Mapping uncertain geographical attributes: incorporating robustness into choropleth classification design

ABSTRACT

Choropleth mapping provides a simple but effective visual presentation of geographical data. Traditional choropleth mapping methods assume that data to be displayed are certain. This may not be true for many real-world problems. For example, attributes generated based on surveys may contain sampling and non-sampling error, and results generated using statistical inferences often come with a certain level of uncertainty. In recent years, several studies have incorporated uncertain geographical attributes into choropleth mapping with a primary focus on identifying the most homogeneous classes. However, no studies have yet accounted for the possibility that an areal unit might be placed in a wrong class due to data uncertainty. This paper addresses this issue by proposing a robustness measure and incorporating it into the optimal design of choropleth maps. In particular, this study proposes a discretization method to solve the new optimization problem along with a novel theoretical bound to evaluate solution quality. The new approach is applied to map the American Community Survey data. Test results suggest a tradeoff between within-class homogeneity and robustness. The study provides an important perspective on addressing data uncertainty in choropleth map design and offers a new approach for spatial analysts and decision-makers to incorporate robustness into the mapmaking process.     

An Alternative Classification Scheme for Uncertain Attribute Mapping

The reality of uncertain data cannot be ignored. Anytime that spatial data are used to assist planning, decision making, or policy generation, it is likely that error or uncertainty in the data will propagate through processing protocols and analytic techniques, potentially leading to biased or incorrect decision making. The ability to directly account for uncertainty in spatial analysis efforts is critically important. This article focuses on addressing data uncertainty in one of the most important and widely used exploratory spatial data analysis (ESDA) techniques—choropleth mapping—and proposes an alternative map classification method for uncertain spatial data. The classification approach maximizes within-class homogeneity under data uncertainty while explicitly integrating spatial characteristics to reduce visual map complexity and to facilitate pattern perception. The method is demonstrated by mapping the 2009 to 2013 American Community Survey estimates of median household income in Salt Lake County, Utah, at the census tract level.     

Two-stage permutation tests for determining homogeneity within a spatial cluster

The discovery of spatial clusters formed by proximal spatial units with similar non-spatial attribute values plays an important role in spatial data analysis. Although several spatial contiguity-constrained clustering methods are currently available, almost all of them discover clusters in a geographical dataset, even though the dataset has no natural clustering structure. Statistically evaluating the significance of the degree of homogeneity within a single spatial cluster is difficult. To overcome this limitation, this study develops a permutation test approach Specifically, the homogeneity of a spatial cluster is measured based on the local variance and cluster member permutation, and two-stage permutation tests are developed to determine the significance of the degree of homogeneity within each spatial cluster. The proposed permutation tests can be integrated into the existing spatial clustering algorithms to detect homogeneous spatial clusters. The proposed tests are compared with four existing tests (i.e., Park’s test, the contiguity-constrained nonparametric analysis of variance (COCOPAN) method, spatial scan statistic, and q-statistic) using two simulated and two meteorological datasets. The comparison shows that the proposed two-stage permutation tests are more effective to identify homogeneous spatial clusters and to determine homogeneous clustering structures in practical applications.     

Multi-criteria modelling and clustering of spatial information

To improve the formal integration of verbally given spatial information in a geographical information system, a methodology for converting such information to a geographical representation was developed. This was applied to examples of a spatial-related analysis of natural language text messages in the domain of disaster management. This article presents an approach for such a conversion by using a suitable knowledge representation as well as formal modelling structures. The structures are provided by an ontology-supported knowledge base. With respect to spatial uncertainty, a formal representation based on possibility theory was defined. Moreover, a cluster algorithm was developed for handling information of different sources and building a spatial context.     

SPIDER—an interactive statistical tool for the analysis of spatially distributed data

Interactive statistical graphics are reviewed in the contexts of spatial data and geographical information systems (GIS). GIS provide the user with an active geographical view of the data—a map that can be used as an entry point to the data base. Prototype software—SPIDER—illustrates the possibilities of using statistical graphics as further views of the data, which can be made active and thus provide alternative means of querying the data. These views can be cross-referenced by 'linking'. It is argued that such a system can provide a very rich environment for pursuing exploratory statistical analysis of spatial data.     

