PROBLEM

• Movement data are collected in huge and constantly growing amounts.
• Movement data have recently got attention of researchers in different analytical disciplines
• There are many scattered methods addressing this or that aspect but no holistic picture and no systematic treatment of the subject

OUR CONTRIBUTION

• Conceptual foundations for analysis of movement data
• Multi-perspective view of movement data: trajectories, spatial events, local time series, spatial situations
• Systematic presentation of visual analytics methods (computation + visualization + interaction) oriented to the different views of movement and analysis tasks
• Transformations between different representations of movement
• Discussion of properties of movement data that affect the analysis and methods for investigating them
• Many illustrated examples using diverse real datasets

OUR POTENTIAL "CUSTOMERS"

• Researchers: conceptual model representing different aspects of movement and a system of possible analysis tasks to be addressed by research
• Method developers: analysis tasks that may need support, existing approaches to build on, data transformations to use, data properties to be aware of
• Practical analysts: systematically presented state-of-the-art methods covering the possible representations of movement data and the respective classes of tasks, many examples of analyses

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .  1
1.1 A Single Trajectory  . . . . . . . . . . . . . . . . . . . . .  2
1.2 Multiple Trajectories of a Single Object . . . . . . . . . . .  8
1.3 Simultaneous Movements of Many Objects . . . . . . . . . . . . 21
1.4 What Should Have Been Achieved by These Examples . . . . . . . 28
1.5 Visual Analytics . . . . . . . . . . . . . . . . . . . . . . . 29
1.6 Structure of The Book  . . . . . . . . . . . . . . . . . . . . 31
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Abstract. This chapter provides an informal introduction of the main concepts related to analysis of movement. The concepts are introduced by illustrated examples, which also demonstrate some techniques that may be used for visual exploration and analysis of movement data. The examples show how the capabilities of the computer and human can be combined to extract knowledge from movement data. This sets the stage for introducing the concept of visual analytics. The chapter also explains the objectives and the structure of the book.

Fig.1.18. Clusters of car trajectories by route similarity are represented in a space–time cube. The time references in the trajectories have been transformed to times of the same day. Hence, the trajectories are vertically positioned in the cube according to the times of the day when they occurred

2 Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . 33
2.1 Foundations  . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Fundamental Sets: Space, Time, and Objects . . . . . . . . . . 35
2.2.1 Space  . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.2 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.3 Objects  . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3 Characteristics of Objects, Locations, and Times . . . . . . . 38
2.4 Basic Types of Spatio-temporal Data  . . . . . . . . . . . . . 41
2.5 Event-Based View of Movement . . . . . . . . . . . . . . . . . 43
2.6 Multi-Perspective View of Movement . . . . . . . . . . . . . . 45
2.7 Spatio-temporal Context  . . . . . . . . . . . . . . . . . . . 46
2.8 Relations  . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.8.1 Relations of Objects . . . . . . . . . . . . . . . . . . . . 49
2.8.2 Relations of Locations and Times . . . . . . . . . . . . . . 53
2.9 Movement Data and Context Data . . . . . . . . . . . . . . . . 55
2.9.1 Forms and Sources of Movement Data . . . . . . . . . . . . . 55
2.9.2 Properties of Movement Data  . . . . . . . . . . . . . . . . 56
2.9.3 Context Data . . . . . . . . . . . . . . . . . . . . . . . . 58
2.10 Example Data Sets Used in the Book  . . . . . . . . . . . . . 59
2.10.1 Personal Driving  . . . . . . . . . . . . . . . . . . . . . 59
2.10.2 Cars in Milan . . . . . . . . . . . . . . . . . . . . . . . 60
2.10.3 Vessels in the North Sea  . . . . . . . . . . . . . . . . . 60
2.10.4 Public Transport in Helsinki  . . . . . . . . . . . . . . . 61
2.10.5 A Group Walk of Workshop Participants . . . . . . . . . . . 61
2.10.6 Trajectories of Flickr and Twitter Users  . . . . . . . . . 61
2.10.7 VAST Challenge 2011 . . . . . . . . . . . . . . . . . . . . 62
2.10.8 Tracks of Wild Animals in a National Park . . . . . . . . . 63
2.10.9 Movements of Laboratory Mice  . . . . . . . . . . . . . . . 64
2.10.10 Movements of Visitors of Car Races . . . . . . . . . . . . 65
2.11 Types of Movement Behaviours  . . . . . . . . . . . . . . . . 65
2.12 Types of Movement Analysis Tasks  . . . . . . . . . . . . . . 68
2.13 Recap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Abstract. We introduce a conceptual framework intended to describe in a systematic and comprehensive way the types of information contained in movement data and the respective types of analytical tasks. The framework is based on the consideration of three fundamental sets: space, time, and objects. In the set of objects, we separately consider two types of spatio-temporal objects playing the most important role in the phenomenon of movement, moving objects (shortly, movers), and spatial events. Elements of the fundamental sets can be characterized in terms of the elements of the other sets. Based on these characteristics, we introduce multi-perspective view of movement, including mover perspective, space perspective, time perspective, and spatial event perspective. We suggest a typology of movement analysis tasks, where classes of tasks are defi ned according to the possible foci, which correspond to the different perspective of movement. Tasks are also distinguished according to the level of analysis, which may be elementary (addressing specifi c elements of the sets) or synoptic (addressing the sets or their subsets).

