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In recent years, deep reinforcement learning (DRL) has proved its great potential in multi-agent cooperation. However, how to apply DRL to multi-target tracking (MTT) problem for unmanned aerial vehicle (UAV) swarms is challenging: 1) the scale of UAVs may be large, but the existing multi-agent reinforcement learning (MARL) methods that rely on global or joint information of all agents suffer from the dimensionality curse; 2) the dimension of each UAV’s received information is variable, which is incompatible with the neural networks with fixed input dimensions; 3) the UAVs are homogeneous and interchangeable that each UAV’s policy should be irrelevant to the permutation of its received information. To this end, we propose a DRL method for UAV swarms to solve the MTT problem. Firstly, a decentralized swarm-oriented Markov Decision Process (MDP) model is presented for UAV swarms, which involves each UAV’s local communication and partial observation. Secondly, to achieve better scalability, a cartogram feature representation (FR) is proposed to integrate the variable-dimensional information set into a fixed-shape input variable, and the cartogram FR can also maintain the permutation irrelevance to the information. Then, the double deep Q-learning network with dueling architecture is adapted to the MTT problem, and the experience-sharing training mechanism is adopted to learn the shared cooperative policy for UAV swarms. Extensive experiments are provided and the results show that our method can successfully learn a cooperative tracking policy for UAV swarms and outperforms the baseline method in the tracking ratio and scalability.

Gaze data visualization constitutes one of the most critical processes during eye-tracking analysis. Considering that modern devices are able to collect gaze data in extremely high frequencies, the visualization of the collected aggregated gaze data is quite challenging. In the present study, contiguous irregular cartograms are used as a method to visualize eye-tracking data captured by several observers during the observation of a visual stimulus. The followed approach utilizes a statistical grayscale heatmap as the main input and, hence, it is independent of the total number of the recorded raw gaze data. Indicative examples, based on different parameters/conditions and heatmap grid sizes, are provided in order to highlight their influence on the final image of the produced visualization. Moreover, two analysis metrics, referred to as center displacement (CD) and area change (AC), are proposed and implemented in order to quantify the geometric changes (in both position and area) that accompany the topological transformation of the initial heatmap grids, as well as to deliver specific guidelines for the execution of the used algorithm. The provided visualizations are generated using open-source software in a geographic information system.

Relative accessibility is a widely studied approach that recognizes access to major locations as subjective and shaped by individual circumstances (e.g., individual preferences, habits, and cultural norms). One missing element in the knowledge base is how relative accessibility can be effectively mapped for decision-making. To fill the research gap, this paper evaluates whether cartograms are an appropriate tool for mapping relative accessibility, taking the city of Zaragoza, Spain as a case study. The research design included three phases: (i) elaboration of grid-based maps on relative non-motorized accessibility; (ii) elaboration of cartograms on relative non-motorized accessibility; (iii) an end-user evaluation with 30 local practitioners to analyze the effectiveness of cartograms to map relative accessibility compared to grid-based maps. Participants signaled that diffusion-based cartograms could be complementary to grid-based maps, providing better visualization of spatial dissimilarity patterns of accessibility between population groups. However, participants noted greater difficulty in identifying Dorling cartograms as an effective technique for mapping relative accessibility. The paper closes with a review of the strengths and weaknesses of the potential application of these visualization techniques in the field of accessibility planning.

Most people use maps for navigation. Geographic maps visually represent physical distance between locations. These maps sometimes provide a false impression of travel times. Two cities geographically close to each other might be “far apart” in terms of travel time because of slower connections, whereas two cities geographically distant might be “nearby” in terms of travel time because of faster connections. Under such circumstances, visualizing a transport network using time as a distance measure can make the transport network more understandable. This study integrates several (carto)graphic representations—a time line, a distance line, a time prism, a time cartogram, and a geographic map—in an interactive linked-views environment to model reachability in transport networks. A prototype is implemented in a web environment using D3.js. The implementation can be applied to any transport network. In this research, the approach is illustrated with railroad network data for the Dutch province of Overijssel. The solution provides an alternative and insightful perspective for analyzing the data. In addition to complementing a wide variety of methods to visualizing travel times, the approach could be applied in areas such as spatial analysis and transport planning.

Automatic production of contiguous area cartograms has become practical with computer algorithms, particularly applying forces to rubber-sheets and simulating diffusion processes. Reformulating the...

The article presents the results of the application of geographic information systems for environmental auditing, which allows you to monitor the ecological situation on the objects, food and chemical industries and to ensure environmental safety of natural and industrial areas. The authors propose a mathematical model that performs monitoring of environmental objects. The computational experiment is performed in Matlab for classifying the soil measurement conditions. The results of the analysis and the electronic cartograms constructed on their basis are used to predict the location of the points exceeding the parasitological indices in the soil. The assessment of the condition of the soil in different districts of the Voronezh city is made with the help of the created neural networks. The results are compared with the same indicators, measured in 2017. Data is taken from the information Bulletin «Evaluation of the influence of environmental factors on the health of the population of the Voronezh region on indicators of socio-hygienic monitoring». Information was prepared by the Office of Rospotrebnadzor in the Voronezh region. A study cited in the article was conducted at the Department of information and control systems of the Voronezh state University of engineering technologies. Geographic information system was built with the help of MapInfo software product. It can be used to simulate the environmental situation and to inform about its current state with the help of cartography. Thus, the geoinformation research method reviewed in this article allows predicting the emission of harmful substances into the environment and it can be used by regulatory agencies of the state authorities to control the environmental state of the territory.

