Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> Migration maps represent patterns of geographical movement by arrows or bands between places, using information arriving in “from-to” tables. In the most interesting cases the tables are of large size, suggesting that computer assistance would be useful in the preparation of the maps. A computer program prepared for this purpose shows that graphical representation is feasible for tables as large as fifty by fifty, and possibly larger. The program contains options for alternate forms of movement depiction, and rules are suggested for the parsing of migration tables prior to the cartographic display, without loss of spatial resolution. <s> BIB001 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> Cartographers have long used flow maps to show the movement of objects from one location to another, such as the number of people in a migration, the amount of goods being traded, or the number of packets in a network. The advantage of flow maps is that they reduce visual clutter by merging edges. Most flow maps are drawn by hand and there are few computer algorithms available. We present a method for generating flow maps using hierarchical clustering given a set of nodes, positions, and flow data between the nodes. Our techniques are inspired by graph layout algorithms that minimize edge crossings and distort node positions while maintaining their relative position to one another. We demonstrate our technique by producing flow maps for network traffic, census data, and trade data. <s> BIB002 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> The research reported here integrates computational, visual and cartographic methods to develop a geovisual analytic approach for exploring and understanding spatio-temporal and multivariate patterns. The developed methodology and tools can help analysts investigate complex patterns across multivariate, spatial and temporal dimensions via clustering, sorting and visualization. Specifically, the approach involves a self-organizing map, a parallel coordinate plot, several forms of reorderable matrices (including several ordering methods), a geographic small multiple display and a 2-dimensional cartographic color design method. The coupling among these methods leverages their independent strengths and facilitates a visual exploration of patterns that are difficult to discover otherwise. The visualization system we developed supports overview of complex patterns and through a variety of interactions, enables users to focus on specific patterns and examine detailed views. We demonstrate the system with an application to the IEEE InfoVis 2005 contest data set, which contains time-varying, geographically referenced and multivariate data for technology companies in the US <s> BIB003 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> Population mobility, i.e. the movement and contact of individuals across geographic space, is one of the essential factors that determine the course of a pandemic disease spread. This research views both individual-based daily activities and a pandemic spread as spatial interaction problems, where locations interact with each other via the visitors that they share or the virus that is transmitted from one place to another. The research proposes a general visual analytic approach to synthesize very large spatial interaction data and discover interesting (and unknown) patterns. The proposed approach involves a suite of visual and computational techniques, including (1) a new graph partitioning method to segment a very large interaction graph into a moderate number of spatially contiguous subgraphs (regions); (2) a reorderable matrix, with regions 'optimally' ordered on the diagonal, to effectively present a holistic view of major spatial interaction patterns; and (3) a modified flow map, interactively linked to the reorderable matrix, to enable pattern interpretation in a geographical context. The implemented system is able to visualize both people's daily movements and a disease spread over space in a similar way. The discovered spatial interaction patterns provide valuable insight for designing effective pandemic mitigation strategies and supporting decision-making in time-critical situations. <s> BIB004 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> Flow maps are thematic maps that visualize the movement of objects, such as people or goods, between geographic regions. One or more sources are connected to several targets by lines whose thickness corresponds to the amount of flow between a source and a target. Good flow maps reduce visual clutter by merging (bundling) lines smoothly and by avoiding self-intersections. Most flow maps are still drawn by hand and only few automated methods exist. Some of the known algorithms do not support edge-bundling and those that do, cannot guarantee crossing-free flows. We present a new algorithmic method that uses edge-bundling and computes crossing-free flows of high visual quality. Our method is based on so-called spiral trees, a novel type of Steiner tree which uses logarithmic spirals. Spiral trees naturally induce a clustering on the targets and smoothly bundle lines. Our flows can also avoid obstacles, such as map features, region outlines, or even the targets. We demonstrate our approach with extensive experiments. <s> BIB005 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> In this paper, we present a novel approach for constructing bundled layouts of general graphs. As layout cues for bundles, we use medial axes, or skeletons, of edges which are similar in terms of position information. We combine edge clustering, distance fields, and 2D skeletonization to construct progressively bundled layouts for general graphs by iteratively attracting edges towards the centerlines of level sets of their distance fields. Apart from clustering, our entire pipeline is image-based with an efficient implementation in graphics hardware. Besides speed and implementation simplicity, our method allows explicit control of the emphasis on structure of the bundled layout, i.e. the creation of strongly branching (organic-like) or smooth bundles. We demonstrate our method on several large real-world graphs. <s> BIB006 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> Many origin-destination datasets have become available in the recent years, e.g. flows of people, animals, money, material, or network traffic between pairs of locations, but appropriate techniques for their exploration still have to be developed. Especially, supporting the analysis of datasets with a temporal dimension remains a significant challenge. Many techniques for the exploration of spatio-temporal data have been developed, but they prove to be only of limited use when applied to temporal origin-destination datasets. We present Flowstrates, a new interactive