Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> Information that contains a geographic component is becoming increasingly prevalent and can be used both to analyse relatively complex behaviours in time and space and to combat the potential for information overload by assessing the geographic relevance of information. Such analysis can be combined with mobile communications technology to fuel location-based services that offer information pertinent in terms of geography, time, experience and preference. This paper aims to raise some issues relating to these advances and describes novel representations designed for interactive graphical exploratory data analysis (EDA). A number of graphical techniques and representation methods are introduced to establish the nature of the kinds of data that are being collected and the suitability of visualization for EDA of spatio-temporal data. These include the interactive views provided by the Location Trends Extractor, 'spotlights'--continuous density surfaces of recorded spatio-temporal activity, networks of morphometric features derived from continuous surfaces representing density of activity and geocentric parallel plots presented in a spatial multimedia environment for data exploration. Some of the benefits and limitations of the techniques are outlined along with suggestions as to how the visualization tools might be utilized and developed to improve our understanding of behaviour in time and space and evaluate and model geographic relevance. <s> BIB001 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> Abstract This work presents an exploratory data analysis of the trajectories of deer and elk moving about in the Starkey Experimental Forest and Range in eastern Oregon. The animals’ movements may be affected by habitat variables and the behavior of the other animals. In the work of this paper a stochastic differential equation-based model is developed in successive stages. Equations of motion are set down motivated by corresponding equations of physics. Functional parameters appearing in the equations are estimated nonparametrically and plots of vector fields of animal movements are prepared. Residuals are used to look for interactions amongst the movements of the animals. There are exploratory analyses of various sorts. Statistical inferences are based on Fourier transforms of the data, which are unequally spaced. The sections of the paper start with motivating quotes and aphorisms from the writings of John W. Tukey. <s> BIB002 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> We demonstrate and reflect upon the use of enhanced treemaps that incorporate spatial and temporal ordering for exploring a large multivariate spatio-temporal data set. The resulting data-dense views summarise and simultaneously present hundreds of space-, time-, and variable-constrained subsets of a large multivariate data set in a structure that facilitates their meaningful comparison and supports visual analysis. Interactive techniques allow localised patterns to be explored and subsets of interest selected and compared with the spatial aggregate. Spatial variation is considered through interactive raster maps and high-resolution local road maps. The techniques are developed in the context of 42.2 million records of vehicular activity in a 98 km2 area of central London and informally evaluated through a design used in the exploratory visualisation of this data set. The main advantages of our technique are the means to simultaneously display hundreds of summaries of the data and to interactively browse hundreds of variable combinations with ordering and symbolism that are consistent and appropriate for space- and time-based variables. These capabilities are difficult to achieve in the case of spatio-temporal data with categorical attributes using existing geovisualisation methods. We acknowledge limitations in the treemap representation but enhance the cognitive plausibility of this popular layout through our two-dimensional ordering algorithm and interactions. Patterns that are expected (e.g. more traffic in central London), interesting (e.g. the spatial and temporal distribution of particular vehicle types) and anomalous (e.g. low speeds on particular road sections) are detected at various scales and locations using the approach. In many cases, anomalies identify biases that may have implications for future use of the data set for analyses and applications. Ordered treemaps appear to have potential as interactive interfaces for variable selection in spatio-temporal visualisation. <s> BIB003 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> Existing treemap layout algorithms suffer to some extent from poor or inconsistent mappings between data order and visual ordering in their representation, reducing their cognitive plausibility. While attempts have been made to quantify this mismatch, and algorithms proposed to minimize inconsistency, solutions provided tend to concentrate on one-dimensional ordering. We propose extensions to the existing squarified layout algorithm that exploit the two-dimensional arrangement of treemap nodes more effectively. Our proposed spatial squarified layout algorithm provides a more consistent arrangement of nodes while maintaining low aspect ratios. It is suitable for the arrangement of data with a geographic component and can be used to create tessellated cartograms for geovisualization. Locational consistency is measured and visualized and a number of layout algorithms are compared. CIELab color space and displacement vector overlays are used to assess and emphasize the spatial layout of treemap nodes. A case study involving locations of tagged photographs in the Flickr database is described. <s> BIB004 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> The timeline or