The subject of the research is the method of constructing areal, linear and volumetric anamorphoses cartographic models for the analysis of geodata. The object of the research is the process of creating various types of anamorphoses cartographic models. The aim of the work is to improve the quality of geodata perception in cartographic models based on a new approach to their visualization, provided by an unusual representation of the geodata structure while taking into account a large number of parameters that they contain. Conclusions: Methods for constructing areal, linear and volume anamorphoses cartographic models have been developed, a mathematical model and an algorithm for creating anamorphoses cartographic models using the ArcGIS software package have been obtained. The methodology for constructing areal anamorphoses cartographic models, in particular, provides, through the use of the Cartogram module, the possibility of implementing anamorphoses cartographic models of demographic position in Ukraine based on data on the population size in the ArcMap package ArcGIS. At the same time, it is also possible to obtain volumetric anamorphoses cartographic models of the demographic state. In addition, based on an analysis of the activities of Wizz Air (as an example of modern lowcost air carriers), a methodology has been developed for constructing linear anamorphoses cartographic flight models performed by this company from Ukraine in the ArcMap environment. At the same time, the mandatory components of such cartographic models are specially implemented relational geodatabases containing comprehensive flight characteristics. The technique is universal and can be used for any airline and geolocation flights. The proposed methods for constructing anamorphic cartographic models allow obtaining their various types, due to specific visualization providing an opportunity to look at the geodata under study from different sides and gain new knowledge on nearby natural and technogenic phenomena. It is anamorphoses cartographic models that provide a unique opportunity to visually present non-obvious facts with the possibility of illuminating hidden natural and geographical patterns, analyzing the relationships between environmental phenomena against the background of their defining characteristics., Предметом исследования является методика построения площадных, линейных и объемных анаморфозных картографических моделей для анализа геоданных. Объектом исследования является процесс создания различных типов анаморфозных картографических моделей. Целью работы является повышение качества восприятия геоданных в картографических моделях на основании нового подхода к их визуализации, что обеспечивается необычным представлением структуры геоданных при одновременном учете большого количества параметров, которые они содержат. Выводы. Разработаны методики построения площадных, линейных и объемных анаморфозных картографических моделей, получена математическая модель и алгоритм процесса создания анаморфозных картографических моделей с использованием программного пакета ArcGIS. Методика построения площадных анаморфозных картографических моделей, в частности, предусматривает, благодаря использованию модуля Cartogram, возможность реализации в среде ArcMap пакета ArcGIS анаморфозных картографических моделей демографической ситуации в Украине на основании данных о численности населения. При этом обеспечивается возможность получения также и объемных анаморфозных картографических моделей демографического состояния. Кроме того, на основании анализа деятельности авиакомпании Wizz Аir (в качестве примера современных lowcost-авиаперевозчиков) разработана методика построения в среде ArcMap линейных анаморфозных картографических моделей перелетов, выполняемых данной компанией из Украины. При этом обязательными составляющими таких картографических моделей являются специально внедренные реляционные базы геоданных, содержащих исчерпывающие характеристики авиарейсов. Методика является универсальной и может применяться для любых авиакомпаний и геолокаций перелетов. Предложенные методики построения анаморфозных картографических моделей позволяют получать наиразнообразнейшиеих типы, которые за счет специфической визуализации обеспечивают возможность с разных сторон взглянуть на исследуемые геоданные и получить новые знания об окружающих природных и техногенных явлениях. Именно анаморфозные картографические модели дают уникальную возможность визуально представить неочевидные факты с возможностью освещения скрытых природно-географических закономерностей и проведения анализа взаимосвязей между явлениями окружающей среды на фоне их определяющих характеристик., Предметом дослідження є методика побудови площадкових, лінійних та об’ємних анаморфозних картографічних моделей для аналізу геоданих. Об’єктом дослідження є процес створювання різноманітних типів анаморфозних картографічних моделей. Метою роботи є підвищення якості сприйняття геоданих в картографічних моделях на підставі нового підходу до їх візуалізації, що забезпечується незвичним представленням структури геоданих при одночасному врахуванні великої кількості параметрів, які вони містять. Висновки. Розроблено методики побудови площадкових, лінійних та об’ємних анаморфозних картографічних моделей, отримано математичну модель та алгоритм процесу створення анаморфозних картографічних моделей з використанням програмного пакетуArcGIS. Методика побудови площадкових анаморфозних картографічних моделей, зокрема, передбачає, завдяки використанню додаткового модуля Cartogram, можливість реалізації в середовищі ArcMap пакету ArcGIS анаморфозних картографічних моделей демографічного стану в Україні на підставі даних про кількість населення. При цьому забезпечується можливість отримання також і об’ємних анаморфозних картографічних моделей демографічного стану. Крім того, на підставі аналізу діяльності авіакомпанії Wizz Аir (у якості прикладу сучасних lowcost-авіаперевізників) розроблено методику побудови в середовищі ArcMap лінійних анаморфозних картографічних моделей перельотів, що виконуються даною компанією з України. При цьому обов’язковими складовими таких картографічних моделей є спеціально впроваджені реляційні бази геоданих, що містять вичерпні характеристики авіарейсів. Методика є універсальною і може застосовуватись для будь-яких авіакомпаній і геолокацій перельотів. Запропоновані методики побудови анаморфозних картографічних моделей дозволяють отримувати їх найрізноманітніші типи, що за рахунок специфічної візуалізації забезпечують можливість з різних боків поглянути на досліджувані геодані та отримати нові знання щодо довколишніх природних і техногенних явищ. Саме анаморфозні картографічні моделі дають унікальну можливість візуально представити неочевидні факти з можливістю висвітлення прихованих природно-географічних закономірностей та проведення аналізу взаємозв’язків між явищами довкілля на тлі їх визначальних характеристик.

