ColorBrewer.org: An Online Tool for Selecting Colour Schemes for Maps

Abstract

Choosing effective colour schemes for thematic maps is surprisingly difficult. ColorBrewer is an online tool designed to take some of the guesswork out of this process by helping users select appropriate colour schemes for their specific mapping needs by considering: the number of data classes; the nature of their data (matched with sequential, diverging and qualitative schemes); and the end-use environment for the map (e.g., CRT, LCD, printed, projected, photocopied). ColorBrewer contains 'learn more' tutorials to help guide users, prompts them to test-drive colour schemes as both map and legend, and provides output in five colour specification systems.     

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 the Use of Grid Squares in Computerised Choropleth Maps

Abstract

There are numerous computer programs to produce choropleth maps and some work has also been published on the use of a grid matrix as a way of dividing an area into discrete units. The purpose of this paper is to combine the two approaches and evaluate the suitability of using a network of grid cells, each containing a representative value of the variable being mapped, as a way of producing choropleth maps on a computer.     

A heuristic multi-criteria classification approach incorporating data quality information for choropleth mapping

ABSTRACT

Despite conceptual and technology advancements in cartography over the decades, choropleth map design and classification fail to address a fundamental issue: estimates that are statistically indifferent may be assigned to different classes on maps or vice versa. Recently, the class separability concept was introduced as a map classification criterion to evaluate the likelihood that estimates in two classes are statistical different. Unfortunately, choropleth maps created according to the separability criterion usually have highly unbalanced classes. To produce reasonably separable but more balanced classes, we propose a heuristic classification approach to consider not just the class separability criterion but also other classification criteria such as evenness and intra-class variability. A geovisual-analytic package was developed to support the heuristic mapping process to evaluate the trade-off between relevant criteria and to select the most preferable classification. Class break values can be adjusted to improve the performance of a classification.     

Analysing regional industrialisation in Jiangsu province using geographically weighted regression

 Industry is the most important sector in the Chinese economy. To identify the spatial interaction between the level of regional industrialisation and various factors, this paper takes Jiangsu province of China as a case study. To unravel the existence of spatial nonstationarity, geographically weighted regression (GWR) is employed in this article. Conventional regression analysis can only produce `average' and `global' parameter estimates rather than `local' parameter estimates which vary over space in some spatial systems. Geographically weighted regression (GWR), on the other hand, is a relatively simple, but useful new technique for the analysis of spatial nonstationarity. Using the GWR technique to study regional industrialisation in Jiangsu province, it is found that there is a significant difference between the ordinary linear regression (OLR) and GWR models. The relationships between the level of regional industrialisation and various factors show considerable spatial variability. Received: 4 April 2001 / Accepted: 17 November 2001     

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.     

Generating and mapping population density surfaces within a geographical information system

Abstract

The spatially discontinuous choropleth map is a poor representation of the underlying continuous distribution of population density. A possible alternative is to derive dasymetric maps at a fine spatial resolution by making use of satellite imagery in a geographical information system. However, there are cartographic problems when these maps are displayed and further processing is needed in order to obtain approximations to a continuous density surface. Isarithmic maps of these density surfaces retain a high degree of spatial accuracy while providing pleasing and highly adaptable presentations.

The methods used to generate dasymetric and isarithmic maps are readily implemented in most raster based geographical information systems. For example, the classification of remotely sensed imagery, the subsequent processing and integration of data, and most of the cartographic display, were all undertaken in this work using the low cost IDRISI GIS that operates on standard IBM PC compatible hardware.     

利用搜索引擎数据模拟疾病空间分布

互联网记录了人们的日常生活,对带有位置信息的搜索引擎数据进行分析和挖掘可以获得隐藏于其中的地理信息。本文通过分析中国各省流感月度发病数与相关关键词百度搜索指数之间的相关性,选取相关性较高关键词的百度指数作为解释变量,发病数作为因变量,在采用主成分分析法消除变量共线性后,分别使用普通最小二乘回归（OLS）、地理加权回归（GWR）及时空地理加权回归（GTWR）构建流感发病数的空间分布模型。模型的拟合度能够从OLS的0.737、GWR的0.915提高到GTWR的0.959,赤池信息准则（AIC）也表明,GTWR模型明显优于OLS与GWR模型。验证结果显示,GTWR模型能准确识别流感高发地区,将该方法与搜索引擎数据结合能较好地模拟流感空间分布,为空间流行病学的研究提供预测模型和统计解释。     