Fig.2.4. Four perspectives of the phenomenon of movement

3 Transformations of Movement Data . . . . . . . . . . . . . . .   73
3.1 Interpolation and Re-sampling  . . . . . . . . . . . . . . .   73
3.2 Division of Movement Tracks and Trajectories . . . . . . . .   74
3.3 Transformations of Temporal and Spatial References . . . . .   75
3.4 Derivation of New Thematic Attributes  . . . . . . . . . . .   79
3.5 Extraction of Spatial Events . . . . . . . . . . . . . . . .   82
3.5.1 Extraction of Movement Events from Trajectories  . . . . .   82
3.5.2 Detection of Stop Events . . . . . . . . . . . . . . . . .   84
3.5.3 Extraction of Spatial Events from Other Data Types . . . .   86
3.6 Spatial and Temporal Generalization  . . . . . . . . . . . .   86
3.7 Trajectory Abstraction (Simplifi cation) . . . . . . . . . .   88
3.8 Spatio-Temporal Aggregation  . . . . . . . . . . . . . . . .   90
3.9 Transformations Between Data Types . . . . . . . . . . . . .   97
3.10 Recap . . . . . . . . . . . . . . . . . . . . . . . . . . .   98
References . . . . . . . . . . . . . . . . . . . . . . . . . . .  100

Abstract. This chapter introduces common transformations that are often used in analysis of movement data: interpolation and re-sampling, division of trajectories, alignment of temporal and spatial references, derivation of new thematic attributes, extraction of movement events, generalization, simplifi cation, and aggregation. These transformations can adapt available data to the analysis goals or to specifi c requirements of the methods that the analyst wants to apply. Transformations can extract relevant parts of the data or reduce irrelevant details. Some transformations convert movement data from one form to another, to support different task foci: movers, spatial, events, space, and time.

Data transformations play an auxiliary role in analysis since they are not intended to provide answers to questions. Their role is to prepare data for analysis, that is, to convert data to a form fitting a task or required by an analytical tool. Some transformations change the structure of the data. In the previous chapter, we have introduced a formal representation for data structures based on the components O (objects), in particular, moving objects M and spatial events E , S (space), T (time), and A (thematic attributes), see Sects. 2.4 and 2.9. We shall use this formalism in describing the possible transformations of data structures.

Fig.3.11. Transformations between different types of spatio-temporal data

Visual Analytics Infrastructure  . . . . . . . . . . . . . . . .  103
4.1 Interactive Visualizations . . . . . . . . . . . . . . . . .  103
4.2 Interactive Filtering  . . . . . . . . . . . . . . . . . . .  113
4.2.1 Spatial, Temporal, and Attribute Filtering . . . . . . . .  114
4.2.2 Filtering of Object Classes and Individual Objects . . . .  117
4.2.3 Filtering of Trajectory Segments . . . . . . . . . . . . .  118
4.2.4 Filtering of Related Object Sets . . . . . . . . . . . . .  121
4.3 Dynamic Aggregation  . . . . . . . . . . . . . . . . . . . .  124
4.4 Recap  . . . . . . . . . . . . . . . . . . . . . . . . . . .  126
References . . . . . . . . . . . . . . . . . . . . . . . . . . .  128

Abstract. In this chapter, we describe basic visualization and interaction tech-niques that enable viewing and exploration of movement data and other types of spatio-temporal data and facilitate data transformations and joint analysis of different data types. Cartographic maps and space-time cubes are universal types of display for visualizing various kinds of spatio-temporal objects and data, including trajectories of moving objects, spatial events, aggregate movements (flows), and time series of attribute values. However, they provide limited opportunities for representing temporal and thematic (attributive) aspects of the data; thus, additional forms of data display are required. Time graphs and temporal bar charts are useful for representing the temporal and attributive aspects. Multiple co-existing displays showing different aspects or components of the data need to be visually linked. This is achieved by means of consistent visual encodings (e.g. same colours) and simultaneous consistent reaction of different displays to various user interactions, in particular, to data filtering. Filtering helps the user to reduce display clutter and occlusions, to focus on relevant parts of the data, to establish relationships between different components of the data, and to integrate information coming from different displays. Interactive filtering can be done according to different aspects of the data: spatial, temporal, thematic (attributive), or class/group membership. For complex objects, such as trajectories, filtering can be applied to object components (points and segments). Filtering may also change secondary data that have been earlier derived from the data that are filtered, such as results of data aggregation. The displays representing the secondary data can be updated to reflect the changes.