track of any individual, mobile, sentient organism, whether animal or human being, represents a fundamental building block in understanding the interactions of such entities with their environment and with each other. New technologies have emerged to capture the (x, y, t) dimension of such timelines in large volumes and at relatively low cost, with various degrees of precision and with different sampling properties. This has proved a catalyst to research on data mining and visualizing such movement fields. However, a good proportion of this research can only infer, implicitly or explicitly, the activity of the individual at any point in time. This paper in contrast focuses on a data set in which activity is known. It uses this to explore ways to visualize large movement fields of individuals, using activity as the prime referential dimension for investigating space-time patterns. Visually central to the paper is the ringmap, a representation of cyclic time and activity, that is itself quasi spatial and is directly linked to a variety of visualizations of other dimensions and representations of spatio-temporal activity. Conceptuatly central is the ability to explore different levels of generalization in each of the space, time and activity dimensions, and to do this in any combination of the (s, t, a) phenomena. The fundamental tenet for this approach is that activity drives movement, and logically it is the key to comprehending pattern. The paper discusses these issues, illustrates the approach with specific example visualizations and invites critiques of the progress to date. <s> BIB005 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> We propose a geographical visualization to support operators of coastal surveillance systems and decision making analysts to get insights in vessel movements. For a possibly unknown area, they want to know where significant maritime areas, like highways and anchoring zones, are located. We show these features as an overlay on a map. As source data we use AIS data: Many vessels are currently equipped with advanced GPS devices that frequently sample the state of the vessels and broadcast them. Our visualization is based on density fields that are derived from convolution of the dynamic vessel positions with a kernel. The density fields are shown as illuminated height maps. Combination of two fields, with a large and small kernel provides overview and detail. A large kernel provides an overview of area usage revealing vessel highways. Details of speed variations of individual vessels are shown with a small kernel, highlighting anchoring zones where multiple vessels stop. Besides for maritime applications we expect that this approach is useful for the visualization of moving object data in general. <s> BIB006 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> Spatiotemporal analysis of sensor logs is a challenging research field due to three facts: a) traditional two-dimensional maps do not support multiple events to occur at the same spatial location, b) three-dimensional solutions introduce ambiguity and are hard to navigate, and c) map distortions to solve the overlap problem are unfamiliar to most users. This paper introduces a novel approach to represent spatial data changing over time by plotting a number of non-overlapping pixels, close to the sensor positions in a map. Thereby, we encode the amount of time that a subject spent at a particular sensor to the number of plotted pixels. Color is used in a twofold manner; while distinct colors distinguish between sensor nodes in different regions, the colors' intensity is used as an indicator to the temporal property of the subjects' activity. The resulting visualization technique, called growth ring maps, enables users to find similarities and extract patterns of interest in spatiotemporal data by using humans' perceptual abilities. We demonstrate the newly introduced technique on a dataset that shows the behavior of healthy and Alzheimer transgenic, male and female mice. We motivate the new technique by showing that the temporal analysis based on hierarchical clustering and the spatial analysis based on transition matrices only reveal limited results. Results and findings are cross-validated using multidimensional scaling. While the focus of this paper is to apply our visualization for monitoring animal behavior, the technique is also applicable for analyzing data, such as packet tracing, geographic monitoring of sales development, or mobile phone capacity planning. <s> BIB007 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <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> BIB008 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> Modern positioning and identification technologies enable tracking of almost any type of moving object. A remarkable amount of new trajectory data is thus available for the analysis of various phenomena. In cartography, a typical way to visualise and explore such data is to use a space-time cube, where trajectories are shown as 3D polylines through space and time. With increasingly large movement datasets becoming available, this type of display quickly becomes cluttered and unclear. In this article, we introduce the concept of 3D space-time density of trajectories to solve the problem of cluttering in the space-time cube. The space-time density is a generalisation of standard 2D kernel density around 2D point data into 3D density around 3D polyline data (i.e. trajectories). We present the algorithm for space-time density, test it on simulated data, show some basic visualisations of the resulting density volume and observe particular types of spatio-temporal patterns in the density that are specific to trajectory data. We also present an application to real-time movement data, that is, vessel movement trajectories