visualization approach in which the origins and the destinations of the flows are displayed in two separate maps, and the changes over time of the flow magnitudes are represented in a separate heatmap view in the middle. This allows the users to perform spatial visual queries, focusing on different regions of interest for the origins and destinations, and to analyze the changes over time provided with the means of flow ordering, filtering and aggregation in the heatmap. In this paper, we discuss the challenges associated with the visualization of temporal origin-destination data, introduce our solution, and present several usage scenarios showing how the tool we have developed supports them. <s> BIB007 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> We explore the potential of applying graph theory measures of centrality to the network of movements extracted from sequences of georeferenced photo captures in order to identify interesting places and explore city structure. We adopt a systematic procedure composed of a series of stages involving the combination of computational methods and interactive visual analytics techniques. The approach is demonstrated using a collection of Flickr photos from the Seattle metropolitan area. <s> BIB008 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> Movement data (trajectories of moving agents) are hard to visualize: numerous intersections and overlapping between trajectories make the display heavily cluttered and illegible. It is necessary to use appropriate data abstraction methods. We suggest a method for spatial generalization and aggregation of movement data, which transforms trajectories into aggregate flows between areas. It is assumed that no predefined areas are given. We have devised a special method for partitioning the underlying territory into appropriate areas. The method is based on extracting significant points from the trajectories. The resulting abstraction conveys essential characteristics of the movement. The degree of abstraction can be controlled through the parameters of the method. We introduce local and global numeric measures of the quality of the generalization, and suggest an approach to improve the quality in selected parts of the territory where this is deemed necessary. The suggested method can be used in interactive visual exploration of movement data and for creating legible flow maps for presentation purposes. <s> BIB009 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> The analysis of time-dependent data is an important task in various application domains. Often, the analyzed data objects belong to groups. The group memberships may stem from natural arrangements (e.g., animal herds), or may be constructed during analysis (e.g., by clustering). Group membership may change over time. Therefore, one important analytical aspect is to examine these changes (e.g., which herds change members and when). In this paper, we present a technique for visual analysis of group changes over time. We combine their visualization and automatic analysis. Interactive functions allow for tracking the data changes over time on group, set and individual level. We also consider added and removed objects (e.g., newly born or died animals). For large time series, automatic data analysis selects interesting time points and group changes for detailed examination. We apply our approach on the VAST 2008 challenge data set revealing new insights. <s> BIB010 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Tracing flows <s> Continuing advances in modern data acquisition techniques result in rapidly growing amounts of geo-referenced data about moving objects and in emergence of new data types. We define episodic movement data as a new complex data type to be considered in the research fields relevant to data analysis. In episodic movement data, position measurements may be separated by large time gaps, in which the positions of the moving objects are unknown and cannot be reliably reconstructed. Many of the existing methods for movement analysis are designed for data with fine temporal resolution and cannot be applied to discontinuous trajectories. We present an approach utilising Visual Analytics methods to explore and understand the temporal variation of spatial situations derived from episodic movement data by means of spatio-temporal aggregation. The situations are defined in terms of the presence of moving objects in different places and in terms of flows (collective movements) between the places. The approach, which combines interactive visual displays with clustering of the spatial situations, is presented by example of a real dataset collected by Bluetooth sensors. <s> BIB011
In the previous section, we have considered spatial aggregation of movement data by locations (space compartments). Another way of spatial aggregation is by pairs of locations: for two locations A and B, the moves (transitions) from A to B are summarized. This can result in such aggregate attributes as number of transitions, number of different objects that moved from A to B, statistics of the speed, transition duration, and so on. The term 'flow' is often used to refer to aggregated movements between locations. The respective amount of movement (i.e. count of moving objects or count of transitions) may be called 'flow magnitude'. There are two possible ways to aggregate trajectories into flows. Assuming that each trajectory represents a full trip of a moving object from some origin to some destination, the trajectories can be aggregated by origin-destination pairs, ignoring the intermediate locations. A well-known representation of the resulting aggregates is origin-destination (OD) matrix, where the rows and columns correspond to the locations and the cells contain aggregate values. OD matrices are often represented graphically as matrices with shaded or coloured cells. The rows and columns can be automatically or interactively reordered for uncovering connectivity patterns such as clusters of strongly connected locations and 'hubs', that is locations strongly connected to many others. BIB004 A disadvantage of the matrix display is the lack of spatial context. Guo et al. BIB003 use multiple small maps each showing flows to/from one place by colouring or shading the other places according to the respective flow magnitudes. The maps are arranged similarly to the relative positions of the places in the geographical space. Wood et al.   devised an algorithm to generate so-called OD maps, in which multiple OD matrices are arranged according to the geographic positions of the places. Another way to visualize flows is a flow map, in which flows are represented by straight or curved lines or arrows connecting locations; the flow magnitudes are represented by proportional widths and/or colouring or shading of the symbols.  