Fig.4.15e. The hulls, events, and trajectories selected by the combination of the filters

5 Visual Analytics Focusing on Movers  . . . . . . . . . . . . .  131
5.1 Characteristics  . . . . . . . . . . . . . . . . . . . . . .  132
5.1.1 Spatial Summarization of Trajectories  . . . . . . . . . .  133
5.1.2 Clustering of Trajectories . . . . . . . . . . . . . . . .  141
5.1.2.1 Partition-Based Clustering According to Trajectory 
        Features . . . . . . . . . . . . . . . . . . . . . . . .  142
5.1.2.2 Density-Based Clustering Using Special Distance 
        Functions  . . . . . . . . . . . . . . . . . . . . . . .  145 
5.1.2.3 Progressive Clustering . . . . . . . . . . . . . . . . .  148
5.1.2.4 Variety of Distance Functions for Trajectories . . . . .  152
5.1.2.5 Clustering of Very Large Sets of Trajectories  . . . . .  156
5.1.3 Visualization of Positional Attributes . . . . . . . . . .  165
5.1.4 Analysis of Multiple Positional Attributes . . . . . . . .  170
5.2 Relations  . . . . . . . . . . . . . . . . . . . . . . . . .  172
5.2.1 Encounters Between Moving Objects  . . . . . . . . . . . .  173
5.2.2 Relations in a Group of Movers . . . . . . . . . . . . . .  180
5.2.3 Relations of Movers to the Environment . . . . . . . . . .  194
5.3 Recap  . . . . . . . . . . . . . . . . . . . . . . . . . . .  202
References . . . . . . . . . . . . . . . . . . . . . . . . . . .  206

Abstract. In this chapter, we present visualization and analysis methods that can support analysis tasks focusing on characteristics of movers and their relations to the context (Fig.5.1). These methods deal with movement data in the form of trajectories of moving objects. For gaining an overview of a set of trajectories, a flow map is built based on a territory tessellation reflecting the spatial distribution of charac-teristic points of trajectories. The method for trajectory summarization can be applied to a whole set of trajectories and to subsets, in particular, to groups of similar trajectories resulting from clustering. Density-based clustering algorithms in com-bination with trajectory-specific distance functions (i.e., methods for assessing the dissimilarity of trajectories) are more suitable for trajectories than partition-based clustering algorithms that take distances in a multi-dimensional space of features (attribute values) as measures of object dissimilarity. We argue for the use of a library of relatively simple distance functions addressing different properties of trajectories. We describe several distance functions that are useful in analyzing trajectories and present an analytical procedure of progressive clustering, in which cluster analysis is done in a sequence of steps. In each step, one distance function from a library is applied to the whole set of trajectories or to one or several clus-ters discovered earlier. In this way, the simple distance functions are combined for enabling sophisticated analyses.

Visual exploration of positional attributes in groups (clusters) of spatially similar trajectories is supported by a three-dimensional trajectory wall display. Com-binations of multiple positional attributes can be analyzed using multi-attribute clustering of trajectory segments. For analyzing relations among movers and between movers and elements of the spatio-temporal context, we suggest several methods and approaches. One method detects encounters of movers, when two movers come close to each other. Another method builds a central trajectory of a group of objects moving together and computes a set of positional attributes ena-bling identification of relations among the movers in the group, such as leadership, centrality, and relative spatial arrangement. An approach to analyzing relations between movers and static spatial objects, movers of another kind, or spatial events is based on computing positional attributes expressing spatial and temporal distances between trajectory positions and elements of the spatio-temporal context.

Fig.5.1. This chapter addresses analysis tasks focusing on characteristics of movers and their relations to the context. Characteristics of movers are represented by movement data in the form of trajectories (cf. Fig. 3.13)

Fig.5.33. The values of the computed positional attribute “distance from the group centre along the group movement vector” in the individual trajectories are visualized on a trajectory wall (top) and a temporal bar chart (bottom)

