Abstract: Aggregating areas into larger regions is a common problem in spatial planning, geographic information science, and cartography. The aim can be to group administrative areal units into electoral districts or sales territories, in which case the problem is known as districting. In other cases, area aggregation is seen as a generalization or visualization task, which aims to reveal spatial patterns in geographic data. Despite these different motivations, the heart of the problem is the same: given a planar partition, one wants to aggregate several elements of this partition to regions. These often must have or exceed a particular size, be homogeneous with respect to some attribute, contiguous, and geometrically compact. Even simple problem variants are known to be NP-hard, meaning that there is no reasonable hope for an efficient exact algorithm. Nevertheless, the problem has been attacked with heuristic and exact methods. In this article we present a new exact method for area aggregation and compare it with a state-of-the-art method for the same problem. Our method results in a substantial decrease of the running time and, in particular, allowed us to solve certain instances that the existing method could not solve within five days. Both our new method and the existing method use integer linear programming, which allows existing problem solvers to be applied. Other than the existing method, however, our method employs a cutting-plane method, which is an advanced constraint-handling approach. We discuss this approach in detail and present its application to the aggregation of areas in choropleth maps.

Abstract: In statistics, we quantify uncertainty to help determine the accuracy of estimates, yet this crucial piece of information is rarely included on maps visualizing areal data estimates. We develop and present three approaches to include uncertainty on maps: (1) the bivariate choropleth map repurposed to visualize uncertainty; (2) the pixelation of counties to include values within an estimate's margin of error; and (3) the rotation of a glyph, located at a county's centroid, to represent an estimate's uncertainty. The second method is presented as both a static map and visuanimation. We use American Community Survey estimates and their corresponding margins of error to demonstrate the methods and highlight the importance of visualizing uncertainty in areal data. An extensive online supplement provides the R code necessary to produce the maps presented in this article as well as alternative versions of them. Copyright © 2017 John Wiley & Sons, Ltd.

Abstract: One critical visual task when using choropleth maps is to identify spatial clusters in the data. If spatial units have the same color and are in the same neighborhood, this region can be visually identified as a spatial cluster. However, the choice of classification method used to create the choropleth map determines the visual output. The critical map elements in the classification scheme are those that lie near the classification boundary as those elements could potentially belong to different classes with a slight adjustment of the classification boundary. Thus, these elements have the most potential to impact the visual features (i.e., spatial clusters) that occur in the choropleth map. We present a methodology to enable analysts and designers to identify spatial regions where the visual appearance may be the result of spurious data artifacts. The proposed methodology automatically detects the critical boundary cases that can impact the overall visual presentation of the choropleth map using a classification metric of cluster stability. The map elements that belong to a critical boundary case are then automatically assessed to quantify the visual impact of classification edge effects. Our results demonstrate the impact of boundary elements on the resulting visualization and suggest that special attention should be given to these elements during map design.

Abstract: A choropleth map frequently is used to portray the spatial pattern of attributes, and its mapping result heavily relies on map classification. Uncertainty in an attribute has an influence on map cl...

Abstract: The rich history of cartography and typography indicates that typographic attributes, such as bold, italic and size, can be used to represent data in labels on thematic maps. These typographic attributes are itemized and characterized for encoding literal, categorical and quantitative data. Label-based thematic maps are shown, including examples that scale to multiple data attributes and a large number of entities. Multiple approaches to handle long labels are considered. Positional and proportional encoding apply attributes to portions of labels for encoding a large number of data attributes or quantitative values. Quantitative evaluation indicates label-based thematic maps may outperform choropleth maps for some tasks. Qualitative evaluation provides guidance for design considerations.

Abstract: Abstract The discovery in the cartographic collections of the Faculty of Geography and Regional Studies at the University of Warsaw of an original map by Charles Dupin – the first choropleth map – provided an opportunity to conduct a closer methodological analysis of the map and to investigate the subsequent development of this presentation method during the first half of 19th century. From relatively early on, the accepted principle was for choropleth map presentations to use statistical data still imprecisely referred to as relative, as well as using a distribution series as a method of generalizing data.