探索性空间分析及其与GIS集成模式探讨

探索性空间分析基于让数据说话的理念,可以避免野值或非典型观测值的误导。在对探索性空间分析的基本原理和概念界定的基础上,探讨交互式和动态空间数据分析、地学可视化及可视化空间分布、确认性空间分析、空间数据挖掘等探索性空间分析的主要技术。由于统计分析软件和GIS的数据格式差异很大,直接将二者简单集成存在一定困难,因此切实可行的集成方式是采用对象连接和嵌入(OLE)技术,分别调用统计分析软件的探索性分析功能(或者函数)以及GIS的地图显示和空间分析功能,并进行必要开发,实现二者的集成。最后对探索性空间分析的发展方向进行展望。     

Generation of integral maps using the territory of a municipal district as an example

This paper further develops the ideas of V. B. Sochava’s Siberian school of thematic mapping concerning an integral approach in generating synthesis and assessment maps of the habitat on objective grounds confirmed by quantitative calculations. Maps of the natural environment display the invariant structure of the sites of a territory and their variable states. Integral indicators of the state of environment combine differentquality spatial information on the geographical location of the sites having regard to the scientific principles of qualimetry. An unbiased calculation of integral indicators is ensured through the use of the method of principal component analysis. The first principal component characterizes a maximum of variation in information on the geosystem, and the second component refers to a stable environment background. Their difference for each location corresponds to the potential of geosystem variability. The resulting integral indicators are displayed on assessment cartograms. The entire array of independent principal components is used for a classification of geosystems using the method of k-means clustering to create the typological map of the territory. Calculations are based on data for forest management of the Slyudyanka Leskhoz within the boundaries of the Slyudyanka municipal district of Irkutsk oblast. The territorial norm of the geographical environment corresponds to geosystems of the mountain-taiga belt of the Siberian stone pine and larch taiga on different-aspect slopes. Negative deviations from the norm are induced by high-mountain goletz and subgoletz geosystems on steep slopes, and positive deviations correspond to flat interfluves and gentle slopes.     

我国省域创新产出的空间特征和时空演化——基于探索性空间数据分析的实证

以我国31个省域作为空间观测单元,以专利申请受理数作为创新产出的衡量指标,对我国1997～2008年期间省域创新产出的空间分布进行了探索性空间数据分析(ESDA)。通过计算区位基尼系数和集中度指数,发现我国的创新活动显示了相当高水平的空间集中,并且这种集中程度在过去的十多年里表现出了稳定的增长趋势;对全局的Moran’s I统计分析表明:省际创新活动之间存在着显著的空间自相关(空间依赖性),证明了知识溢出的存在性和空间局限性;对局部的Moran’s I分析进一步揭示了省际创新活动水平的相关模式,Moran散点图刻画了创新活动的空间集聚模式及其时空演变态势。研究结果说明经过十几年的发展,我国省域创新活动的地域性特征十分显著。     

Algebraic approach to spatial reasoning

Abstract

A simple, exemplary system is described that performs reasoning about the spatial relationships between members of a set of spatial objects. The main problem of interest is to make sound and complete inferences about the set of all spatial relationships that hold between the objects, given prior information about a subset of the relationships. The spatial inferences are formalized within the framework of relation algebra and procedurally implemented in terms of constraint satisfaction procedures. Although the approach is general, the particular example employs a new ‘complete’ set of topological relationships that have been published elsewhere. In particular, a relation algebra for these topological relations is developed and a computational implementation of this algebra is described. Systems with such reasoning capabilities have many applications in geographical analysis and could be usefully incorporated into geographical information systems and related systems.     

论地理信息系统及其在地理学中的地位

地理信息系统技术的兴起代表了地理学发展的一个重要方向。地理信息系统是一门处理地理(空间)数据的综合信息技术,它属于技术地理学的范畴,它为资源与环境的管理和规划以及地理学的研究提供了一个革命性工具。另一方面,地理信息系统的建立和应用又依赖于地理学理论和实用模型的发展。进一步勾通地理信息系统与空间分析之间的关系是目前促进地理信息系统发展的重要课题。     

General multidimensional cloud model and its application on spatial clustering in Zhanjiang, Guangdong

Traditional spatial clustering methods have the disadvantage of “hardware division”, and can not describe the physical characteristics of spatial entity effectively. In view of the above, this paper sets forth a general multi-dimensional cloud model, which describes the characteristics of spatial objects more reasonably according to the idea of non-homogeneous and non-symmetry. Based on infrastructures’ classification and demarcation in Zhanjiang, a detailed interpretation of clustering results is made from the spatial distribution of membership degree of clustering, the comparative study of Fuzzy C-means and a coupled analysis of residential land prices. General multi-dimensional cloud model reflects the integrated characteristics of spatial objects better, reveals the spatial distribution of potential information, and realizes spatial division more accurately in complex circumstances. However, due to the complexity of spatial interactions between geographical entities, the generation of cloud model is a specific and challenging task.     