6 Visual Analytics Focusing on Spatial Events  . . . . . . . . .  209
6.1 Extraction of Composite Spatial Events by Clustering . . . .  211
6.1.1 A Distance Function for Spatial Events . . . . . . . . . .  212
6.1.2 Selection of Thresholds  . . . . . . . . . . . . . . . . .  213
6.1.3 Scalable Clustering of Events  . . . . . . . . . . . . . .  214
6.1.4 An Example of Scalable Clustering of Spatial Events  . . .  218
6.2 Characteristics  . . . . . . . . . . . . . . . . . . . . . .  221
6.2.1 Growth Ring Maps . . . . . . . . . . . . . . . . . . . . .  223
6.2.2 Flower Diagrams  . . . . . . . . . . . . . . . . . . . . .  229
6.2.3 Textual Characteristics of Composite Events  . . . . . . .  232
6.3 Relations  . . . . . . . . . . . . . . . . . . . . . . . . .  239
6.3.1 Spatio-Temporal Relations Between Events . . . . . . . . .  239
6.3.2 Relations Between Events, Trajectories, and Context  . . .  240
6.4 Recap  . . . . . . . . . . . . . . . . . . . . . . . . . . .  249
References . . . . . . . . . . . . . . . . . . . . . . . . . . .  250

Abstract. In this chapter, we present visualization and analysis methods that can support movement analysis tasks focusing on spatial events. The appropriate form of movement data is spatial event data. From spatial event data describing elementary events, composite spatial events can be generated, in particular, spatio-temporal clusters of spatial events. We present an approach to finding spatio-temporal clusters in very large sets of spatial events that do not fit in RAM.

We suggest two methods for visualization of spatially colocated spatial events that do not involve computational aggregation. Growth Ring Maps represent clusters of events by placing pixels representing individual events in a radial layout around cluster centres. The pixels can be coloured according to the absolute temporal positions of the events or their relative positions within temporal cycles. Flower diagrams represent clusters of events by compositions of circle sectors radiating from a common centre. The angular position of a sector represents the po-sition of the respective event in a temporal cycle and the length (radius) the event duration. Overlapping of several sectors shows event density.

Spatial events may have textual characteristics. Composite events may be characterized by text aggregates, i.e., by frequent words and combinations occurring in the texts of the smaller events the composite events comprise. To facilitate interactive exploration of text aggregates by means of spatial and temporal filtering, we represent each frequent word or combination by a text event having the same spatial and temporal positions as the composite event.

We also discuss how spatial, temporal, and spatio-temporal relations among spatial events and between spatial events and other objects (particularly, trajectories of movers) can be investigated using spatial, temporal, and spatio-temporal displays, computation of spatial and temporal distances, and interactive filtering.

Fig.6.1. This chapter addresses analysis tasks focusing on characteristics of spatial events and their relations to the context. Characteristics of spatial events are represented by movement data in the form of spatial event data (cf. Fig. 3.13)

Fig.6.24. The space–time cube shows the spatio-temporal distribution of the primary messages about the flu-like disease (red) and stomach disease (light blue)

7 Visual Analytics Focusing on Space . . . . . . . . . . . . . .  253
7.1 Obtaining Places of Interest from Movement Data  . . . . . .  254
7.1.1 Space Tessellation . . . . . . . . . . . . . . . . . . . .  255
7.1.2 Grouping of Close Locations  . . . . . . . . . . . . . . .  257
7.1.3 Event-Based Place Extraction . . . . . . . . . . . . . . .  258
7.1.4 Extraction of Personal Places  . . . . . . . . . . . . . .  259
7.2 Characteristics  . . . . . . . . . . . . . . . . . . . . . .  261
7.2.1 Visualization of Time Series . . . . . . . . . . . . . . .  261
7.2.2 Transformations of Time Series . . . . . . . . . . . . . .  263
7.2.3 Clustering of Time Series  . . . . . . . . . . . . . . . .  266
7.2.4 Time Series Modelling  . . . . . . . . . . . . . . . . . .  269
7.2.5 Event Extraction from Time Series  . . . . . . . . . . . .  274
7.2.6 Interpretation of Personal Places  . . . . . . . . . . . .  279
7.3 Relations  . . . . . . . . . . . . . . . . . . . . . . . . .  283
7.3.1 Analysis of Binary Links Between Places  . . . . . . . . .  283
7.3.2 Relations Between Link Attributes  . . . . . . . . . . . .  287
7.3.3 Relations Between Several Places . . . . . . . . . . . . .  291
7.3.4 Discovery of Frequent Sequences  . . . . . . . . . . . . .  296
7.4 Recap  . . . . . . . . . . . . . . . . . . . . . . . . . . .  302
References . . . . . . . . . . . . . . . . . . . . . . . . . . .  304

Abstract. This chapter considers analytical tasks focusing on space treated as a discrete set of places of interest. We present several methods for defining a set of places of interest based on the available movement data and depending on the analysis goals. For visual exploration of time series associated with places or with links between places, we suggest a time graph display enhanced with tools for data summarization and various computational transformations. Other analysis methods include clustering of time series by similarity, time series modelling, and computational extraction of peaks or other features followed by representing them as spatial events. These methods are supported by interactive visual techniques.

