Visual analytics of movement: An overview of methods, tools and procedures <s> Looking inside trajectories: attributes, events and patterns <s> At the end of the sixties Hagerstrand introduced a space-time model which included features such as a Space-TimePath, and a Space-Time-Prism. His model is often seen as the start of the time-geography studies. Throughout the years his model has been applied and improved to understand our movements through space. Problems studied can be found in different fields of geography, and range from those on an individual movement to whole theories to optimize transportation. From a visualization perspective the Space-Time-Cube was the most prominent element in Hagerstrand’s approach. In its basic appearance these images consist of a cube with on its base a representation of geography (along the x- and y-axis), while the cube’s height represents time (z-axis). A typical Space-Time-Cube could contain the space time-paths of for instance individuals or bus routes. However, when the concept was introduced the options to create the graphics were limited to manual methods and the user could only experience the single view created by the draftsperson. An alternative view on the cube would mean to go through a laborious drawing exercise. Today’s software has options to automatically create the cube and its contents from a database. Data acquisition of space-time paths for both individuals and groups is also made easier using GPS. Today, the user’s viewing environment is, by default, interactive and allows one to view the cube from any direction. In this paper an extended interactive and dynamic visualization environment is proposed, and demonstrated, in which the user has full flexibility to view, manipulate and query the data in a Space-Time-Cube. Included are options to move slider planes along each of the axes to for instance select, or highlight a period in time or location in space. Examples will be discussed in which the time axis is manipulated by for instance changing world time for event time (time cartograms). Creativity should not stop here since it has been shown that especially an alternative perspective on the data will sparkle the mind with new ideas. The user should be allowed to for instance let the x- and/or y-axis be represented by other variables of the theme studied. Since the cube is seen as an integral part of a geovisualization environment the option to link other views with other graphic representation does exist. <s> BIB001 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Looking inside trajectories: attributes, events and patterns <s> Abstract To be able to explore visually large amounts of movement data, it is necessary to apply methods for aggregation and summarisation of the data. The goal of our research has been to systemize the possible approaches to aggregation of movement data into a framework clearly defining what kinds of exploratory tasks each approach is suitable for. On the basis of a formal model of movement of multiple entities, we consider two possible views of movement data, situation-oriented and trajectory-oriented. For each view, we discuss the appropriate methods of data aggregation and the visualisation techniques representing the results of aggregation and supporting data exploration. Special attention is given to dynamic aggregation working in combination with interactive filtering and classification of movement data (CR categories and subject descriptors: H.1·2 [user/machine systems]: human information processing - visual analytics; I.6·9 [visualisation]: information visualisation). <s> BIB002 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Looking inside trajectories: attributes, events and patterns <s> We propose a visual analytics procedure for analyzing movement data, i.e., recorded tracks of moving objects. It is oriented to a class of problems where it is required to determine significant places on the basis of certain types of events occurring repeatedly in movement data. The procedure consists of four major steps: (1) event extraction from trajectories; (2) event clustering and extraction of relevant places; (3) spatio-temporal aggregation of events or trajectories; (4) analysis of the aggregated data. All steps are scalable with respect to the amount of the data under analysis. We demonstrate the use of the procedure by example of two real-world problems requiring analysis at different spatial scales. <s> BIB003 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Looking inside trajectories: attributes, events and patterns <s> In this paper, we present an interactive visual analytics system, Triple Perspective Visual Trajectory Analytics (TripVista), for exploring and analyzing complex traffic trajectory data. The users are equipped with a carefully designed interface to inspect data interactively from three perspectives (spatial, temporal and multi-dimensional views). While most previous works, in both visualization and transportation research, focused on the macro aspects of traffic flows, we develop visualization methods to investigate and analyze microscopic traffic patterns and abnormal behaviors. In the spatial view of our system, traffic trajectories with various presentation styles are directly interactive with user brushing, together with convenient pattern exploration and selection through ring-style sliders. Improved ThemeRiver, embedded with glyphs indicating directional information, and multiple scatterplots with time as horizontal axes illustrate temporal information of the traffic flows. Our system also harnesses the power of parallel coordinates to visualize the multi-dimensional aspects of the traffic trajectory data. The above three view components are linked closely and interactively to provide access to multiple perspectives for users. Experiments show that our system is capable of effectively finding both regular and abnormal traffic flow patterns. <s> BIB004 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Looking inside trajectories: attributes, events and patterns <s> The analysis of trajectories has become an important field in geographic visualization, as cheap GPS sensors have become commonplace and, in many cases, valuable information