Exploring the Hidden Potential of Common Spatial Data Models to Visualize Uncertainty

Common Spatial Data Models (SDMs) such the vector, raster, and quadtree have well understood and widely practiced conventions of storage and visualization. This paper explores what happens when the conventions of visualization are not strictly adhered to, and the SDMs are used in an atypical fashion. A framework based on a quasi similarity measure is presented, which quantifies (in terms of "distance") the relationship between the storage format and the visualization output, following an accepted protocol. This research used a transformation process (Tp) to define this distance. Then, the atypical use of the quadtree SDM to represent choropleth spatial boundary uncertainty and attribute uncertainty was quantified using the same framework. This research shows that if a SDM is used outside of its original context, then the distance between the storage format and its visual output can alter; in our case, the distance decreased. This result was interpreted as evidence for the creation of a new spatial data structure. The formalization of the relationship between an SDM and its visual output will be valuable for future exploration of the non-conventional visualization of common SDMs.     

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.     

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.     

Cumulative spatial impact layers: A novel multivariate spatio‐temporal analytical summarization tool

Scientific inquiry often requires analysis of multiple spatio‐temporal datasets, ranging in type and size, using complex multi‐step processes demanding an understanding of GIS theory and software. Cumulative spatial impact layers (CSIL) is a GIS‐based tool that summarizes spatio‐temporal datasets based on overlapping features and attributes. Leveraging a recursive quadtree method, and applying multiple additive frameworks, the CSIL tool allows users to analyze raster and vector datasets by calculating data, record, or attribute density. Providing an efficient and robust method for summarizing disparate, multi‐format, multi‐source geospatial data, CSIL addresses the need for a new integration approach and resulting geospatial product. The built‐in flexibility of the CSIL tool allows users to answer a range of spatially driven questions. Example applications are provided in this article to illustrate the versatility and variety of uses for this CSIL tool and method. Use cases include addressing regulatory decision‐making needs, economic modeling, and resource management. Performance reviews for each use case are also presented, demonstrating how CSIL provides a more efficient and robust approach to assess a range of multivariate spatial data for a variety of uses.     

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.     

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.     

Complexity reduction in choropleth map animations by autocorrelation weighted generalization of time-series data

Choropleth map animation is widely used to show the development of spatial processes over time. Although animation congruently depicts change, the rapid succession of complex map scenes easily exceeds the human cognitive capacity, causing map users to miss important information. Hence, a reduction of the visual complexity of map animations is desirable. This article builds on research related to complexity reduction of static choropleth maps. It proposes value generalization of choropleth time-series data in space and time, by using a method that adapts to the degree of global spatiotemporal autocorrelation within the dataset. A combination with upstream algorithms for local outlier detection results in less complex map animations focusing on large-scale patterns while still preserving significant local deviations in space and time. An according software application allows for in-depth exploration of the spatial and temporal autocorrelation structures in time-series data and provides control over the whole process of generalization.     

A Review and Evaluation of Uncertainty Classification and the Error‐Band Geometry Model

Advances in computer technologies have improved the quality of maps, making map comparison and analysis easier, but uncertainty and error still exist in GIS when overlaying geographic data with multiple or unknown confidence levels. The goals of this research are to review current geospatial uncertainty literature, present the Error‐Band Geometry Model (EBGM) for classifying the size and shape of spatial confidence intervals for vector GIS data, and to analyze the interpretability of the model by looking at how people use metadata to classify the uncertainty of geographic objects. The results from this research are positive and provide important insight into how people interpret maps and geographic data. They suggest that uncertainty is more easily interpreted for well defined point data and GPS data. When data is poorly defined, people are unable to determine an approach to model uncertainty and generate error‐bands. There is potential for using the EBGM to aid in the development of a GIS tool that can help individuals parameterize and model spatial confidence intervals, but more research is needed to refine the process by which people use the decision tree. A series of guiding questions or an “uncertainty wizard” tool that helps one select an uncertainty modeling approach might improve the way people apply this model to real‐world applications.     

The hierarchical tessellation model and its use in spatial analysis

The hierarchid tessellation model belongs to a class of spatial data models based on the recursive decomposition of space. The quadtree is one such tessellation and is characterized by square cells and a 1:4 decomposition ratio. To relax these constraints in the tessellation, a generalized hierarchical tessellation data model, called Adaptive Recursive Tessellations (ART), has been proposed. ART increases flexibility in the tessellation by the use of rectangular cells and variable decomposition ratios. In ART, users can specify cell sizes which are intuitively meaningful to their applications, or which can reflect the scales of data. ART is implemented in a data structure called Adaptive Recursive Run-Encoding (ARRE), which is a variant of two-dimensional run-encoding whose running path can vary with the different tessellation structures incorporated in an ART model. Given the recognition of the benefits of implementing statistical spatial analysis in GIS, the use of hierarchical tessellation models such as ART in spatial analysis is discussed. Three examples are introduced to show how ART can: (1) be applied to solve the quadrat size problem in quadrat analysis of point patterns; (2) act as the data model in the variable resolution block kriging technique for geostatistical data to reduce variation in kriging error; and (3) facilitate the evaluation of spatial autocorrelation for area data at multiple map resolutions via the construction of a connectivity matrix for calculating spatial autocorrelation indices based on ARRE.     