Binary relations between places are analysed by combining flow maps with time graphs. We also consider dependencies between attributes of flows emerging when the movement is constrained by channels with limited capacities, such as in a street network. The dependencies can be represented by regression models, which can be built, evaluated, and refined with support of interactive visual tools.

We consider also the ways to reveal and explore ordering and temporal rela-tions involving more than two places. When places of interest are few, these rela-tions can be revealed and investigated by means of interactive visual displays. When places are more numerous, frequently occurring sequences of visited places can be discovered by means of sequence mining algorithms after transforming trajectories of movers into sequences of strings representing visited places. The algorithms return frequently occurring subsequences, which can be interpreted and explored in the spatial context after being transformed to trajectories. Sequence mining may particularly useful in analysis of episodic movement data.

Fig.7.1. This chapter addresses analysis tasks focusing on movement-specifi c characteristics of locations and their relations to the context. Characteristics of locations are represented by movement data in the form of local time series (cf. Fig. 3.13)

Fig.7.21. A flow map (a) represents links between places clustered by the similarity of the TS of the move counts and average speeds. The flows are coloured according to their cluster membership. The colours are assigned to the clusters by means of the projection of the cluster centres onto a two-dimensional colour space (b). The scatterplot (c) shows the value combinations of move counts and average speeds occurring in different clusters. The time graph (d) shows the envelopes of the clusters of the TS of move counts. The frequency histogram (e) shows the statistical distribution of the average speed values for the clusters.

8 Visual Analytics Focusing on Time  . . . . . . . . . . . . . .  307
8.1 Characteristics  . . . . . . . . . . . . . . . . . . . . . .  308
8.1.1 Clustering of Times by Similarity of Spatial Situations  .  309
8.1.2 Event Extraction from Spatial Situations . . . . . . . . .  319
8.2 Relations  . . . . . . . . . . . . . . . . . . . . . . . . .  325
8.3 Recap  . . . . . . . . . . . . . . . . . . . . . . . . . . .  332
References . . . . . . . . . . . . . . . . . . . . . . . . . . .  333

Abstract. This chapter presents methods and procedures that can support move-ment analysis tasks focusing on time units. Spatial situations characterize time units in terms of the spatial positions and movement characteristics of the existing moving objects. Spatial situations can be represented in an aggregated form by spatial presence and flow distributions. When the number of spatial situations is large, clustering by similarity is a suitable way to reduce the analytical workload. For each cluster, a representative spatial situation is constructed or selected. A complementary method for analyzing characteristics of spatial situations is extraction of local features, such as local maxima or minima, and representing them by spatial events, which may be then analyzed by means of methods suitable for spatial events. Quantitative changes between spatial situations can be analyzed with the help of change maps. Changes of object positions (displacements) can be visualized on flow maps or by origin-destination matrices. A DCDV display (Dynamic Categorical Data View) enables exploring object positions changes over multiple selected time units when the number of different places is small or the places can be grouped into a small number of place categories.

Fig.8.1. This chapter addresses analysis tasks focusing on movement-specific characteristics of time units and their relations to the context. Characteristics of time units are represented by movement data in the form of spatial distributions (cf. Fig. 3.13)

Fig.8.14. A DCDV display presents an overview of the movements of the car races visitors during two days. The colours represent different categories of places of interest; see Fig. 8.15a

9 Discussion and Outlook . . . . . . . . . . . . . . . . . . . .  335
9.1 Multi-Perspective View of Movement and Task Typology . . . .  335
9.2 Properties of Movement Data  . . . . . . . . . . . . . . . .  338
9.2.1 Temporal Properties  . . . . . . . . . . . . . . . . . . .  339
9.2.2 Spatial Properties . . . . . . . . . . . . . . . . . . . .  343
9.2.3 Mover Set and Mover Identity Properties  . . . . . . . . .  344
9.2.4 Data Collection Properties . . . . . . . . . . . . . . . .  347
9.3 General Procedures of Movement Analysis  . . . . . . . . . .  352
9.4 Movement in Context  . . . . . . . . . . . . . . . . . . . .  354
9.4.1 Visual Tools for Observation of Relations  . . . . . . . .  355
9.4.2 Computational Enhancement to Observation of Relations  . .  357
9.4.3 Extraction of Relation Occurrences . . . . . . . . . . . .  360
9.4.4 Support of Analytical Reasoning  . . . . . . . . . . . . .  361
9.5 Movement Behaviours  . . . . . . . . . . . . . . . . . . . .  361
9.6 Personal Privacy . . . . . . . . . . . . . . . . . . . . . .  367
9.7 Future Perspectives  . . . . . . . . . . . . . . . . . . . .  369
9.8 Suggested Exercises  . . . . . . . . . . . . . . . . . . . .  373
9.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . .  374
References . . . . . . . . . . . . . . . . . . . . . . . . . . .  375