Mapping multiple tree species classes using a hierarchical procedure with optimized node variables and thresholds based on high spatial resolution satellite data

ABSTRACT

Tree species distribution mapping using remotely sensed data has long been an important research area. However, previous studies have rarely established a comprehensive and efficient classification procedure to obtain an accurate result. This study proposes a hierarchical classification procedure with optimized node variables and thresholds to classify tree species based on high spatial resolution satellite imagery. A classification tree structure consisting of parent and leaf nodes was designed based on user experience and visual interpretation. Spectral, textural, and topographic variables were extracted based on pre-segmented images. The random forest algorithm was used to select variables by ranking the impact of all variables. An iterating approach was used to optimize variables and thresholds in each loop by comprehensively considering the test accuracy and selected variables. The threshold range for each selected variable was determined by a statistical method considering the mean and standard deviation for two subnode types at each parent node. Classification of tree species was implemented using the optimized variables and thresholds. The results show that (1) the proposed procedure can accurately map the tree species distribution, with an overall accuracy of over 86% for both training and test stages; (2) critical variables for each class can be identified using this proposed procedure, and optimal variables of most tree plantation nodes are spectra related; (3) the overall forest classification accuracy using the proposed method is more accurate than that using the random forest (RF) and classification and regression tree (CART). The proposed approach provides results with 3.21% and 7.56% higher overall land cover classification accuracy and 4.68% and 10.28% higher overall forest classification accuracy than RF and CART, respectively.     

Mapping local regression for spatial object-pairs

Local regression methods such as geographically weighted regression (GWR) can provide specific information about individual locations (or places) in spatial analysis that is useful for mapping nonstationary covariate relationships. However, the distance-based weighting schemes used in GWR are only adaptable for spatial objects that are point or area features. In particular, spatial object-pairs pose a challenge for local analysis because they have a linear dimensionality rather than a point dimensionality. This paper proposes using an alternative local regression model – quantile regression (QR) – for investigating the stationarity of regression parameters with respect to these linear features as well as facilitating the visualization of the results. An empirical example of a gravity model analysis of trade patterns within Europe is used to illustrate the utility of the proposed method.     

Bayesian and Geostatistical Approaches to Combining Categorical Data Derived from Visual and Digital Processing of Remotely Sensed Images

This paper seeks a synthesis of Bayesian and geostatistical approaches to combining categorical data in the context of remote sensing classification. By experiment with aerial photographs and Landsat TM data, accuracy of spectral, spatial, and combined classification results was evaluated. It was confirmed that the incorporation of spatial information in spectral classification increases accuracy significantly. Secondly, through test with a 5-class and a 3-class classification schemes, it was revealed that setting a proper semantic framework for classification is fundamental to any endeavors of categorical mapping and the most important factor affecting accuracy. Lastly, this paper promotes non-parametric methods for both definition of class membership profiling based on band-specific histograms of image intensities and derivation of spatial probability via indicator kriging, a non-parametric geostatistical technique.     

Bayesian and geostatistical approaches to combining categorical data derived from visual and digital processing of remotely sensed images

This paper seeks a synthesis of Bayesian and geostatistical approaches to combining categorical data in the context of remote sensing classification. By experiment with aerial photographs and Landsat TM data, accuracy of spectral, spatial, and combined classification results was evaluated. It was confirmed that the incorporation of spatial information in spectral classification increases accuracy significantly. Secondly, through test with a 5-class and a 3-class classification schemes, it was revealed that setting a proper semantic framework for classification is fundamental to any endeavors of categorical mapping and the most important factor affecting accuracy. Lastly, this paper promotes non-parametric methods for both definition of class membership profiling based on band-specific histograms of image intensities and derivation of spatial probability via indicator kriging, a non-parametric geostatistical technique.     