acquired using the Automatic Identification System (AIS) equipment on ships in the Gulf of Finland. Finally, we consider the wider ramifications to spatial analysis of using this novel type of spatio-temporal visualisation. <s> BIB009 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> Spatiotemporal data pose serious challenges to analysts in geographic and other domains. Owing to the complexity of the geospatial and temporal components, this kind of data cannot be analyzed by fully automatic methods but require the involvement of the human analyst's expertise. For a comprehensive analysis, the data need to be considered from two complementary perspectives: (1) as spatial distributions (situations) changing over time and (2) as profiles of local temporal variation distributed over space. In order to support the visual analysis of spatiotemporal data, we suggest a framework based on the "Self-Organizing Map" (SOM) method combined with a set of interactive visual tools supporting both analytic perspectives. SOM can be considered as a combination of clustering and dimensionality reduction. In the first perspective, SOM is applied to the spatial situations at different time moments or intervals. In the other perspective, SOM is applied to the local temporal evolution profiles. The integrated visual analytics environment includes interactive coordinated displays enabling various transformations of spatiotemporal data and post-processing of SOM results. The SOM matrix display offers an overview of the groupings of data objects and their two-dimensional arrangement by similarity. This view is linked to a cartographic map display, a time series graph, and a periodic pattern view. The linkage of these views supports the analysis of SOM results in both the spatial and temporal contexts. The variable SOM grid coloring serves as an instrument for linking the SOM with the corresponding items in the other displays. The framework has been validated on a large dataset with real city traffic data, where expected spatiotemporal patterns have been successfully uncovered. We also describe the use of the framework for discovery of previously unknown patterns in 41-years time series of 7 crime rate attributes in the states of the USA. <s> BIB010 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> We consider moving objects as multivariate time-series. By visually analyzing the attributes, patterns may appear that explain why certain movements have occurred. Density maps as proposed by Scheepens et al. [25] are a way to reveal these patterns by means of aggregations of filtered subsets of trajectories. Since filtering is often not sufficient for analysts to express their domain knowledge, we propose to use expressions instead. We present a flexible architecture for density maps to enable custom, versatile exploration using multiple density fields. The flexibility comes from a script, depicted in this paper as a block diagram, which defines an advanced computation of a density field. We define six different types of blocks to create, compose, and enhance trajectories or density fields. Blocks are customized by means of expressions that allow the analyst to model domain knowledge. The versatility of our architecture is demonstrated with several maritime use cases developed with domain experts. Our approach is expected to be useful for the analysis of objects in other domains. <s> BIB011 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <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> BIB012 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <s> Technological advances in sensing technologies and wireless telecommunication devices enable research fields related to the management of trajectory data. The challenge after storing the data is the implementation of appropriate analytics for extracting useful knowledge. However, traditional data warehousing systems and techniques were not designed for analyzing trajectory data. In this paper, the authors demonstrate a framework that transforms the traditional data cube model into a trajectory warehouse. As a proof-of-concept, the authors implement T-Warehouse, a system that incorporates all the required steps for Visual Trajectory Data Warehousing, from trajectory reconstruction and ETL processing to Visual OLAP analysis on mobility data. <s> BIB013 </s> Visual analytics of movement: An overview of methods, tools and procedures <s> Analysing presence and density <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> BIB014
The presence of moving objects in a location during a particular time interval can be characterized in terms of the count of different objects that visited the location, the count of the visits (some objects might visit the location more than once) and the total or average time spent in the location. Statistics of various attributes describing the objects, their movements, or their activities in the location may also be of interest. To obtain these measures, movement data are aggregated spatially into continuous density surfaces (fields) BIB006 BIB001 or discrete grids. BIB008  While the most common approach is to aggregate points of trajectories and point-related attributes, Willems et al. BIB006 have developed a specific kernel density estimation method for trajectories, which involves interpolation between consecutive trajectory points taking into account speed and acceleration. Density fields built using kernels with different radii can be combined into one field to expose simultaneously large-scale patterns and fine features ( Figure 5(a) ). Density fields are visualized on a map using colour-coding and/or shading by means of an illumination model. A more recent paper BIB011 suggests a library of methods and a scripting-based architecture for creation, transformation, combination and