Abstract. We re-visit the key parts of the conceptual framework from chapter 2 and link them to the transformational and analytical methods from chapters 3-8. We put the methods in correspondence with the types of analysis tasks. We show how the properties of available movement data can be investigated and explain their implications for the analysis. We suggest general analytical procedures composed of different types of tasks for gaining comprehensive knowledge from movement data. We discuss the methods and procedures allowing detection and analysis of various kinds of relations between movement and its spatio-temporal context. We reason about specific and general movement behaviours of individuals and collectives and argue that only visual analytics approaches can currently support reconstruction of general movement behaviours from movement data. Regarding the necessity to protect personal privacy of people whose positions are contained in movement data, we outline the approaches to privacy protection depending on the types of analysis tasks. We conclude the chapter with a discussion of future perspectives and suggest several exercises to the readers.

Fig.9.8. The flow chart represents possible sequences of tasks in movement analysis

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . .  377

behaviour: The way and manner in which organisms, systems, or artificial entities act in conjunction with their environment, which includes other system, organisms, and entities as well as the physical environment. This book specifically addresses movement behaviour.

clustering: A process that groups a set of entities into homogeneous groups (clusters) such that objects in the same cluster share a common property, i.e., they are similar with respect to some similarity measure and are dissimilar with respect to the same measure from objects in the remaining clusters.

collective movement behaviour: Movement behaviour of multiple objects moving simultaneously within the same space.

collective movement event: a movement event occurring to two or more movers. Collective movement events are defined in terms of relations between the movers: encounter event, spatial concentration (cluster) event, parallel movement event, opposite movement event, etc. A collective movement event includes at least one point from the trajectory of each mover.

context: The conditions (circumstances) in which an event, action, movement, etc. takes place. In particular, spatio-temporal context of movement consists of properties of locations and time units and of objects existing in space and time: static spatial objects, moving objects, and events, in particular, spatial events.

cumulative movement characteristics (attributes): Positional attributes 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. Cumulative characteristics include all interval characteristics and the temporal distances to the starts and ends of the trajectories.

data mining: The process of analyzing large amounts of data to identify unexpected or unknown patterns that might be of value to an application. Data mining is usually used as a synonym of knowledge discovery. However, data mining refers to a particular step in the knowledge discovery process.

data pre-processing: A step of the knowledge discovery process where data are prepared before analysis methods can be applied. This step may include data cleaning (removing noise and/or outliers, handling missing values, resolving inconsistencies), integration, formatting, reduction, etc.

data transformation: A step of the knowledge discovery process where data are converted to a form matching a particular task or suitable for application of a particular analytical tool.

database: A shared collection of logically related data, and a description of this data, designed to meet the information needs of an organization and to support its activities.

density map: A map that shows the presence of a phenomenon over space, for example, the presence of moving objects, represented as the number per area unit (i.e., density). Densities are often represented by colour-coding, where brighter colours correspond to higher densities.

distance function: An algorithm assessing the dissimilarity between objects. Distance functions are used in clustering. The most common distance function assesses the dissimilarity as the Euclidean or, more generally, Minkowski distance between vectors or points in a multi-dimensional space of object features, i.e., values of multiple attributes.

dynamic attribute: An attribute whose values change over time.

episodic movement data: Data about spatial positions of moving objects where the positions between the measurements cannot be reliably reconstructed by means of interpolation, map matching, or other methods due to large time intervals between the measurements. Examples are positions of mobile phone calls or credit card transactions.

event, or temporal object: A physical or abstract entity having a specific position in time, i.e., instant or interval of its existence. An event can be considered as instantaneous if its duration is negligibly small or not relevant to an application. Examples of events are a snowfall, a football game, or a traffic congestion.

event data: Data describing existential changes, i.e., appearance and disappearance of temporal objects (events). For each event, the data specify the time interval of its existence.

flow: An aggregate of multiple movements from one location to another. Examples include count of commuting people or amount of transported goods. A flow can be seen as a vector connecting two locations and associated with one or more aggregate attributes derived from the individual movements that have been summarized.

flow map: A cartographic representation of flows shown in a geographic space. Typically, flows are represented by straight or curved lines connecting the start and end locations with the thickness proportional to the aggregate attributes. Alternatively, the attributes can be represented by varying levels of transparency or by colour-coding. Flow maps are not meant to show the actual paths between the locations.

general movement behaviour: Individual or collective movement behaviour can be general in terms of movers, space, and/or time. In terms of movers, it is the typical behaviour pertaining to a population or class of movers or to a type of collective. It includes possible variations depending on the properties of the movers. In terms of space, it is the common behaviour that can be observed in multiple parts of space, including possible variations depending on the spatio-temporal context. In terms of time, it is the common behaviour that can be observed during a sufficiently long time period or in multiple time units, including possible variations depending on the spatio-temporal context. A general movement behaviour is a common basis for multiple specific movement behaviours.