Abstract: Following the general demand for task-orientation in map design, one specific task will be examined here: the preservation and highlighting of local extreme values in choropleth maps Extreme value polygons are ones that show a larger (local maximum) or smaller (local minimum) attribute value compared to all directly neighboring polygons For a visual identification in a classified choropleth map, such a polygon must belong to a class other than the surrounding polygons However, data classification methods that are commonly used in the process of generating choropleth maps are data-driven, ie, the intervals are determined solely on the basis of the present frequency distribution of the original values With such a division along the number line, the spatial context of the underlying data is completely neglected and with that the desired categorization for local extreme values is not guaranteed As a consequence, a new method (called PLEX) is presented for this purpose The application and the effectiveness of this method will be demonstrated using real-world examples

Abstract: Although unclassed choropleth maps lead to a more accurate representation of data, grouping of data into classes is still common. Commonly-used data classification techniques such as equal-interval, quantiles, and natural breaks produce very different and possibly misleading representations. An unclassed map creates a distinct color for each unique value. The method was introduced by Tobler in 1973 using an x, y coordinate plotter that created crossed-line shadings. Tobler’s unclassed proposal used grayscale values because color displays were not yet available. Current color monitors have the ability to display 16.7 million colors, while most GIS software packages have limits to their color ramps. QGIS defines color ramps with up to 999 classes. It is also possible to define up to 1000 classes in ArcMap, and ArcGIS Pro has an “Unclassed” option when styling choropleth maps. Utilizing more color classes results in a more truthful map due to minimizing error from the grouping of data. The unclassed method is examined here along with color ramps and classification schemes in QGIS and Esri’s ArcMap/ArcGIS Pro. It is demonstrated that it is usually impossible to create a truly unclassed choropleth map using the default color schemes in these programs.

Abstract: Voltage control zones are commonly used within power systems, for applications like Secondary Voltage Control and localized reactive power markets. The idea is to partition a power system into zones that are weakly coupled in terms of voltage control. Conventionally, these control zones are defined with a deterministic approach and are fixed. However, recent research has demonstrated that they may be altered due to variation of the network structure and therefore suggested on-line reconfiguration of the zones. This paper goes a further step to probabilistically asses how the zoning could be affected by the uncertainties of operating condition (i.e., how the zones vary within a certain amount of time). Forced network outage, as the uncertain factor that affects the electrical distance between buses, is modeled in a realistic manner. Choropleth map is used to visualize the results. The 39-bus New England Test System (NETS) is used for demonstration.

Abstract: Visual analytics is widely used to explore data patterns and trends. This work leverages cancer data collected by World Health Organization (WHO) across over a hundred of cancer registries worldwide. In this study, we present a visual analytics platform, IBM Watson Analytics, to explore the patterns of global cancer incidence. We included 26 cancers from different geographic regions. An interactive interface was applied to plot a choropleth map to show global cancer distribution, and line charts to demonstrate historical cancer trends over 29 years. Subgroup analyses were conducted for different age groups. With real-time interactive features, we can easily explore the data with a selection of any cancer type, gender, age group, or geographical region. This platform is running on the cloud, so it can handle data in huge volumes, and is assessable by any computer connected to the Internet.

Abstract: Pesticide Residue is one of main sources resulted in food safety problems. It is necessary to analyze the distribution pattern of pesticide residue in order to supervision and management the overuse of pesticide. Thematic map is an effective approach for visualizing data combined with a specific geographic area. The most popular of the thematic maps are Choropleth, in which the values of the attribute are encoded as points or colored regions on the map. However, when the density of attribute-points on an area is different with that region's area, the data overlap will be produced. In this paper, we present a method for visualizing multidimensional data based on Cartogram. With this method, we first create Cartogram and Choropleth for presenting the geospatial distribution of data at the same time in order to avoid data overlapping, in which the Cartogram is generated by using diffusion algorithm; Second, we create thematic geographic heat map for presenting the pesticide residue pollution index by means of Inverse Distance Weighted interpolation to reckon missing data, in which the pesticide residue pollution index is calculated by using multiple linear regression algorithm; Thirdly, a multi-view spatial-temporal data visualization system, which combines maps, time axis, bar chart, bubble chart, pie chart etc. is presented to help user analyzing the data. A variety of interactive means such as region selection, data filtering, time cursor dragging, are also introduced to the system. The system uses two different ways to combine spatial with time. The results of user evaluation demonstrated that our method and system can effectively help user to analyze geospatial distribution of pesticide residue pollution.