The visualisation of spatial information is a powerful tool for researchers in urban analytics seeking to convey their findings to the wider research community and the public in an accessible way. Yet, even the most well-intentioned cartographer may introduce misrepresentation by mapping irregularly shaped and sized areas. This paper explores the extent to which different methods of visualising area-based data can remedy (or exacerbate) this misrepresentation by presenting results from a crowdsourced survey. Data from the 2016 European Union referendum at Local Authority level in England are visualised using four alternative methods (balanced cartogram, hexogram, hexagonal grid, square grid) and compared to a traditional choropleth map, in terms of people’s understanding of the authors’ intended message, through a crowdsourced survey questionnaire. Results indicate that mapping out original boundaries can introduce misrepresentation, which can be mitigated by using balanced cartograms and hexograms to improve the accuracy of visualisations.

Visualization of statistical data is used for a good communication among involved personals. Taking an example of question on earthquake, it is important to review information where it will be occurred and how strong intensity is. Cartogram types of maps allow to easily see such information at a glance for everyone.In case of insurance companies who develop their business worldwide, the map let them understand where we see earthquake risks without knowing local location information. This means that a European underwriter can review it even if this personal do not know Japanese earthquake risk at all, for example. So, the map is one of fundamental tools to assess where the company shall take insurance risks more or do not take it. In other word, where they efficiently do marketing to provide insurance? For marketing strategy, it is needed to see and to analyse several issues at once, i.e., how much exposures they are retaining within their portfolio, how much loss they will pay in future and how many expected clients they will have. Analysis for each aspect can be done by using a map to visualize relevant data. This is known as statistical map.However, a simultaneous observation of different maps is not easy to see and understand how each aspect of alanysis should be considered with others. Now, this paper aim to show a capability of Jacques Bertin’s Ordinal Matrix. So, information on maps is taken and integrated by Bertin’s Matrix to analyse all information at once. And we will see how the Matrix lead us to make a decision for future strategy.

The choropleth is a widely used thematic map type. But it is not always ideal to visualize social data in engaging and accurate ways, especially as a standalone map. In this paper we discuss choropleths and two thematic map types with altered geometry: area cartograms and tile maps with repeating icons. To identify benefits and drawbacks of each, we created a choropleth, contiguous cartogram, and repeating icon tile map visualizing the same data from the United Nations Sustainable Development Goal (SDG) indicator about the proportion of women and girls aged 15–49 who have undergone female genital mutilation/cutting in African countries, from SDG 5, on Gender Equality. We conducted a qualitative online survey to collect users evaluations, through informational tasks, quality ratings, and open-ended questions based on interaction with the maps. Results of this preliminary investigation suggest that though users are familiar and therefore more comfortable with choropleth maps, they interpreted thematic map types differently. Specifically, the relative novelty and unfamiliarity of the distorted geometry of cartograms and tile maps may have caused users to engage more thoughtfully with the visualized data and in the cartogram and tile map which are generally considered non-standard thematic maps.

This paper evaluates the potential of using cartograms for visualizing and interpreting forecasts of weather-driven natural hazards in the context of global weather forecasting and early warning systems. The use of cartograms is intended to supplement traditional cartographic representations of the hazards in order to highlight the severity of an upcoming event. Cartogrammetric transformations are applied to forecasts of floods, heatwaves, windstorms and snowstorms taken from the European Centre for Medium-range Weather Forecasts (ECMWF) forecast archive. Key cartogram design principles in standard weather forecast visualization are tested. Optimal cartogram transformation is found to be dependent on geographical features (such as coastlines) and forecast features (such as snowstorm intensity). For highly spatially autocorrelated weather variables used in analysing several upcoming natural hazards such as 2m temperature anomaly, the visualization of the distortion provides a promising addition to standard forecast visualizations for highlighting upcoming weather-driven natural hazards.

Qualitative land accounting plays an important role in the efficient use of agricultural land, the targeted placement of crops and the imposition of taxes on land users. Today, the quality of irrigated agricultural land shows the use of traditional methods in determining, assessing and mapping is inefficient in terms of time and cost. This, in turn, increases the need for fast, resource-efficient and science-based methods of modern geographic information system (GIS) technologies to address these issues. This article describes the results of scientific research on the compilation of histogram maps of soil quality indicators and geostatistical analysis using GIS technologies to determine the quality of irrigated agricultural lands. Hereby, the quality of soils was mapped in an automated system using the method of quality colors, the results of geostatistical analysis were converted into cartographic data and a new scale of values was developed. Geostatic analysis was performed in ArcGIS based on agrochemical cartogram data of land contours.

In this chapter, a conceptual triangular-plot model is introduced to discuss how maps vary according to two parameters that we consider important to map literacy and to the distribution of map-reading knowledge and skills. The graphic is an upright equilateral triangle. The first parameter represents a map’s position on a continuum from purely locational information on the left to purely thematic information on the right. The second parameter, which represents the level (a judgment) of the map’s generalization and distortion, positions the map vertically in the triangle.

Unfamiliar or esoteric visual forms arise in many areas of visualization. While such forms can be intriguing, it can be unclear how to make effective use of them without long periods of practice or costly user studies. In this work we analyze the table cartogram-a graphic which visualizes tabular data by bringing the areas of a grid of quadrilaterals into correspondence with the input data, like a heat map that has been "area-ed" rather than colored. Despite having existed for several years, little is known about its appropriate usage. We mend this gap by using Algebraic Visualization Design to show that they are best suited to relatively small tables with ordinal axes for some comparison and outlier identification tasks. In doing so we demonstrate a discount theory-based analysis that can be used to cheaply determine best practices for unknown visualizations., Comment: EuroVis Camera Ready. 16 Pages, 19 Figures, including appendix

