, and inferences

This paper provides a survey of the existing literature on the specification and estimation of dynamic spatial panel data models, a collection of models for spatial panels extended to include one or more of the following variables and/or error terms: a dependent variable lagged in time, a dependent variable lagged in space, a dependent variable lagged in both space and time, independent variables lagged in time, independent variables lagged in space, serial error autocorrelation, spatial error autocorrelation, spatial-specific and time-period-specific effects. The survey also examines the reasoning behind different model specifications and the purposes for which they can be used, which should be useful for practitioners.     

基于过渡投影面的室内地图统一数学基础转换方法

室内外统一的地图数学基础是室内外空间数据共享和使用的重要基础,是室内外一体化位置服务的重要保证,并且对于复杂室内及地下空间的安全管理与应急响应具有重要作用。室内地图通常采用自定义局部平面坐标系,造成室内与室外地图以及不同建筑室内地图之间数学基础的不一致。针对此,将地理坐标系作为室内地图统一遵循的数学基础,研究了室内地图从局部平面坐标系到地理坐标系的转换方法。分析了传统地图数学基础转换方法的适用性之后,提出了一种基于过渡投影面的室内地图统一数学基础转换方法。选取某住宅区的实测数据进行了转换试验,结果表明该方法可以显著提高室内地图统一数学基础转换的精度。     

Animation of Reliability in Computer-generated Dot Maps and Elevation Models

Visualization of reliability in spatial data has been the subject of considerable recent research activity. Animation has been suggested as one method to achieve this, and its application to various measures associated with class-area maps (classified satellite images and soil maps) has been discussed elsewhere. Animation is achieved by randomly selecting a location and then assigning it to a different map unit (cover or soil type) according to the information on the reliability associated with the original map or map units. In this article the same basic method is extended to mapping locational reliability in dot maps and surface error in a digital elevation model (DEM). In the former case, the dots, which are randomly located in the first place, are randomly relocated so that any meaningless positional information implicit in the location of the dots is lost while the meaningful information (the number of dots within a region) remains constant. In the DEM, animation uses a random field as an error surface, based upon the root mean squared error (RMSE). The amount of error at a location is constantly changed, giving no impression that the elevation is precisely known. The ability to vary the spatial autocorrelation within the error field provides a graphic illustration that the usual RMSE is not a sufficient method for the reporting of error in spatial databases. In both examples animation of reliability is believed to make a novel, but appropriate, use of the computer in cartography.     

栅格地图注记一致性探测与度量

一致性是空间数据质量的重要标准。空间数据的一致性探测对于多源、多尺度空间数据的融合具有重要意义。注记是地图的重要组成元素,包含了丰富的地理位置信息。由于制图综合、资料来源等原因,使得多个尺度的注记当中存在大量不一致现象。尝试从栅格地图中进行多尺度注记一致性的探测。在已有的空间目标变化类型基础上,提出了地图注记的12种基本变化类型,对地图注记在不同表达之间的一致程度进行量化表达,并提出了针对栅格地图注记一致性探测的方法。利用该方法对瓦片地图上的不同尺度的注记进行一致性探测与度量,证明了该方法的合理性和有效性。