The Visualisation of Uncertainty for Spatially Referenced Census Data Using Hierarchical Tessellations

This paper explains why it is vital to account for uncertainty when utilising socioeco‐nomic data in a GIS, focusing on a novel and intuitive method to visually represent the uncertainty. In common with other data, it is not possible to know exactly how far from the truth socioeconomic data are. Therefore, when such data are used in a decision‐making environment an approximate measure given for correctness of data is an essential component. This is illustrated, using choropleth mapping techniques on census data as an example. Both attribute and spatial uncertainty are considered, with Monte Carlo statistical simulations being used to model attribute uncertainty. An appropriate visualisation technique to manage certain choropleth issues and uncer‐tainty in census type data is introduced, catering for attribute and spatial uncertainty simultaneously. This is done using the output from hierarchical spatial data structures, in particular the region quadtree and the HoR (Hexagon or Rhombus) quadtree. The variable cell size of these structures expresses uncertainty, with larger cell size indicating large uncertainty, and vice versa. This technique is illustrated using the New Zealand 2001 census data, and the TRUST (The Representation of Uncertainty using Scale‐unspecific Tessellations) software suite, designed to show spatial and attribute uncertainty whilst simultaneously displaying the original data.     

Comparison of Geographically Weighted Regression and Regression Kriging for Estimating the Spatial Distribution of Soil Organic Matter

Soil organic matter (SOM) is an important component of soils, and knowing the spatial distribution and variation of SOM is the premise for sustainably utilizing soils. The objective of this study was to compare geographically weighted regression (GWR) with regression kriging (RK) for estimating the spatial distribution of SOM using field-sample data in SOM and auxiliary data in correlated environmental variables (e.g., elevation, slope, ferrous minerals index, and Normalized Difference Vegetation Index). Results showed that GWR was a relatively better method and could provide promising results for SOM prediction in comparison with RK. The map interpolated by GWR showed similar spatial patterns influenced by environmental variables and the nonapparent effect of data outliers, but with higher accuracies, compared to that interpolated by RK.     

Exploring the Impact of Non-normality on Spatial Non-stationarity in Geographically Weighted Regression Analyses: Tobacco Outlet Density in New Jersey

The principal rationale for applying geographically weighted regression (GWR) techniques is to investigate the potential spatial non-stationarity of the relationship between the dependent and independent variables—i.e., that the same stimulus would provoke different responses in different locations. The calibration of GWR employs a geographically weighted local least squares regression approach. To obtain meaningful inference, it assumes that the regression residual follows a normal or asymptotically normal distribution. In many classical econometric analyses, the assumption of normality is often readily relaxed, although it has been observed that such relaxation might lead to unreliable inference of the estimated coefficients' statistical significance. No studies, however, have examined the behavior of residual non-normality and its consequences for the modeled relationships in GWR. This study attempts to address this issue for the first time by examining a set of tobacco-outlet-density and demographic variables (i.e., percent African American residents, percent Hispanic residents, and median household income) at the census tract level in New Jersey in a GWR analysis. The regression residual using the raw data is apparently non-normal. When GWR is estimated using the raw data, we find that there is no significant spatial variation of the coefficients between tobacco outlet density and percentage of African American and Hispanics. After transforming the dependent variable and making the residual asymptotically normal, all coefficients exhibit significant variation across space. This finding suggests that relaxation of the normality assumption could potentially conceal the spatial non-stationarity of the modeled relationships in GWR. The empirical evidence of the current study implies that researchers should verify the normality assumption prior to applying GWR techniques in analyses of spatial non-stationarity.     

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.     

Spatial and semantic effects of LUCAS samples on fully automated land use/land cover classification in high-resolution Sentinel-2 data

In this study, we test the use of Land Use and Coverage Area frame Survey (LUCAS) in-situ reference data for classifying high-resolution Sentinel-2 imagery at a large scale. We compare several pre-processing schemes (PS) for LUCAS data and propose a new PS for a fully automated classification of satellite imagery on the national level. The image data utilizes a high-dimensional Sentinel-2-based image feature space. Key elements of LUCAS data pre-processing include two positioning approaches and three semantic selection approaches. The latter approaches differ in the applied quality measures for identifying valid reference points and by the number of LU/LC classes (7–12). In an iterative training process, the impact of the chosen PS on a Random Forest image classifier is evaluated. The results are compared to LUCAS reference points that are not pre-processed, which act as a benchmark, and the classification quality is evaluated by independent sets of validation points. The classification results show that the positional correction of LUCAS points has an especially positive effect on the overall classification accuracy. On average, this improves the accuracy by 3.7%. This improvement is lowest for the most rigid sample selection approach, PS₂, and highest for the benchmark data set, PS₀. The highest overall accuracy is 93.1% which is achieved by using the newly developed PS₃; all PS achieve overall accuracies of 80% and higher on average. While the difference in overall accuracy between the PS is likely to be influenced by the respective number of LU/LC classes, we conclude that, overall, LUCAS in-situ data is a suitable source for reference information for large scale high resolution LC mapping using Sentinel-2 imagery. Existing sample selection approaches developed for Landsat imagery can be transferred to Sentinel-2 imagery, achieving comparable semantic accuracies while increasing the spatial resolution. The resulting LC classification product that uses the newly developed PS is available for Germany via DOI: https://doi.org/10.15489/1ccmlap3mn39.     