can be derived either from the data themselves or their metadata if processed and visualized in the right way. However, showing the "right" information to highlight dependencies or correlations between different measurements remains a challenge, because the technical intricacies of applying a combination of automatic and visual analysis methods prevents the majority of domain experts from analyzing and exploring the full wealth of their movement data. This paper presents an exploration through enrichment approach, which enables iterative generation of metadata based on exploratory findings and is aimed at enabling domain experts to explore their data beyond traditional means. <s> BIB005 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Looking inside trajectories: attributes, events and patterns <s> Current tracking technologies enable collection of data, describing movements of various kinds of objects, including people, animals, icebergs, vehicles, containers with goods and so on. Analysis of movement data is now a hot research topic. However, most of the suggested analysis methods deal with movement data alone. Little has been done to support the analysis of movement in its spatio-temporal context, which includes various spatial and temporal objects as well as diverse properties associated with spatial locations and time moments. Comprehensive analysis of movement requires detection and analysis of relations that occur between moving objects and elements of the context in the process of the movement. We suggest a conceptual model in which movement is considered as a combination of spatial events of diverse types and extents in space and time. Spatial and temporal relations occur between movement events and elements of the spatial and temporal contexts. The model gives a ground to a generic approach based on extraction of interesting events from trajectories and treating the events as independent objects. By means of a prototype implementation, we tested the approach on complex real data about movement of wild animals. The testing showed the validity of the approach. <s> BIB006 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Looking inside trajectories: attributes, events and patterns <s> In previous work, we have proposed a tool for Spatiotemporal Pattern Query. It matches individual moving object trajectories against a given movement pattern. For example, it can be used to find the situations of Missed Approach in ATC data (Air Traffic Control systems, used for tracking the movement of aircrafts), where the landing of the aircraft was interrupted for some reason. This tool expresses the pattern as a set of predicates that must be fulfilled in a certain temporal order. It is implemented as a Plugin to the Secondo DBMS system. Although the tool is generic and flexible, domain expertise is required to formulate and tune queries. The user has to decide the set of predicates, their arguments, and the temporal constraints that best describe the pattern. This paper demonstrates a novel solution where a Visual Analytics system, V-Analytics, is used in integration with this query tool to help a human analyst explore such patterns. The demonstration is based on a real ATC data set. <s> BIB007 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Looking inside trajectories: attributes, events and patterns <s> Movement data link together space, time, and objects positioned in space and time. They hold valuable and multifaceted information about moving objects, properties of space and time as well as events and processes occurring in space and time. We present a conceptual framework that describes in a systematic and comprehensive way the possible types of information that can be extracted from movement data and on this basis defines the respective types of analytical tasks. Tasks are distinguished according to the type of information they target and according to the level of analysis, which may be elementary (i.e. addressing specific elements of a set) or synoptic (i.e. addressing a set or subsets). We also present a taxonomy of generic analytic techniques, in which the types of tasks are linked to the corresponding classes of techniques that can support fulfilling them. We include techniques from several research fields: visualization and visual analytics, geographic information science, database technology, and data mining. We expect the taxonomy to be valuable for analysts and researchers. Analysts will receive guidance in choosing suitable analytic techniques for their data and tasks. Researchers will learn what approaches exist in different fields and compare or relate them to the approaches they are going to undertake. <s> BIB008 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Looking inside trajectories: attributes, events and patterns <s> Visualizing trajectory attribute data is challenging because it involves showing the trajectories in their spatio-temporal context as well as the attribute values associated with the individual points of trajectories. Previous work on trajectory visualization addresses selected aspects of this problem, but not all of them. We present a novel approach to visualizing trajectory attribute data. Our solution covers space, time, and attribute values. Based on an analysis of relevant visualization tasks, we designed the visualization solution around the principle of stacking trajectory bands. The core of our approach is a hybrid 2D/3D display. A 2D map serves as a reference for the spatial context, and the trajectories are visualized as stacked 3D trajectory bands along which attribute values are encoded by color. Time is integrated through appropriate ordering of bands and through a dynamic query mechanism that feeds temporally aggregated information to a circular time display. An additional 2D time graph shows temporal information in full detail by stacking 2D trajectory bands. Our solution is equipped with analytical and interactive mechanisms for selecting and ordering of trajectories, and adjusting the color mapping, as well as coordinated highlighting and dedicated 3D navigation. We demonstrate the usefulness of our novel visualization by three examples related to radiation surveillance, traffic analysis, and maritime navigation. User feedback obtained in a small experiment indicates that our hybrid 2D/3D solution can be operated quite well. <s> BIB009