广义多维云模型及在空间聚类中的应用

传统的空间聚类方法难于脱离"硬划分"的束缚,且不能有效描述空间对象的复杂特征.一维云模型无法准确反映现实世界的多属性特征.简单的数据融合丢失了空间对象的必要信息.标准二维云模型克服了一维云的不足,但是在模拟复杂地理现象的非齐性和非对称性方面显得捉襟见肘.基于以上考虑,提出了广义多维云模型,以分段特性来体现空间对象的综合特征,并推导出模型的数学表达式.在实证研究的基础上,从空间聚类的隶属程度空间分布特征、与模糊C均值的对比研究及与住宅地价的耦合分析三个视角,详实解读了聚类结果.分析发现,广义多维云模型更能体现空间对象的综合特征,空间聚类结果能够反映出空间分布的潜在信息.更为准确的实现了复杂情况下的空间划分.该模型在刻画地理现象中更为合理,但由于地理实体的空间作用极其复杂.建立模型是一项既具体又充满挑战的任务.     

地理国情分类区划模型构建及实证研究——以河南省为例

地理国情分类区划是认知和分析地理国情的有效途径,是研究认识地理国情类型特征、组合及其演变趋势的区域差异和地理国情空间分异的基础。本文通过对地理国情普查的基本统计数据进行分析,制定了地理国情分类区划的指标体系;基于多维尺度分析和聚类分析,构建了地理国情分类区划模型。选择河南省地理国情普查数据,对其进行分类区划实验。通过对地理国情数据进行多维尺度分析,根据分析的可视化结果,可直观地确定地理国情的分类区划数,并将此设置为初始的聚类数;在此基础上进行k均值聚类,可实现河南省地理国情的分类区划,通过对各聚类簇中指标数据特征进行分析,并根据各聚类簇中心对区划各类型进行定义和解释,最后对聚类结果进行空间化表达。结果表明：河南省地理国情可划分为指标数据极值区、指标数据低值区、指标数据中值区和指标数据高值区4类,且根据空间集聚性分析,可判断分类区划的空间集聚效应显著,各区划类型间相互包容和渗透,集聚呈4条西南?东北的条状带。该项工作可为统筹地理国情与区域可持续发展,制定切实可行的区域发展政策提供科学依据。     

General multidimensional cloud model and its application on spatial clustering in Zhanjiang,Guangdong

Traditional spatial clustering methods have the disadvantage of “hardware division“, and can not describe the physical characteristics of spatial entity effectively. In view of the above, this paper sets forth a general multi-dimensional cloud model, which describes the characteristics of spatial objects more reasonably according to the idea of non-homogeneous and non-symmetry. Based on infrastructures’ classification and demarcation in Zhanjiang, a detailed interpretation of clustering results is made from the spatial distribution of membership degree of clustering, the comparative study of Fuzzy C-means and a coupled analysis of residential land prices. General multi-dimensional cloud model reflects the integrated characteristics of spatial objects better, reveals the spatial distribution of potential information, and realizes spatial division more accurately in complex circumstances. However, due to the complexity of spatial interactions between geographical entities, the generation of cloud model is a specific and challenging task.     

Using moment invariants to analyze cluster shapes and hypothesize potential causes

Although there are many algorithms and statistical tests to detect clustering of geographical phenomena, such as disease cases, the follow-up task of analyzing the cluster to explain its existence and mitigate the cluster is generally left to the researcher. These cluster detection methods are useful only for part of the process of identifying, understanding, and mitigating disease clusters. This research develops and presents a computer program that uses the information about the shape of the cluster to evaluate the hypotheses about potential causes. To achieve this, the shapes of the clusters are represented by image moment invariant statistics developed in the field of computer vision, and these shape statistics are compared against a database of moment invariants of shapes representative of several geographical processes, such as diffusion along roads and wind diffusion. Experiments using simulated data of different types of disease transmission were carried out, and the ability of the program to accurately classify the different types of diffusion demonstrates the viability of this approach to automated cluster analysis.     

Spatial representation of economic and financial measures used in agriculture via wavelet analysis

A foundation is set forth for use of the wavelet transform as a spatial analysis tool for modelling the geographical representation of economic and financial measures used in agriculture. This provides a framework from which to estimate a smooth nonparametric function which describes complex, multivariate relationships embedded in spatial data, with the resulting maps conveying large amounts of information in a familiar format. We illustrate this approach for tasks which include the graphical presentation of information, density estimation and wavelet-based nonparametric regression. A redundant wavelet transform is used, and we detail the properties which make it particularly appropriate for these objectives.     