Extreme Coefficients in Geographically Weighted Regression and Their Effects on Mapping

This study deals with the issue of extreme coefficients in geographically weighted regression (GWR) and their effects on mapping coefficients using three datasets with different spatial resolutions. We found that although GWR yields extreme coefficients regardless of the resolution of the dataset or types of kernel function: (1) GWR tends to generate extreme coefficients for less spatially dense datasets; (2) coefficient maps based on polygon data representing aggregated areal units are more sensitive to extreme coefficients; and (3) coefficient maps using bandwidths generated by a fixed calibration procedure are more vulnerable to the extreme coefficients than adaptive calibration.     

Arc_Mat: a Matlab-based spatial data analysis toolbox

This article presents an overview of Arc_Mat, a Matlab-based spatial data analysis software package whose source code has been placed in the public domain. An earlier version of the Arc_Mat toolbox was developed to extract map polygon and database information from ESRI shapefiles and provide high quality mapping in the Matlab software environment. We discuss revisions to the toolbox that: utilize enhanced computing and graphing capabilities of more recent versions of Matlab, restructure the toolbox with object-oriented programming features, and provide more comprehensive functions for spatial data analysis. The Arc_Mat toolbox functionality includes basic choropleth mapping; exploratory spatial data analysis that provides exploratory views of spatial data through various graphs, for example, histogram, Moran scatterplot, three-dimensional scatterplot, density distribution plot, and parallel coordinate plots; and more formal spatial data modeling that draws on the extensive Spatial Econometrics Toolbox functions. A brief review of the design aspects of the revised Arc_Mat is described, and we provide some illustrative examples that highlight representative uses of the toolbox. Finally, we discuss programming with and customizing the Arc_Mat toolbox functionalities.     

Evaluation of Landsat TM data for forest cover type and landuse classification in subtropical forests of Kumaon Himalaya (U.P.)

LANDSAT-TM has been evaluated for forest cover type and landuse classification in subtropical forests of Kumaon Himalaya (U.P.) Comparative evaluation of false colour composite generated by using various band combinations has been made. Digital image processing of Landsat-TM data on VIPS-32 RRSSC computer system has been carried out to stratify vegetation types. Conventional band combination in false colour composite is Bands 2, 3 and 4 in Red/Green/Blue sequence of Landsat TM for landuse classification. The present study however suggests that false colour combination using Landsat TM bands viz., 4, 5 and 3 in Red/Green/Blue sequence is the most suitable for visual interpretation of various forest cover types and landuse classes. It is felt that to extract full information from increased spatial and spectral resolution of Landsat TM, it is necessary to process the data digitally to classify land cover features like vegetation. Supervised classification using maximum likelihood algorithm has been attemped to stratify the forest vegetation. Only four bands are sufficient enough to classify vegetaton types. These bands are 2,3,4 and 5. The classification results were smoothed digitaly to increase the readiability of the map. Finally, the classification carred out using digital technique were evaluated using systematic sampling design. It is observed that forest cover type mapping can be achieved upto 80% overall mapping accuracy. Monospecies stand Chirpine can be mapped in two density classes viz., dense pine (<40%) with more than 90% accuracy. Poor accuracy (66%) was observed while mapping pine medium dense areas. The digital smoothening reduced the overall mapping accuracy. Conclusively, Landsat-TM can be used as operatonal sensor for forest cover type mapping even in complex landuse-terrain of Kumaon Himalaya (U.P.)