Choosing Geographic Units for Choropleth Rate Maps,with an Emphasis on Public Health Applications

Choropleth maps are the most widely used map type for mapping rates, such as those involving disease, crime, and socioeconomic indicators. The essential step of choosing a geographic unit to map is often made in an ad hoc manner. Among the desirable characteristics of choropleth mapping units are high degree of resolution, homogeneity of population size, homogeneity of land area, observation of minimum population thresholds and land area thresholds, temporal stability and currency, compactness of shape, audience familiarity, data availability, and the functional relevance of the unit to the phenomena mapped. Because of the uneven distribution of human populations, no single geographic unit can meet all of these characteristics in practice, and a well designed choropleth map necessarily involves some compromise. We present guidelines for choosing geographic units that take into account the above criteria, considering 12 geographic units ranging from census blocks to states. Even allowing for differences in scale and purpose, some units confer clear advantages over others.     

基于扩展关系模型的整体空间数据管理

空间数据模型和数据管理是地理信息系统 (GIS)最重要的研究领域之一。该文介绍一体化的数据模型———扩展关系模型和以此为基础的 ,由作者设计的GIS软件原型系统———GEODBMS。GEODBMS使用统一的数据库管理系统 (DBMS)同时管理图形和属性数据 ;使用改进的四叉树———交叠四叉树索引空间目标 ;使用扩展的SQL语言进行空间查询 ;使用数据恢复和并发控制方法来加强分布式环境下数据的安全性和一致性维护     

Variable Grid Method: An Intuitive Approach for Simultaneously Quantifying and Visualizing Spatial Data and Uncertainty

Efforts to develop applications and methods that effectively quantify and communicate uncertainty associated with spatial data remains a focus within many scientific communities. However, the inherent complexity of uncertainty makes it difficult to define, characterize, and represent. Frequently, the products of spatial and spatio‐temporal data are presented without a clear explanation of the inherent uncertainty underlying the data. As uses and applications for spatial data and their products continues to increase, so does the importance for utilizing reliable approaches to effectively communicate spatial data along with their inherent uncertainties. To address this need, the Variable Grid Method (VGM) was developed as an intuitive approach that simultaneously communicates both spatial patterns and trends and the uncertainty associated with data or their analyses. This article details the VGM approach and demonstrates the utility of the VGM to provide critical information about the relationship between uncertainty and spatial data, necessary to support the increasing utilization of spatial information for a wide range of research and other needs.     

A Microsoft VBA Application for Generating Heat Maps

A choropleth map is a form of thematic map used to portray the structural characteristics of some particular geographical distribution not apparent in data presented in tabular form. Preparation of a choropleth map starts with the assignment of map features to classes based on the value of a specific feature attribute followed by the association of classes of features with appropriate map colors or symbols. Map features are often geographical regions with naturally or artificially defined boundaries, but choropleth maps can also be prepared by segmenting the area to be mapped into a regular grid of regions. Maps prepared with each grid shaded in an intuitive manner such as blue for grids with the lowest attribute values to red for the highest values can be termed “heat maps”. This technical note describes the HeatMap Microsoft Excel application which converts information contained in a worksheet into a heat map, and then converts the heat map into a file suitable for display using mapping systems such as Google Earth. An example illustrates how the application can be used to visualize the seventeenth century frontier between the Polish/Lithuanian Commonwealth and the Ottoman Empire.     

SPAWNN: A Toolkit for SPatial Analysis With Self‐Organizing Neural Networks

This article introduces the SPAWNN toolkit, an innovative toolkit for spatial analysis with self‐organizing neural networks, which is published as free and open‐source software ( http://www.spawnn.org ). It extends existing toolkits in three important ways. First, the SPAWNN toolkit distinguishes between self‐organizing neural networks and spatial context models with which the networks can be combined to incorporate spatial dependence and provides implementations for both. This distinction maintains modularity and enables a multitude of useful combinations for analyzing spatial data with self‐organizing neural networks. Second, SPAWNN interactively links different self‐organizing networks and data visualizations in an intuitive manner to facilitate explorative data analysis. Third, it implements cutting‐edge clustering algorithms for identifying clusters in the trained networks. Toolkits such as SPAWNN are particularly needed when researchers and practitioners are confronted with large amounts of complex and high‐dimensional data. The computational performance of the implemented algorithms is empirically demonstrated using high‐dimensional synthetic data sets, while the practical functionality highlighting the distinctive features of the toolkit is illustrated with a case study using socioeconomic data of the city of Philadelphia, Pennsylvania.     