THE SOCIAL EQUITY OF URBAN SERVICE DISTRIBUTION: AN EXPLORATION OF PARK ACCESS IN PUEBLO,COLORADO, AND MACON,GEORGIA

The degree to which urban resources are distributed equitably is a research question that continues to be debated. While research dealing with urban service delivery has proliferated during the last 20 years, few studies have directly linked the spatial distribution of facilities (in the form of accessibility measures) with the spatial distribution of population subgroups in an effort to assess equity issues. In part, this may be caused by the methodological difficulties involved in trying to link these distributions. In this paper, I offer a methodological as well as an empirical contribution to the assessment of equitability in facility distribution. Utilizing data on parks in Pueblo, Colorado, and Macon, Georgia, I analyze the equitability of park distribution by comparing the spatial clustering of park access scores with the spatial clustering of selected socioeconomic variables. There is some empirical evidence that the spatial pattern of low access for Macon corresponds in certain areas to spatial clusters of high housing value and low percentages of non-White residents, while the reverse situation is true for Pueblo (i.e., low access corresponds with low housing value and high percentages of Hispanics). Thus, the results of the analysis do not support the notion of “unpatterned inequality” in urban service distribution. The paper is an application of ideas from exploratory spatial data analysis (ESDA) and represents a new approach to the investigation of equity in the distribution of urban park facilities.     

Spatial video and GIS

GIS elemental unit representations of spatial data are often defined in terms of points, lines and areas. However, another type of spatial data that is becoming frequently captured, but as yet is largely ignored in GIS, is that of video. While digital video recording is a commonly encountered medium in modern society and encompasses many forms, from simple personal camcorders through to sophisticated survey and surveillance systems, its geographical representation in a GIS has not been fully examined or realised. In the majority of cases the video footage is usually captured while the device and/or the objects being viewed are in motion. What is of particular interest is when video streams can be, or have been, associated with spatial data such as location and orientation to create geographically referenced videographic data, which, for simplicity, will be defined as spatial video. Fundamentally, the nature of video is to record space, so when spatial properties can be accurately acquired and associated with this footage, an important geographical element can be considered for integration and analysis within a GIS.

Existing spatial video systems, both commercial and research, are predominantly used in survey or LBS roles and are usually bespoke and application specific. These systems do not model spatial video to any recognised standards that is generalised to be both data and platform independent. They do not support GIS integration and/or analysis from a purely spatial content perspective. A video-image/remote-sensing centric approach prevails where usage options range from simple visualisation interfaces to interactive computer vision systems. What has been largely overlooked is a spatial approach where the inherent geographical extent recorded in each video frame can be modelled and used in a geo-spatial analysis context. While this modelling approach has not been fully realised, it does exist in a GIS form based on Open Geospatial Consortium standards, where the spatial context of video is defined in a structure called a ViewCone. However, a ViewCone only defines a 2D model of the geographical extent of each frame and is restricted to a three-or-five sided polygon representation.

Thus, this article examines the potential of modelling spatial video through the use of elemental data types within GIS; gives some examples of using this approach; describes some problems in using spatial video within GIS; and then demonstrates how these problems are being solved. This is done in three stages: Firstly, a detailed overview of spatial video in its current GIS role is provided – this is achieved through a complete introduction to the distinct elements of spatial video followed by a review of its use in both commercial and academic application areas. Secondly, a brief theoretical overview of an alternative GIS-constrained ViewCone data structure is given that defines a more flexible spatial video model for both 2D and 3D GIS analysis and visualisation. Thirdly, a selective sample of results is presented based on an implementation of this approach being applied to a constrained spatial video data source in a specific study area.     

区域喀斯特石漠化信息系统的设计研究

本系统采用ArcGIS 软件作为基本平台, 以广西都安县为例, 借助其中的空间叠加分析与 地理统计分析方法, 构建了基于ArcObjects 的专业型GIS———区域喀斯特石漠化信息系统 (RKRDIS)。该系统是以喀斯特石漠化专业分析模型为核心, 以空间数据为信息材料, 以计算机网 络为传输载体, 解决喀斯特石漠化研究数据分析、查询、显示和管理等信息处理技术, 实现从“数 据”提取“信息”, 提供喀斯特石漠化的空间数据分析、动态监测、驱动诊断、预警分析、灾害评估和 辅助决策等多方面支持。