Background: For effective allocations of limited human resources, it is significant to have accurate estimates of future elderly care demands at the regional level, especially in areas where aging and population decline vary by region, such as Hokkaido prefecture in Japan.Objectives: The present study aimed to estimate the numbers of short-stay service recipients in all administrative units in Hokkaido from 2020 to 2045 with the machine learning approaches and reviewed the changing trends of spatial distributions of the service recipients with cartograms.Methods: A machine learning approach was used for the estimation. To develop the model to estimate, population data in Japan from 2015 to 2017 were used as input signals, whereas data on the numbers of short-stay service recipients at each level of needs for long-term care (levels 1–5) from 2015 to 2017 were used as a supervisory signal. Three models were developed to avoid problems of repeatability. Then, data of the projected population in Hokkaido every 5 years from 2020 to 2045 were fed into each model to estimate the numbers of the service recipients for the 188 administrative units of Hokkaido. The medians of the estimations from the models were considered as the final results; the estimates for 188 administrative units were presented with continuous area cartograms on the map of Hokkaido.Results: The developed models predicted that the number of the service recipients in Hokkaido would peak at 18,016 in 2035 and the number of people at level 3 in particular would increase. The cartograms for levels 2 and 3 from 2020 to 2030 and level 3 for 2035 were heavily distorted in the populated areas in Hokkaido.Discussion: The large correlation coefficients indicated the accuracy of estimations by the developed models. The growing number of the service recipients especially at level 3 by 2035 was assumed to be related to aging of the first baby boomers in Japan. The distortions of the cartograms suggested that the majority of the service recipients would be concentrated in the populated areas in Hokkaido. Future allocations of human resources were discussed on the basis of the findings.

We investigate the memorability of two types of cartograms, both in terms of recognition of the visualization and recall of the data. A cartogram, or a value-by-area map, is a representation of a map in which geographic regions are modified to reflect a given statistic, such as population or income. Of the many different types of cartograms, the contiguous and Dorling types are among the most popular and most effective. With this in mind, we evaluate the memorability of these two cartogram types with a human-subjects study, using task-based experimental data and cartogram visualization tasks based on Bertin's map reading levels. In particular, our results indicate that Dorling cartograms are associated with better recall of general patterns and trends. This, together with additional significant differences between the two most popular cartogram types, has implications for the design and use of cartograms, in the context of memorability.

The paper presents the designing and development of the Atlas Information System (AIS) of hazardous hydrometeorological events (HHME) in the Ural Prikamye region. AIS integrates classic mapping approaches and modern web mapping service technologies. AIS information basis includes several data sources, both ground-based and satellite observations. The basic techniques and algorithms for mapping of HHME spatiotemporal distribution and the main AIS content are briefly described. Examples are provided of periodicity and intensity mapping of various HHME types, as well as zoning results of the study area in terms of prevailing types of hazardous weather events. The AIS content functionality is considered, including various techniques of data visualization, connection to external databases, search and query generation, building of cartograms and structural diagrams. AIS is published in open access as cartographic web map service (http://ais.maps.psu.ru). The main result of the project for the Perm region is the development of the unique reference and information cartographic resource on the current climatic conditions of the region, its typical HHME, their spatiotemporal distribution, as well as HHME-related damage.

We describe bivariate cartograms , a technique specifically designed to allow for the simultaneous comparison of two geo-statistical variables. Traditional cartograms are designed to show only a single statistical variable, but in practice, it is often useful to show two variables (e.g., the total sales for two competing companies) simultaneously. We illustrate bivariate cartograms using Dorling-style cartograms, yet the technique is simple and generalizable to other cartogram types, such as contiguous cartograms, rectangular cartograms, and non-contiguous cartograms. An interactive feature makes it possible to switch between bivariate cartograms, and the traditional (monovariate) cartograms. Bivariate cartograms make it easy to find more geographic patterns and outliers in a pre-attentive way than previous approaches, as shown in Fig. 2 . They are most effective for showing two variables from the same domain (e.g., population in two different years, sales for two different companies), although they can also be used for variables from different domains (e.g., population and income). We also describe a small-scale evaluation of the proposed techniques that indicates bivariate cartograms are especially effective for finding geo-statistical patterns, trends and outliers.

The article provides an overview of the features of the Magrit web application: a free online thematic mapping tool, presenting a strong pedagogical dimension and making possible to mobilize all the elements necessary for the realization of a thematic map. In this tool, several simple modes of representation are proposed such as proportional maps or choropleth maps. Other, more complex modes are also available such as smoothed maps and cartograms. Each map can be finalized thanks to layout and customization features (projection, scale, orientation, toponyms, etc.) and exported in vector format. Magrit is therefore a complete, light and versatile tool particularly adapted to cartography teaching at the university.

The value-by-alpha map is a recently proposed method for mapping bivariate spatial information. It is theoretically advantageous, but no thorough evaluations have yet been reported. Here we conducted a systematic evaluation of its usability in terms of effectiveness, efficiency and satisfaction. Major conclusions from this study are the following: (1) value-by-alpha maps are as effective and as efficient as area cartograms in bivariate mapping, but are generally less effective and efficient than bivariate proportional symbol maps, and (2) in terms of satisfaction, value-by-alpha maps are as popular as bivariate proportional symbol maps and are more popular than bivariate area cartograms.

A travel-time cartogram is an effective method for representing travel time distances from a given point to the other points on a map and the geographic space is deformed accordingly. Compared with other map representations, users can identify travel-time distances on travel-time cartograms more easily because of the geometric deformations according to travel time. However, there are challenges when generating travel-time cartograms, including inconsistent map scales, topological errors and a lack of spatial deformation visualization. In this paper, we suggest a framework for addressing these challenges. More specifica lly, we propose: (1) three design principles to keep the scale of the transformed map the same with its original map; (2) a number of constraints to adjust topological errors generated by the process of transformation based on Moving Least Squares (MLS); and (3) 2-D and 3-D visualization methods to represent travel-time cartograms and their deformation. We use the travel time of trains from Munich to other selected cities in Bavaria as a case study. The results show that our method is applicable and the visualizations depict the time distance relationship between Munich and other cities from different perspectives.