The methods described in the previous section deal with trajectories as wholes, that is they treat them as atomic objects. Here we consider the methods operating on the level of points and segments of trajectories. Such methods visualize and analyse the variation of movement characteristics and other dynamic attributes associated with trajectory positions or segments. These may be existing (measured) attributes or attributes derived from the position records (i.e. coordinates and times). Derived attributes may express instant, interval and cumulative characteristics of the movement. BIB003 Instant movement characteristics include instant speed, direction, acceleration (change of speed) and turn (change of direction). Interval characteristics are computed for time intervals of a chosen constant length before, after or around a given time moment. They include travelled distance, displacement, average speed, sinuosity and tortuosity, as well as statistics of the instant characteristics. Cumulative characteristics are computed for the interval from the start of the trajectory to a given time moment or for the remaining interval to the end of the trajectory. The most obvious way to visualize position-related attributes is by dividing the lines or bands representing trajectories on a map or in a 3D display into segments and varying the appearance of these segments. Attribute values can be represented by colouring or shading of the segments BIB004  BIB005 or by symbols (glyphs) drawn on the segments.  Spretke et al. BIB005 suggest an interactive tool for segmenting trajectories by dividing ranges of one or more position-related attributes into suitable intervals. Furthermore, clustering may be applied to join adjacent segments with similar characteristics. This allows the user to detect and locate different movement behaviours, for example day migration, night migration and stopovers of migrating birds. These behaviours are shown by different colouring of line segments on a map. Kraak and Huisman 26 use STC to visualize not only known spatio-temporal positions of moving objects but also space-time prisms, that is sets of positions that could potentially be visited by the objects during the time intervals between the known positions. The space-time prisms are computed taking into account the maximal possible speeds of the objects and visualized as volumes (3D bodies) in the STC. Representing dynamic attributes of trajectories on a map or in an STC may be ineffective because of display clutter and occlusions, especially when trajectories or their parts overlap in space. Therefore, position-related dynamic attributes are often visualized using additional displays. A time graph, also known as line chart, can be used for visualizing temporal variation of attribute values. BIB001  One dimension (usually horizontal) of such a graph represents time and the other dimension is used for representing attribute values by positions. Each trajectory is represented by a curve or polygonal line. Wö rner and Ertl 28 suggest a display which is similar to a time graph except that the base dimension represents space rather than time. This is possible for movements along a standard route, for example movements of public transport vehicles. A time graph or a 'route graph' representing multiple trajectories can suffer from visual clutter and overlapping of lines. To avoid overlapping, the idea of stacking is often used:  BIB006 BIB009 trajectories are represented by bars or bands stacked within a temporal or spatial display. The bars or bands are divided into segments, which are coloured according to values of some dynamic attributes. Examples are shown in Figure  3 (a) and (c). Figure 3 (a) demonstrates a time bars display in which the horizontal dimension represents time. Each trajectory is represented by a horizontal bar such that the horizontal position and length of the bar correspond to the start time and duration of the trajectory. The vertical dimension of the display is used to arrange the bars, which can be sorted based on one or more attributes of the trajectories (start time in our example). Colouring of bar segments encodes values of some user-selected dynamic attribute associated with the positions in the trajectories. This may be an existing attribute or an attribute derived 'on the fly' from the position records. To represent attribute values by colours, the value range is divided into intervals, and each interval is assigned a distinct colour or shade. The display in Figure 3(a) represents the values of the attribute 'course difference' expressing the difference between the ship heading and its actual movement direction in each trajectory point. The shades of blue and red represent negative and positive differences, respectively. Darker shades correspond to higher absolute values of the differences. Light yellow is used for values around zero. The legend on the left of the display explains the colour-coding. A disadvantage of temporal displays of trajectory attributes, such as time graph and time bars, is that they lack spatial information. To alleviate this, temporal displays are linked to spatial displays through interactive techniques. An example is shown in Figure  3 (a) and (b). The mouse cursor in Figure 3(a) is positioned on one of the bars. In Figure 3 (b) the trajectory represented by the bar is highlighted on a map display. The intersection of the horizontal and vertical lines marks the spatial location corresponding to the position of the mouse cursor in the time bars display. This means that the ship was in this location at the time selected by the mouse cursor. Such interactive links between displays are useful for exploring in detail one or a few particular trajectories, but are not suitable for exploration of a large number of trajectories. To show multiple trajectories in their spatial context while avoiding overlapping, the trajectory wall display BIB009 ( Figure 3(c) ) uses the same idea of stacking as the time bars display. A trajectory wall is a 3D view where the space is represented on a horizontal