enhancement of movement density fields. This approach allows an expert user to involve domain knowledge in the process of building density fields. Mountain  further processes density surfaces generated from movement data to extract their topological features: peaks, pits, ridges, saddles, etc. An example of spatial aggregation using a discrete grid is given in Figure 5 (b). The irregular grid has been built according to the spatial distribution of characteristic points from ship trajectories as described by Andrienko and Andrienko. BIB012 The darkness of the shading of the grid cells is proportional to the total number of visits. Additionally, each cell contains a circle with the area proportional to the mean duration of a visit. It can be observed that the average duration of a visit in the cells with dense traffic (dark shading) is mostly low; longer times are spent in cells that are not intensively visited. Presence and density maps do not convey information about the movement directions. Brillinger et al. BIB002 use arrow symbols to represent the prevailing movement directions in cells of a discrete grid. The lengths and widths of the symbols are proportional to the average speed and the number of moving objects, respectively. This approach is suitable when the movement is mostly coherent (i.e. objects moving closely in space tend to have the same direction, which is not always the case). Movements in different directions can be represented by directional diagrams positioned on a map within grid cells. BIB008 A diagram consists of bars arranged in a radial layout and orientated in different compass directions, as in a wind rose. The lengths of the bars are proportional to the counts of objects that moved in the respective directions, or to their average speeds, or to any other numerical statistics associated with the directions. This approach combines two kinds of aggregation: by spatial positions and by movement directions. To combine spatial aggregation with aggregation by several arbitrary attributes, researchers from City University of London suggest spatially-ordered treemaps. BIB003 BIB004 Generally, a treemap 41 is a space-filling hierarchical layout of rectangles, typically labelled, differing in size and, optionally, colouring or shading. Each rectangle represents a group of objects with close values of some attribute so that the size of the rectangle is proportional to the size of the group. The group can be further subdivided according to values of another attribute, and the rectangle representing the group is also partitioned into smaller rectangles. The method of creating a spatially ordered treemap is illustrated in Figure 4 . The territory can be divided into compartments, for example using a regular grid, as in Figure 4 (a) (irregular divisions can also be used). Each compartment is represented by a rectangle with the size (area) proportional to the number of trajectory points occurring in the compartment. According to the general idea of a treemap, the rectangles are subdivided into sections proportionally to the numbers of trajectory points with different values of a selected attribute; in our example, ship type. In Figure 4 (b) the rectangles are located in the display according to the spatial positions of the respective compartments. To get rid of the occlusions and display clutter, the rectangles are shifted and reshaped so that each one can receive its individual portion of the display space (Figure 4(c) ). This is done in such a way that the relative spatial positions of the rectangles are distorted as little as possible. The transitions between the views shown in Figure 4 (b) and (c) can be animated to help the user understand how the space is transformed. The interpretation of the display requires training but the benefits are the absence of occlusions and the possibility to analyse several attributes simultaneously, for example ship type, destination and average speed. For each additional attribute, the sections of the rectangles representing the compartments are further subdivided. To investigate the temporal variation of object presence and related attributes across the space, spatial aggregation is combined with temporal aggregation, which can also be continuous or discrete. Demšar and Virrantaus BIB009 extend the idea of spatial density to spatio-temporal density: they aggregate trajectories into density volumes in a 3D space-time continuum by generalizing the standard 2D kernel density around 2D point data into 3D density around 3D polyline data. The resulting volumes are represented in a STC. For discrete temporal aggregation, time is divided into intervals. Depending on the application and analysis goals, the analyst may consider time as a line (i.e. a linearly ordered set of moments) or as a cycle, for example daily, weekly or yearly. Accordingly, the time intervals for the aggregation are defined on the line or within the chosen cycle. The combination of discrete temporal aggregation with continuous spatial aggregation gives a sequence of density surfaces, one for each time interval, which can be visualized by animated density maps. It is also possible to compute differences between two surfaces and visualize them on a map to be able to see changes occurring over time (this technique is known as a change map). The combination of discrete temporal aggregation with discrete spatial aggregation produces one or more aggregate attribute values for each combination of space compartment (e.g. grid cell) and time interval. In other words, each space compartment receives one or more time series of aggregate attribute values. Visualization by animated density/presence maps and change maps is possible as in the case of continuous surfaces. There are also other possibilities. The time series may be shown in an STC by proportionally sized or shaded or coloured symbols, which are vertically aligned above the locations BIB005 ; Figure 5 (c) gives an example. Occlusion of symbols is often a serious problem in such a display. It is also possible to combine presence/density maps with time series displays such as a time graph or temporal histogram.  ,  Zhao et al. BIB005 build circular temporal histograms to explore the dependency of When the number of the space compartments is large and time series are long, it may be difficult to explore the spatio-temporal distribution of object presence using only visual and interactive techniques. It is reasonable to cluster the compartments by similarity of the respective time series and analyse the temporal variation cluster-wise, that is investigate the attribute dynamics within the clusters and perform comparisons between clusters. Andrienko et al. BIB010 perform the clustering using self-organizing maps and create specific visualizations to explore the clustering results; however, other clustering and visualization techniques may also be used. Figure 5(d) demonstrates the outcome of k-means clustering of grid cells according to the time series of the presence of different ships computed by hourly time intervals. Distinct colours have been assigned to the clusters and used for painting the cells on the map. The colours are chosen by projecting the cluster centroids onto a 2D continuous colour map; hence, clusters with close centroids receive similar colours and, vice versa, high difference in colours signifies much dissimilarity between the clusters. The analyst can select the clusters one by one or in pairs for comparison and look at the corresponding time series presented on a time graph (Figure 5(e) and (f) ). In our example, the clusters differ mainly in the value magnitudes and not in the temporal patterns of value variation. A spatially referenced time series is one of two possible views on a result of discrete spatio-temporal aggregation. BIB010 The other possibility is to consider the aggregates as a temporal sequence of spatial situations. BIB014 The term 'spatial situation' denotes spatial distribution of aggregate values of one or more attributes in one time interval. Temporal variation of spatial situations can also be investigated by means of clustering. BIB010 BIB014 In this case, the spatial situations are considered as feature vectors characterizing different time intervals. The clustering groups the time intervals by similarity of these feature vectors. An example is presented in Figure 6 . Spatio-temporal aggregation by cells of an irregular grid and hourly time intervals has been applied separately to 322 trajectories of the passenger and ferry boats (for this purpose, the trajectories have been filtered by the ship type). Then k-means clustering method has been applied to 192 spatial situations (8 days times 24 hours) in terms of the presence of the passenger and ferry boats expressed by their visit counts in the grid cells. The results of the clustering are represented on the time mosaic display in the bottom right corner of the figure. The time intervals are represented by squares arranged in eight columns corresponding to the 8 days and 24 rows corresponding to 24 hours of the day. The squares are painted in the colours assigned to the clusters. After running the clustering tools multiple times with different values of the parameter k (number of clusters), we have chosen the result k=8, since it produces the most prominent periodic patterns on the time mosaic display. We can see that the morning of the first day (1 January 2009, New Year) differs from the mornings of all other days but that from 15.00 the pattern becomes similar to the other days. The time mosaic display indicates that the movement of the boats is mostly regular in character. The multiple maps display summarizes the spatial situations by the time clusters: for each time cluster and each cell, the mean count of visits has been computed from the counts for the time intervals contained in the cluster. The clusters represented by the maps are designated by the coloured captions. It is interesting that the presence situations in the hours 07.00 and 09.00-11.00 on Saturday (day 3) are prominently different than in the same time on the other days. These situations belong to the orange cluster, which is represented by the last map in the bottom row. The map shows that the situations in this cluster are characterized by an unusually high presence of boats at Dunkerque and Brugge. This can probably be explained by people from England visiting the Continent for Saturday shopping. Bak et al. BIB007 represent the presence of moving objects at different locations without explicit spatial aggregation. Each visit is represented on a map by a pixel, coloured according to the time of the visit or value of a particular attribute. The pixels are arranged in a spiral layout around the locations so that identically coloured pixels are placed closely to each other. As a result, a circle emerges around a location in which pixels with same colours form rings; the technique is therefore called 'growth rings'. The layout induces perceptual aggregation: the user does not distinguish individual pixels but perceives them all together as one figure. The size of the whole figure shows the total number of visits while the rings show the proportions of occurrences of the attribute values encoded by the colours. To deal with a very large number of movement data, possibly, not fitting in RAM, discrete spatio-temporal aggregation can be done within a database BIB008 or a data warehouse. BIB013 Only aggregated data are loaded in RAM for visualization and interactive analysis. Using roll-up and drill-down operators of the warehouse, the analyst may vary the level of aggregation.