GPS-track: A movement track recorded by a device that is attached to a moving object and determines object’s geographical positions using the GPS (Global Positioning System).

identifier: One or several attributes that uniquely identify individuals in a database. For example, a Social Security Number uniquely identifies the person with which it is associated.

individual movement behaviour: Movement behaviour of a single moving object.

individual movement event: a movement event occurring to a single mover (i.e., within a single trajectory). Individual movement events may be defined in terms of values of movement attributes (stop event, low speed event, turn event, etc.) or as instances of relations of movers to the context (visit of a place, coming close to an object, passing between two objects, etc.). An individual movement event consists of either one point or several consecutive points of an individual’s trajectory.

instant movement characteristics (attributes): Positional attributes referring to moments (points in time): instant speed, direction, acceleration (change of speed), and turn (change of direction).

interaction: A relation between two or more spatial objects when the objects are so close in space that they may have mutual or reciprocal action or influence upon one another.

interpolation of trajectories: Reconstruction of the most probable object’s positions at the time moments between the moments of the measurements.

interval movement characteristics (attributes): Positional attributes referring to time intervals of a chosen constant length before, after, or around a given time moment: travelled distance, displacement, sinuosity, tortuousity, various statistics of the instant characteristics, etc.

knowledge discovery: The process of extracting useful and non-trivial knowledge from data. When applied to movement data, it is often called mobility knowledge discovery. Knowledge discovery consists of many steps, including data selection, data pre-processing, data transformation, data mining, pattern interpretation, and consolidation of the discovered knowledge.

location: An element of space. The term may refer to points, areas, lines, or volumes, depending on the application and data properties.

map matching: The process of combining electronic map with location information to obtain the real position of a moving object in a network.

medoid: Medoid of a group of points is the point with the minimal average distance to all other points of the group.

movement: The sequence of changes in the spatial position of a moving object. Movement can result from an action performed by a moving object itself to go from one place to another (e.g., a person, a car), or by an action performed by other objects that cause the change of position of the moving object (e.g., a package, a dead leaf).

movement behaviour: The behaviour related to movement; the way and manner in which an object, a set of objects, or a class of objects moves in space over time and interacts with the spatio-temporal context.

movement data: Spatio-temporal data describing changes of spatial positions of one or more moving objects. Movement data consist of movement tracks of the objects.

movement event: An event occurring during movement of one or more objects, for example, change of movement characteristics (speed, direction, etc.), stop, approaching of another object, entering a particular place, etc. Movement events are typically spatial events. Movement events can be extracted from trajectories.

movement pattern: A representation that characterizes a specific movement behaviour shown by one or a set of moving objects. In data mining, it refers to a pattern extracted from movement data by means of data mining algorithms. Examples of movement patterns include flock, leadership, converging, encounter, etc.

movement track: The sequence of position records representing the movement of an object for the whole duration of the movement.

mover: See moving object.

moving object (mover): An object capable of movement or having movement. For simplification, we assume the moving object is spatially represented as a single moving point. We thus ignore shape changes.

moving event: A spatial event whose spatial position changes over time.

object: A physical or abstract entity. Objects can be classified according to their spatial and temporal properties; see spatial object, event, spatial event, moving object.

origin-destination matrix (OD-matrix): A representation of flows in the form of matrix where the rows and columns correspond to different locations and the cells contain the values of the aggregate attributes.

pattern: A representation that characterizes a set (or subset) of data in a summarized way. In data mining, a pattern is a model that represents a summary of the analysed data set with respect to some criteria.

place of interest: A specific location that is of interest in a particular context. Examples include public places such as monuments, hotels, restaurants, etc., or personal places such as home, work, daily shopping place, etc.

point of interest: See place of interest. Notice that point of interest is a generic term which does not necessarily mean that the specific location has point geometry; it can be a line or a region. A more precise term is ‘place of interest’ in which the type of the associated geometry is not specified.

position record: A data record (e.g., made by a sensing device) representing a spatio-temporal position of a moving object. The main components of a position record are spatial (geographical) coordinates and timestamp specifying the time when the object’s position was measured. A position record may also include object identifier and values of thematic attributes related to the position.