A planar cartogram is a two-dimensional map, on which the area of each closed region is in direct proportion to a chosen extensive property. To date, various algorithms have been proposed to construct planar cartograms. This work extends the two-dimensional, diffusion-based, topologically invariant cartogram algorithm proposed by Gastner and Newman onto spheres. Unlike its planar counterpart, the spherical formulation does not require boundary conditions and is invariant to the rotation of input data on the sphere. An implementation of this spherical cartogram transformation is designed to generate readable topology-preserving cartograms on spheres. Lastly, the method is illustrated with applications to global data such as worldwide human population, gross domestic product (purchasing power parity), carbon dioxide emissions and regional data such as the Electoral College of the United States presidential election of 2016.

Proportional circle maps are a popular method for visualizing quantitative data on a map. Circles are scaled proportionally based on the data provided; larger circles represent larger quantities. The circles require two values, a location and a numeric quantity. For data that have a wide range of values, the resulting map will produce clutter and overlap in which large symbols obscure the information contained in smaller circles. Some previous solutions to this problem are modifying and improving the contrast between symbols, or using stacking algorithms so all symbols are visible. This article proposes the displaced proportional symbol map, which displaces the symbol's location based on the amount of overlap between neighbouring circles. At the same time, it preserves the location of non-overlapping symbols, which distinguishes it from the circular cartogram. The displacement is automated through the proximity stress model algorithm for node overlap removal. This algorithm was originally designed for graph layouts with overlapping nodes, but was modified here for circular symbols and map layout. The result is a map with improved clarity and the ability to add labelling to a cluttered proportional circle map.

Rapid advancement of social media tremendously facilitates and accelerates the information diffusion among users around the world. How and to what extent will the information on social media achieve widespread diffusion across the world? How can we quantify the interaction between users from different geolocations in the diffusion process? How will the spatial patterns of information diffusion change over time? To address these questions, a dynamic social gravity model (SGM) is proposed to quantify the dynamic spatial interaction behavior among social media users in information diffusion. The dynamic SGM includes three factors that are theoretically significant to the spatial diffusion of information: geographic distance, cultural proximity, and linguistic similarity. Temporal dimension is also taken into account to help detect recency effect, and ground-truth data is integrated into the model to help measure the diffusion power. Furthermore, SocialWave, a visual analytic system, is developed to support both spatial and temporal investigative tasks. SocialWave provides a temporal visualization that allows users to quickly identify the overall temporal diffusion patterns, which reflect the spatial characteristics of the diffusion network. When a meaningful temporal pattern is identified, SocialWave utilizes a new occlusion-free spatial visualization, which integrates a node-link diagram into a circular cartogram for further analysis. Moreover, we propose a set of rich user interactions that enable in-depth, multi-faceted analysis of the diffusion on social media. The effectiveness and efficiency of the mathematical model and visualization system are evaluated with two datasets on social media, namely, Ebola Epidemics and Ferguson Unrest.

The development of precision farming technology requires a higher level of technical support based on programmable, fully autonomous or remotely controlled unmanned aerial systems that contain complexes of automatic or remotely controlled unmanned aerial vehicles (UAVs). The authors conducted selection and justification of the main parameters of the UAV for agricultural purposes. For variable rate application of plant protection products and fertilizers the agrarians prefer UAVs of reusable, non-aerodrome basing, with small take-off for takeoff or vertical take-off and vertical landing, low-altitude, helicopter, rotary-wing and multi-rotor types equipped with an autopilot and a system for differentiating the distribution of fertilizer working fluids and pesticides for a set program, developed in accordance with the agrochemical cartogram and field phytosanitary condition. The equation of mass balance of UAV of agricultural purpose is made, which allows more precisely to determine the take-off weight taking into account the constituent masses of the payload intended for differentiated dispensing and distribution of working fluids of fertilizers and pesticides. The equation of UAV existence is obtained, which differs in that, in addition to the mass and flight-technical characteristics of the aircraft, it displays the technological parameters of differentiated application of pesticides and fertilizers for a particular field being treated. The technological process of UAV application in the system of precise farming includes sequential interrelated operations: monitoring and sounding of crops (using light UAVs equipped with multispectral cameras), obtaining, processing and transmitting information for crop management, differentiated application of pesticides and fertilizers according to a specified treatment program (UAV through a large payload).

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.

Cartograms are map-based data visualizations in which the area of each map region is proportional to an associated numeric data value (e.g., population or gross domestic product). A cartogram is called contiguous if it conforms to this area principle while also keeping neighboring regions connected. Because of their distorted appearance, contiguous cartograms have been criticized as difficult to read. Some authors have suggested that cartograms may be more legible if they are accompanied by interactive features (e.g., animations, linked brushing, or infotips). We conducted an experiment to evaluate this claim. Participants had to perform visual analysis tasks with interactive and noninteractive contiguous cartograms. The task types covered various aspects of cartogram readability, ranging from elementary lookup tasks to synoptic tasks (i.e., tasks in which participants had to summarize high-level differences between two cartograms). Elementary tasks were carried out equally well with and without interactivity. Synoptic tasks, by contrast, were more difficult without interactive features. With access to interactivity, however, most participants answered even synoptic questions correctly. In a subsequent survey, participants rated the interactive features as "easy to use" and "helpful." Our study suggests that interactivity has the potential to make contiguous cartograms accessible even for those readers who are unfamiliar with interactive computer graphics or do not have a prior affinity to working with maps. Among the interactive features, animations had the strongest positive effect, so we recommend them as a minimum of interactivity when contiguous cartograms are displayed on a computer screen., Comment: 18 pages, 5 figures. Supplemental material available by clicking on "Other formats". To be published in IEEE Transactions on Visualization and Computer Graphics