一种高效的城市部件普查方法

数字化城市管理是经济建设及信息化发展的迫切需求,城市部件普查是将物化的城市管理对象转化成数字化的管理信息,是数字化城市管理的基础。以威海市城市部件普查项目为例,通过分析城市部件的普查需求,采用GPS-RTK测量与移动设备调绘相结合的数据采集方法,以及"粗确权"、"分类别"、"分区域"的部件属性信息调查方法,构建相应的城市部件普查技术体系。基于该体系进行图形数据与属性信息的城管数据库搭建,构建一种高效城市部件普查技术方法。     

An efficient representation of quadtrees and bintrees for multiresolution terrain models

A space-filling curve in 2,3,or higher dimensions can be thought as a path of a continuously moving point.As its main goal is to preserve spatial proximity,this type of curves has been widely used in the design and implementation of spatial data structures and nearest neighbor-finding techniques.This paper is essentially focused on the efficient representation of Digital Ele-vation Models(DEM) that entirely fit into the main memory.We propose a new hierarchical quadtree-like data structure to be built over domains of unrestricted size,and a representation of a quadtree and a binary triangles tree by means of the Hilbert and the Sierpinski space-filling curves,respectively,taking into account the hierarchical nature and the clustering properties of this kind of curves.Some triangulation schemes are described for the space-filling-curves-based approaches to efficiently visualize multiresolu-tion surfaces.     

General entropy model of line segments uncertainty in GIS

Spatial data uncertainty can directly affect the quality of digital products and GIS-based decision making. On the basis of the characteristics of randomicity of positional data and fuzziness of attribute data, taking entropy as a measure, the stochastic entropy model of positional data uncertainty and fuzzy entropy model of attribute data uncertainty are proposed. As both randomicity and fuzziness usually simultaneously exist in linear segments, their omnibus effects are also investigated and quantified. A novel uncertainty measure, general entropy, is presented. The general entropy can be used as a uniform measure to quantify the total uncertainty caused by stochastic uncertainty and fuzzy uncertainty in GIS.     

General Entropy Model of Line Segments Uncerta,nty in GIS

Spatial data uncertainty can directly affect the quality of digital products and GIS-based decision making. On the basis of the characteristics of randomicity of positional data and fuzziness of attribute data, taking entropy as a measure, the stochastic entropy model of positional data uncertainty and fuzzy entropy model of attribute data uncertainty are proposed. As both randomicity and fuzziness usually simultaneously exist in linear segments, their omnibus effects are also investigated and quantified. A novel uncertainty measure, general entropy, is presented. The general entropy can be used as a uniform measure to quantify the total uncertainty caused by stochastic uncertainty and fuzzy uncertainty in GIS.     

General Entropy Model of Line Segments Uncertainty in GIS

Spatial data uncertainty can directly affect the quality of digital products and GIS-based decision making. On the basis of the characteristics of randomicity of positional data and fuzziness of attribute data, taking entropy as a measure, the stochastic entropy model of positional data uncertainty and fuzzy entropy model of attribute data uncertainty are proposed. As both randomic-ity and fuzziness usually simultaneously exist in linear segments, their omnibus effects are also investigated and quantified. A novel uncertainty measure, general entropy, is presented. The general entropy can be used as a uniform measure to quantify the total un-certainty caused by stochastic uncertainty and fuzzy uncertainty in GIS.     

A fast quadtree‐based terrain crack locating method that accounts for adjacency relationships

The repair of terrain cracks is an important process in multi‐resolution three‐dimensional terrain visualization, and rapid and accurate pinpointing of cracks between terrain blocks is of the utmost importance for this process. The existing quadtree‐based crack locating methods are generally slow and inefficient, as they require the traversal of terrain quadtrees to locate terrain cracks. In this research, we propose a fast quadtree‐based terrain crack locating method that accounts for adjacency information. First, terrain quadtrees are constructed that contain information regarding adjacency relationships. Second, dynamic updating is performed for terrain quadtrees and their adjacency information. Finally, terrain cracks are located by using the adjacencies of the quadtree nodes. This proposed method was experimentally validated via the terrain data of a mountainous region in Sichuan Province. The experimental results indicate that the proposed method can be used to efficiently and accurately locate terrain cracks with a strong performance in practical applications.