Abstract: Spatial thinking is a type of reasoning or literacy that can be used for navigating the world. In this context, it is referred to as geospatial thinking or geo-literacy. Maps are the graphical tools that convey this location-based information and geo-literacy, an essential concept for interpreting and using maps. Being geo-literate goes beyond traversing points A to B, and cartographers create many different map types that broadly fall into two categories of reference or thematic maps. Reference maps show where things are and thematic maps communicate a specific message about the world. Some of the mapping techniques and map types that librarians will encounter are defined and illustrated in this chapter.

Abstract: Fundamental to the effective use of visualization as an analytic and descriptive tool is the assurance that presenting data visually provides the capability of making inferences from what we see. This paper explores two related approaches to quantifying the confidence we may have in making visual inferences from mapped geospatial data. We adapt Wickham et al. 's ‘Visual Line-up’ method as a direct analogy with Null Hypothesis Significance Testing (NHST) and propose a new approach for generating more credible spatial null hypotheses. Rather than using as a spatial null hypothesis the unrealistic assumption of complete spatial randomness, we propose spatially autocorrelated simulations as alternative nulls. We conduct a set of crowdsourced experiments (n=361) to determine the just noticeable difference (JND) between pairs of choropleth maps of geographic units controlling for spatial autocorrelation (Moran's I statistic) and geometric configuration (variance in spatial unit area). Results indicate that people's abilities to perceive differences in spatial autocorrelation vary with baseline autocorrelation structure and the geometric configuration of geographic units. These results allow us, for the first time, to construct a visual equivalent of statistical power for geospatial data. Our JND results add to those provided in recent years by Klippel et al. (2011), Harrison et al. (2014) and Kay & Heer (2015) for correlation visualization. Importantly, they provide an empirical basis for an improved construction of visual line-ups for maps and the development of theory to inform geospatial tests of graphical inference.

Abstract: 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.

Abstract: Background Population-based cancer registries provide epidemiological cancer information, but the indicators are often too complex to be interpreted by local authorities and communities, due to numeracy and literacy limitations. The aim of this paper is to compare the commonly used visual formats to funnel plots to enable local public health authorities and communities to access valid and understandable cancer incidence data obtained at the municipal level. Methods A funnel plot representation of standardised incidence ratio (SIR) was generated for the 82 municipalities of the Palermo Province with the 2003–2011 data from the Palermo Province Cancer Registry (Sicily, Italy). The properties of the funnel plot and choropleth map methodologies were compared within the context of disseminating epidemiological data to stakeholders. Results The SIRs of all the municipalities remained within the control limits, except for Palermo city area (SIR=1.12), which was sited outside the upper control limit line of 99.8%. The Palermo Province SIRs funnel plot representation was congruent with the choropleth map generated from the same data, but the former resulted more informative as shown by the comparisons of the weaknesses and strengths of the 2 visual formats. Conclusions Funnel plot should be used as a complementary valuable tool to communicate epidemiological data of cancer registries to communities and local authorities, visually conveying an efficient and simple way to interpret cancer incidence data.

Abstract: The aim of the paper is to map and evaluate the state of the multifunctional landscape of the municipality of Naples (Italy) and its surroundings, through a Spatial Decision-Making support system (SDSS) combining geographic information system (GIS) and a multi-criteria method an analytic hierarchy process (AHP). We conceive a knowledge-mapping-evaluation (KME) framework in order to investigate the landscape as a complex system. The focus of the proposed methodology involving data gathering and processing. Therefore, both the authoritative and the unofficial sources, e.g., volunteered geographical information (VGI), are useful tools to enhance the information flow whenever quality assurance is performed. Thus, the maps of spatial criteria are useful for problem structuring and prioritization by considering the availability of context-aware data. Finally, the identification of landscape services (LS) and ecosystem services (ES) can improve the decision-making processes within a multi-stakeholders perspective involving the evaluation of the trade-off. The results show multi-criteria choropleth maps of the LS and ES with the density of services, the spatial distribution, and the surrounding benefits.

Abstract: maptile makes it easy to map a variable in Stata. It generates choropleth maps, where each area is shaded according to the value of the variable being plotted. By default, maptile divides the geographic units into equal-sized bins (corresponding to quantiles of the plotted variable), then colors the bins in increasing intensity. To generate any particular map, maptile uses a geography, which is a template for that map. These need to be downloaded and installed. If no geography currently exists for the region you want to map, you can create a new one.