The current scenario of the pandemic COVID-19 has been a source of anchorage for researchers, healthcare professionals, and statisticians. Based on the immense data, it has been observed that the role of statistics has been crucial in researching and at the same for predicting the COVID-19 scenario of the entire globe. This paper deals with extensive data collection and predictive modeling to derive a CARD model using statistical tools like regression curve fitting. The exponential growth model has been prevalent in live updates via COVID-19 dashboards maintained by different organizations like WHO, Johns Hopkins University, Indian Council of Medical Research. In a similar tone, the paper discusses a time-varying exponential growth model specific to the Indian condition. However, a generic model has been derived by different researchers of other countries. The model accuracy has been considered satisfactory. Moreover, a State-wise Evaluation Indexing has been performed considering parameters like sanitation, population below the poverty line, literacy rate, and population density. Results have been shown for better data visualization through cartograms. The conclusions are noteworthy, and the CARD model can be trained and developed with better accuracy using the concept of machine and deep learning, keeping in context the huge amount of instantaneous data being generated every day all over the world.

Cartograms are maps in which the areas of regions (e.g. states, provinces) are rescaled to be proportional to statistical data (e.g. population size, gross domestic product). Cartograms are called “contiguous” if they maintain the topology of the conventional map (i.e. regions are displayed as neighbours on the cartogram if and only if they are geographic neighbours) [1]. An example of a contiguous cartogram, showing the 48 conterminous states of the USA with an area proportional to their population, is shown on the right of Figure 1. Such maps are an invaluable addition to a professional geographer’s toolbox. However, producing contiguous cartograms should not be the privilege of only a handful of experts in cartography. Journalists or bloggers, for example, may also benefit from a cartogram as an intriguing illustration of their own data. Similarly, high school students may enrich a term paper with a cartogram that can summarize data more effectively than raw numeric tables.Until now, the creation of contiguous cartograms has been far from user-friendly, requiring computer skills that even experts in data visualization typically do not possess. In the past, publications that introduced new cartogram algorithms rarely included computer code. Some authors of more recent publications have posted their code online [1,2], but their software usually requires technical knowledge (e.g. about shell scripting, compiling, GIS) that pose insurmountable obstacles for most users. To remove these hurdles, we have recently developed the web application go-cart.io [3] with an interface that is easy to use, even for non-experts.Over the past 15 years, several other applets have been posted on the worldwide web, but they either offer only a limited number of precomputed cartograms [4,5] or are no longer actively maintained [5–8]. In particular, the shift away from Java applets has made it challenging to run some of these legacy applications. This status quo has been against the current trend towards “citizen cartography”, mainly driven by online tools that enable even untrained users to produce maps from their own data. It has been shown that most users perceive contiguous cartograms, though potentially challenging to read, as an effective method to display data [9]. It is therefore timely to develop a new web interface that makes it easier to generate cartograms.While previous cartogram generators required users to install software (e.g. Java) on their computer, go-cart.io is based on JavaScript that can be run in any contemporary web browser without additional downloads. We decided to simplify the data input as much as possible. We have curated a “library” of topologies so that users do not need GIS expertise to create geospatial vector data. The entries in this library are currently limited to only a few countries split into administrative divisions (e.g. USA by state, China by province), but we will expand the selection over the coming months. We may also, at a later stage of the project, allow users to upload their own map data. Users can select a country from a dropdown menu (highlighted in Figure 1). Afterwards users specify the desired areas and colours for each region on the cartogram either by editing a spreadsheet in the browser or by uploading a CSV file.After data are transmitted, a remote server calculates the cartogram transformation with the recently developed fast flow-based algorithm [1]. Because the calculation is entirely server-side, we eliminate any dependence on the client’s hardware. We tested the application with various countries and input statistics. For typical input, the calculation finishes within 10 to 15 seconds. If the calculation needs substantially longer, the application displays a bar chart instead of a cartogram as a fallback. The cartogram is displayed in the browser window side by side with the conventional (i.e. equal-area) map (Figure 1). The user can explore both maps with various interactive features implemented using the D3.js library [10]:Linked brushing: when the mouse hovers over a region on the equal-area map, the corresponding region is highlighted on the cartogram and vice versa.Infotip: a text box containing the name and statistical data of the highlighted region appears above the map (Figure 1).Map switching: users can smoothly morph the image from equal-area map to cartogram and vice versa by clicking on the cartogram selector (Figure 1).Users can save all generated equal-area maps and cartograms as SVG vector image files and directly share them on social media (Figure 1). We are currently conducting evaluations to measure how effective the application is in allowing users to easily generate and analyse their own cartograms. Our initial results suggest that these features are well received by users. We believe that, with a user-friendly interface, contiguous cartograms have the potential to gain more popularity as an attractive and engaging method to visualize geographic data.

The paper presents a technique for efficient visualisation of election results in proportional electoral systems. Three cartographic methods (cartogram, inward-oriented buffer and proportional striping) are combined to produce a static map that gives an overview of the distribution of voting power, the electoral abstention and the election results. Unlike the conventional design that shows only the winning subjects, the proposed technique allows reader to analyse the results within a district as well as in the context of the whole country. Regional differences and patterns not present on conventional election maps can be observed. The proposed technique is demonstrated on a map of Slovak parliamentary election held in 2012.

Predicting the geographical distribution of a species is a central topic in ecology, conservation and management of natural resources especially for invasive organisms. Invasive species can modify the structure and function of invaded ecosystems, altering their biodiversity, and causing significant economic losses locally and globally. Therefore, measuring and visualizing the uncertainty inherent in species’ potential distributions is fundamental for effective biodiversity monitoring and planning conservation interventions. This paper discusses a new Bayesian approach to mapping this uncertainty using cartograms, previously published knowledge, and presence/absence data.