positional attributes: Attributes characterizing positions or segments within trajectories. Positional attributes can represent instant, interval, and cumulative characteristics of the movement.

progressive clustering: An analytical procedure consisting of a sequence of steps in which clustering is applied either to the whole dataset or to the members of one or more clusters obtained in the previous steps. In each step, a different distance function or different parameter settings may be used. The purpose is to progressively refine the clustering results and the understanding of the data by the analyst. The procedure needs to be supported by visualization and interaction techniques.

quasi-continuous movement data (quasi-continuous trajectories): Movement data with fine temporal resolution allowing approximate reconstruction of the continuous paths of the moving objects by means of interpolation and/or map matching.

relation event: An occurrence of a particular spatial or spatio-temporal relation between one or more movers and some elements of the spatio-temporal context, such as other movers, static spatial objects, events, etc.

space: A continuous or discrete set consisting of locations. An important property of space is the existence of distances between its elements. Space has no natural origin and no natural ordering between the elements. Locations in space are identified using a spatial reference system, such as geographical coordinates.

space-time cube (STC): A unified representation of space and time as a 3-dimensional cube in which two dimensions represent space and one dimension represents time. Spatio-temporal positions can be represented as points in an STC and trajectories as three-dimensional lines.

space-time prism: The set of all locations that can be reached by a moving object given a maximum possible speed between a starting and an ending point in space-time. A space-time prism can represent the uncertainty about the position of a moving object between two known (measured) positions.

spatial distribution: A distribution of values of one or more attributes over space (i.e., different locations) in a given time unit. In particular, may include attributes expressing the presence of various spatial objects (movers or spatial events) in the locations and their properties, possibly, in an aggregated form.

spatial event: An event having specific position in space, which is not necessarily constant during the time of event's existence. An event may be considered as spatial or not depending on the spatial scale of the analysis.

spatial event data: Spatio-temporal data describing existential changes occurring in space, i.e., appearance and disappearance of spatial events. For each event, the data specify its position in space and the time interval of its existence.

spatial object: An object having a particular position in space in any time moment of its existence.

spatial situation: Spatial positions and dynamic characteristics of spatial objects existing in a given time unit and also an attribute characterizing a time unit in terms of the existing objects and their spatial positions and dynamic characteristics.

spatial time series: Spatio-temporal data describing changes of thematic properties (values of thematic attributes) of locations and spatial objects. The data consist of time series of attribute valuesreferring to different locations or spatial objects.

spatio-temporal context: See context.

spatio-temporal data: Data describing changes occurring in space over time, including existential changes (appearance and disappearance of spatial objects), changes of spatial properties (spatial position, size, shape, and orientation), and changes of thematic properties (values of thematic attributes) of locations and spatial objects.

spatio-temporal object: An object having specific positions in space and time, i.e., a spatial event or a moving object.

spatio-temporal position: A position of a spatio-temporal object at a given time unit, represented by a tuple containing at least two components (time unit, location), where location may be in 2D or 3D.

specific movement behaviour: A particular combination of movement events and/or relation events.

static spatial object: A spatial object that exists during the whole time span under study and whose spatial position does not change during this time. task, analysis task, analytical task: A piece of work aiming to find an answer to some question.

thematic attribute: An attribute whose values do not involve positions in space or in time.

time: a continuous or discrete linearly ordered set consisting of time instants or time intervals, jointly called time units. Time units are identified using a temporal reference system, such as calendar. Besides the linear order, time units may be arranged in cycles. In analyzing spatio-temporal phenomena, such as movement, it may be necessary to account for the natural time cycles resulting from the earth’s daily rotation and annual revolution, cycles of human activities, such as weekly cycle, and/or for application-specific time cycles, such as the cycles of the circulation of public transport on standard routes.

time series: Data describing changes of values of one or more thematic attributes over time. For a sequence of time units, the data specify the corresponding attribute values.

time unit: an element of time. The term may refer to time instants or time intervals.

trajectory: A part of the movement of an object that is of interest for a given application and defined by a time interval that is included inside the lifespan of the movement. The two extreme positions of the trajectory are called its start and end positions.

trajectory attributes: attributes characterizing trajectories as wholes, for example, length, duration, average speed, etc.

trajectory clustering: The process of clustering a set of trajectories into homogeneous groups according to one or more properties characterizing them. These properties can be spatial (e.g., start position, end position, length), temporal (e.g., start time, end time, duration), or dynamic (e.g., position, direction, and speed in different time units).

visual analytics: The science of supporting human understanding, analytical reasoning, knowledge generation, problem solving, and decision making on the basis of large and complex data. Visual analytics technology combines automated analysis techniques with interactive visualizations, which create appropriate conditions for human abstractive perception of relevant information, understanding, and reasoning.