plane and trajectories are represented by bands stacked in the vertical dimension. The technique is especially suitable for exploration of groups of trajectories with similar shapes. As in a time bars display, the bands representing trajectories are divided into segments, which are coloured according to attribute values. In Figure 3 (c), the same attribute and colour-coding are used as in Figure 3 (a). Just as a time bars display lacks spatial information, a trajectory wall display by itself lacks temporal information. This is partly compensated for by including a display element called time lens, which is visible in the lower right corner of the display in Figure 3 (c). The time lens shows temporally aggregated information for an interactively defined spatial query area (a circle of a chosen radius around the mouse cursor position, visible in the lower left corner of Figure 3(c) ). The interior of the time lens shows the relative spatial positions of the trajectory points within the selected area. The points are represented by dots coloured according to the attribute values. The ring of the time lens represents one of the temporal cycles: four-quarters of a year, 12 months of a year, 7 days of a week, or 24 hours of a day. In our example, the last cycle is chosen. The ring is divided into bins corresponding to the units of the chosen cycle. The fill levels of the time bins visualize temporally aggregated information about the trajectories that intersect with the query. One of the possible aggregates is the trajectory count, as in our example. The coloured segments show the distribution of attribute values per time unit. Interactive filtering of trajectory segments according to values of dynamic attributes BIB006 allows the user to explore the spatio-temporal distribution of particular attribute values or value combinations. The trajectory segments that do not satisfy current filter conditions are hidden from the spatial and temporal displays. For example, the user can set the filter so that only the segments with high deviations of the movement direction from the heading will be visible in the time bars display, map and trajectory wall. Trajectory segments can also be filtered according to values of two or more attributes. In our example, the user can add a query condition that the movement speed must be at least 5 km/h in order to disregard direction deviations in anchored ships. Furthermore, the points satisfying filter conditions can be extracted from the trajectories into a separate dataset (information layer) consisting of spatial events, that is objects located in space and time. BIB003 BIB006 This dataset can be visualized and analysed independently of the original trajectories or in combination with them. In Figure 3 (d) and (e), the yellow circles represent the spatial events constructed from the points of the ship trajectories where the deviation of the movement direction from the heading is either below -30 or above 30 and the speed is not less than 5 km/h. The trajectories in which such events occurred are shown by lines; the filtering of the trajectory segments has been cancelled. It can be seen that high deviations of the direction often occur when ships move in the meridian directions. Filtering of trajectory segments according to values of two or more attributes allows the analyst to find the segments where all filter conditions are fulfilled simultaneously. To support searching for more complex patterns of movement, in which filter conditions are fulfilled in a particular temporal order (or, more generally, the time intervals on which each of the filter conditions is fulfilled stand in particular temporal relations), Sakr et al. BIB007 combine interactive visual techniques with queries to a moving object database (MOD). The authors demonstrate findings of complex patterns in aircraft landings such as missed approach (interrupted landing attempt), when an aircraft approaches the airport and descends in order to land but then ascends again. Visual analytics tools are used for an initial exploration of the data, selection of a suitable subset for further analysis by interactive filtering, finding of suitable parameter settings for the MOD queries, and then for viewing and interactive analysis of the query results. The patterns found with the help of the MOD can also be extracted from trajectories as events. Andrienko et al. BIB006 introduce a conceptual model where movement is considered as a composition of spatial events of diverse types and extents in space and time. The model gives ground to a generic approach based on the extraction of interesting events from trajectories and treating the events as independent objects. There are many possible ways that events extracted from trajectories can be further analysed and used, for example in studies of the behaviour of wild animals, BIB006 traffic congestion in a city or connections between airports. BIB003 The last paper suggests a generic visual analytics procedure in which events are extracted from trajectories and clustered in special ways in order to detect significant places and investigate the temporal dynamics of the movements within and between these places. The procedure also involves spatio-temporal aggregation, which is the topic of the next section. Bird's-eye view on movement: generalization and aggregation Generalization and aggregation enable an overall view of the spatial and temporal distribution of multiple movements, which is hard to gain from displays showing individual trajectories. Besides, aggregation is helpful in dealing with a large number of data. An illustrated survey of the aggregation methods used for movement data and the visualization techniques applicable to the results of the aggregation is given by Andrienko and Andrienko. BIB002 These methods and techniques are also presented in a more formal way by Andrienko et al. BIB008 There are two major groups of analysis tasks supported by aggregation: Investigation of the presence of moving objects in different locations in space and the temporal variation of the presence. Investigation of the flows (aggregate movements) of moving objects between different locations in space and the temporal variation of the flows.