Cartograms are popular for visualizing numerical data for map regions. Maintaining correct adjacencies is a primary quality criterion for cartograms. When there are multiple data values per region (over time or different datasets) shown as animated or juxtaposed cartograms, preserving the viewer's mental-map in terms of stability between cartograms is another important criterion. We present a method to compute stable Demers cartograms, where each region is shown as a square and similar data yield similar cartograms. We enforce orthogonal separation constraints with linear programming, and measure quality in terms of keeping adjacent regions close (cartogram quality) and using similar positions for a region between the different data values (stability). Our method guarantees ability to connect most lost adjacencies with minimal leaders. Experiments show our method yields good quality and stability., Comment: Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)

This study assesses the usefulness of cartograms when visualizing extended Floating Car Data (xFCD). Cartograms deform regions in a map proportionally to assigned values. We apply this method for visualizing highresolution extended Floating Car Data (xFCD). Elaborating on this, we perform a case study in Mönchengladbach, Germany using 1.8 Million record points containing information about carbon dioxide (CO2) emissions based on an xFCD dataset. Utilizing a diffusion-based approach, we compute cartograms. Findings indicate a good suitability for identifying areas with a higher (or lower) average emission of CO2. We provide a documented workflow to compute cartograms based on parameters from an extended floating car dataset. The quality and spatial distribution of the basic dataset turns out to be important. Choosing the correct spatial subdivision of the research area as a basis for deforming areas is significant as it strongly influences the visual output.

The proper visualisation of a map is most important to provide information to the user community which is governed by the objective of mapping and accordingly the kind of cartographic techniques that should be applied to fulfil the requirement. This information should be recorded in various types of output in the form of maps and reports. After reading this chapter you should be able to understand the following: Meaning and process of visualisation Factors of geo-visualisation Geo-visualisation techniques GIS output by cartographic and non-cartographic methods

In applications such as VLSI floorplanning and cartogram design, vertices of a graph are represented by geometric objects and edges are captured by contacts between those objects, which are examples of a drawing style called contact graph representations. We study the feasibility of using line segments, triangles and tetrahedra to realize point-side contact representations for a number of graph classes including oriented versions of outerplanar graphs, 2-trees and 3-trees. Our main results show that every orientation of a maximal outerplanar graph of out-degree at most two, a 2-tree of out-degree at most two, and a planar 3-tree of out-degree at most four enjoy point-side contact representations using line segments, triangles, and tetrahedra, respectively. Unlike undirected graphs for which a fairly large amount of results can be found in the literature in the study of contact representations, directed graphs remain largely unexplored, and our study advances this line of research a step further.

When flooding occurs, people should be evacuated safely to designated shelters along the optimal routes to minimize serious damages on lives and properties. However, in general, only limited information related to evacuation procedures and using a directional arrow to indicate existing shelters is provided on the evacuation map. Moreover, the evacuation routes leading to nearby shelters are not presented effectively to people in an emergency situation. This paper aimed to provide an approach to generate a flood evacuation cartogram based on an actual evacuation. The proposed time&ndash, distance cartogram preserves the topological characteristics by minimizing distortion in transforming the evacuation routes. To empirically evaluate its application, we applied the proposed method to Siheung city in Korea. As a result, optimal shelter and evacuation routes were derived by considering significant factors influencing the actual access to the facilities. Moreover, the flood evacuation cartogram provides a more intuitive visualization than classic topographic maps, by relocating shelters and reshaping the routes intended for evacuation. The suggested method is significant as it provides practical flood evacuation information effectively and intuitively, and the generated cartograms as empirical results also provide helpful insights for more efficient evacuation plans.

Visual display is a technique that utilizes tools on the computer to explore and to present information. There are some variation of visual display methods that have been developed and widely used in the needs of geovisualization and cartography such us Parallel Coordinate Plot (PCP), Space Time Cube (STC), Self-Organize Map (SOM) and Cartogram. This research uses these methods includes definitions and functions, recommendations for using an application and their respective advantages and disadvantages. Applying the right visualization is based on the needs or goals of geovisualization because each visual display has unique characteristics.

We introduce an efficient algorithm for drawing spatially-informative linear cartograms: transforming a geometric network such that given edge lengths are realised, while distorting edge directions as little as possible. Our algorithm is based on carefully linearised least squares optimisation, forgoing the need for an iterative solver. This is fast and ensures a well-defined result. The classic application of linear cartograms is drawing travel-time maps; we also discuss drawing schematised metro maps.

Distance Cartograms (DC) distort geographical features so that the measured distance between a single location and any other location on a map indicates absolute travel time. Although studies show that users can efficiently assess travel time with DC, distortion applied in DC may confuse users, and its usefulness "in the wild" is unknown. To understand how real world users perceive DC's benefits and drawbacks, we devise techniques that improve DC's presentation (preserving topological relationships among map features while aiming at retaining shapes) and scalability (presenting accurate live travel time). We developed a DC-enabled system with these techniques, and deployed it to 20 participants for 4 weeks. During this period, participants spent, on average, more than 50% of their time with DC as opposed to a standard map. Participants felt DC to be intuitive and useful for assessing travel time. They indicated intent in adopting DC in their real-life scenarios.