BIB001 As lines or arrows may connect not only neighbouring locations but any two locations at any distance, massive intersections and occlusions of the flow symbols may occur, which makes the map illegible. Several approaches have been suggested for reducing the display clutter. The simplest are filtering BIB001 or reducing the opacity of lesser flows,  but these involve a great deal of information loss. Approaches involving edge bundling BIB002 BIB005 BIB006 work well only for showing flows from one or two locations or in special cases, for example when radial flows from/ to one location prevail over all others. BIB006 Moreover, edge bundling on a map representing geographical rather than abstract space introduces undesired geographical artefacts: bundled edges can give a misleading impression of arterial roads that do not exist in reality. Boyandin et al.  remove the middle parts of the lines connecting the places and colour the remaining starting and ending segments of the lines in two different colours. This reduces the clutter but the flows may not be easy to trace. Boyandin et al. BIB007 use a display with two maps and a table between them. Each row in the table corresponds to one place. Lines representing flows are drawn not between places within a map but between places in the maps and rows in the table. The left and right parts of the display show the out-and ingoing flows, respectively. The rows of the table contain visual representations of the time series of the flow magnitudes. The information content of the display is very high, but the spatial patterns of the flows can hardly be perceived. There is currently no universally good solution for visualizing arbitrary origin-destination flows. Vrotsou et al. BIB008 consider aggregated movement data as a weighted, directed graph in which vertices are the places and arcs are the flows. They compute various centrality measures for the graph vertices, which may be a valuable addition to the other place-related statistics such as counts of visits. The measures are visualised on maps, for example by colouring or shading of the places, but this does not show the connections between the places. The other possible way of transforming trajectories to flows is to represent each trajectory as a sequence of transitions between all visited locations along the path and aggregate the transitions from all trajectories. Movement data that have sufficiently fine temporal granularity or that allow interpolation between known positions may be aggregated so that only neighbouring locations (adjacent spatial compartments) are linked by flows. Such flows can be represented on a flow map without intersections and occlusions of the flow symbols. When there are no predefined locations or space partitioning, the space can be tessellated into larger or smaller compartments to achieve higher or lower degrees of generalization and abstraction. BIB009 This is illustrated in Figure 7 (a) and (b). The same trajectories of ships have been aggregated into flows using finer (a) and coarser (b) territory tessellations. The flows are represented by 'half-arrow' symbols, as suggested by Tobler, BIB001 to distinguish flows between the same locations in the opposite directions. Minor flows (below 20 individual moves) have been hidden to improve the display legibility. The flow maps exhibit the major traffic lanes, which were also visible in the visualization of the original trajectories (Figure 3(a) ) and in the density map ( Figure 5(a) ). However, the movement directions are visible only on the flow maps, and the intensity of the traffic can be judged from the widths of the flow symbols. The territory divisions demonstrated in Figure 7 (a) and (b) result from a method that accounts for the spatial distribution of characteristic points extracted from trajectories. BIB009 It uses a special algorithm for spatial clustering of points that produces clusters of userspecified spatial extent (radius). The geographic or gravity centres of the clusters are then used as generating points for Voronoi tessellation. Depending on the chosen radius, the data can be aggregated at different spatial scales. When movement data are aggregated into flows by time intervals, the result is time series of flow magnitudes. These can be visualized by animated flow maps or by combining flow maps with temporal displays (e.g. Ref. 57) . Flows may be clustered by similarity of the respective time series and the temporal variation analysed cluster-wise, as was suggested for time series of presence indicators in the previous section. Complementarily, time intervals can be clustered by similarity of the spatial situations in terms of flows. BIB011 Bremm at al. BIB010 suggest a visualization technique showing temporal variation of object presence at different locations and flows between the locations on a particular kind of temporal display where the locations are represented by distinct colouring (this can work well for a relatively small number of different locations). The technique is demonstrated in Figure 7(d) ; the map in Figure 7 (c) shows the territory division and colours of the areas that are used in Figure 7 (d). To build this display, the trajectories of the ships have been aligned in time to a common starting time, as mentioned in the 'Transforming times in trajectories' section. Then the transformed time has been divided into hourly intervals. For each time interval, the display contains a bar divided into coloured segments proportionally to the number of moving objects that visited the areas in this interval. Grey is used for unknown positions. In this particular example, grey segments represent the trajectories that ended before the respective time intervals. Aggregated transitions between the areas are represented by bands drawn between the bars. The widths of the bands are proportional to the counts of the objects that moved. Gradient colouring is applied to the bands so that the left end is painted in the colour of the origin area and the right end in the colour of the destination area, or in grey for the trajectories that ended. By interacting with the display, it is possible to explore not only direct transitions between areas but also longer sequences of visited areas. When the user clicks on a bar segment, the movements of the corresponding subset of objects are highlighted in the display (i.e. shown by brighter colours). This is illustrated in Figure 7(d) . By clicking on the green segment of the fifth bar, the user has selected the subset of ships that were in the area of Amsterdam in the fifth hour since the beginning of their movement. We can see the previous and past locations of the selected ships and when the transitions occurred. Analogously, the user can click on a band connecting segments to select the objects participating in the respective transitions and trace their movements.