The purpose of this article is to report a study aimed at systematic assessment of the functionality of commercially available software for the automatic generation of area cartograms. The issue of the wide choice of algorithms developed over the years for generating various types of surfaces has also been raised. Cartograms (called also anamorphic maps) are constructed by changing the surface area of each spatial unit in step with the corresponding value of the mapped thematic variable (area cartogram) or changing accordingly the distance between the preselected focal point and other points on the map (distance cartogram). Depending on the shape of mapping units, the following three types of area cartograms can be distinguished: proportional symbol cartograms were the original shapes of mapping units have been replaced with simple geometric shapes such as squares, rectangles or circles (for example, Dorling Circle Cartograms, square cartogram); continuous regular cartograms where the shapes of areal units on the map resemble the actual shapes of the mapped units but their boundaries have been geometrized to consist of perpendicular sections; continuous irregular cartograms where the shapes of areal units on the map resemble the actual shapes of the mapped units but unit boundaries are not straight lines. Cartograms can also be constructed to preserve spatial contiguity (continuous cartograms) or not (noncontinuous cartograms), with the latter often preserving the underlying neighborhood relationships to some degree. While constructing area cartogram, one needs to decide first the type of a surface to be developed, and therefore, the algorithm to be applied. The next step in map construction is the choice of software, where tool selection depends often on the predetermined type of the cartogram. The study surveyed five programs for the construction of area cartograms – all available free of charge. Each of those software tools was used to generate area cartograms portraying data from the 2010 presidential election in Poland. Two groups of area cartograms where generated for the purpose of this study: maps of the entire Poland by voivodships, showing the number of valid votes cast for the two presidential candidates in each voivodship, and maps of the Mazowieckie voivodship by county, portraying the number of valid votes cast for the individual candidates in each county. The subsequent in-depth assessment of surveyed programs took into account eleven criteria including the number of cartogram types that might be developed using each program, availability of tools for the proper legend construction and display, possibility of supplementing the cartogram with complementary choropleth maps, the option for inserting map labels, the type of spatial data that can be used in the software (reference to points, lines, polygons) and so on. The study has demonstrated that the tool included in the ArcGIS (Cartogram Utility for ArcGIS) best met the survey criteria scoring 9 points. The application Scape Toad placed second (7.5 pts.), while MapViewer 7 came third (6.25 pts.). When generating cartograms in the available GIS programs, one should also pay attention to the visual qualities of the generated maps, and in particular, to the resemblance of shapes of spatial units on the map to the their actual geographic boundaries. Since the shape outlines obtained on the map vary depending on the underlying geodetic reference system, the best coordinate system for the mapped area should be selected. However, if such system cannot be used within a given cartogram generating tool, then the obtained cartogram should be exported and refined with some general software package for graphic editing.

Large amounts of geo-referenced text information such as messages from microblog websites are continuously becoming more popular. In this paper, we introduce a new visualization method based on tag clouds for geo-referenced text information. We process large amounts of geo-referenced text, using several visual metaphors including tag clouds, for the exploration of information on maps, instead of using just conventional cartographic approaches. The results show that this method can be useful for presentation and exploration of such geo-referenced text information.

Significance Geographic maps are a popular means to visualize spatial statistics. Conventionally, each map region is displayed with an area proportional to the actual land area. But equal-area maps can grossly misrepresent demographic data: Densely populated cities should be given more prominence than large, but sparsely populated territories. Cartograms solve this problem by rescaling map regions in proportion to, for example, population or gross domestic products. Until now, it has generally been cumbersome or slow to calculate map projections for contiguous cartograms. Here we describe and benchmark a fast flow-based algorithm that computes cartograms in a matter of seconds, yet maintains the strengths of previous methods—a development which may lead to a more widespread adoption of cartograms., Cartograms are maps that rescale geographic regions (e.g., countries, districts) such that their areas are proportional to quantitative demographic data (e.g., population size, gross domestic product). Unlike conventional bar or pie charts, cartograms can represent correctly which regions share common borders, resulting in insightful visualizations that can be the basis for further spatial statistical analysis. Computer programs can assist data scientists in preparing cartograms, but developing an algorithm that can quickly transform every coordinate on the map (including points that are not exactly on a border) while generating recognizable images has remained a challenge. Methods that translate the cartographic deformations into physics-inspired equations of motion have become popular, but solving these equations with sufficient accuracy can still take several minutes on current hardware. Here we introduce a flow-based algorithm whose equations of motion are numerically easier to solve compared with previous methods. The equations allow straightforward parallelization so that the calculation takes only a few seconds even for complex and detailed input. Despite the speedup, the proposed algorithm still keeps the advantages of previous techniques: With comparable quantitative measures of shape distortion, it accurately scales all areas, correctly fits the regions together, and generates a map projection for every point. We demonstrate the use of our algorithm with applications to the 2016 US election results, the gross domestic products of Indian states and Chinese provinces, and the spatial distribution of deaths in the London borough of Kensington and Chelsea between 2011 and 2014.

The visualization of specific attributes of the maps is not achieved with standard maps representations or area cartograms. Adaptive Maps can deal with multiple attributes like travel time, quality of the road or tourism interest of the path between two points.

Cartogram drawing is a technique for showing geography-related statistical information, such as demographic and epidemiological data. The idea is to distort a map by resizing its regions according to a statistical parameter by keeping the map recognizable. This article describes an R package implementing an algorithm called RecMap which approximates every map region by a rectangle where the area corresponds to the given statistical value (maintain zero cartographic error). The package implements the computationally intensive tasks in C++. This paper's contribution is that it demonstrates on real and synthetic maps how package recmap can be used, how it is implemented and how it is used with other statistical packages., Journal of Statistical Software, 86, ISSN:1548-7660

The most important function of science of statistics is to simplify the complexity of quantitative data and to make them easily understandable. Numeric figures are usually avoided by common man, but pictures, diagrams, and graphs always attract our attention. Diagrams and graphs give a “birds’ eye view” to the entire mass of statistical data that have been collected about any hypothesis. Characteristics of diagrams and rules for drawing these have been discussed with limitations and use of these. There are a variety of diagrams like dimensional drawings, pictograms, cartograms, graphs, curves, and circles or pie diagrams, which have great utility in the presentation of data.