A Primer on Visual Analytics Special focus: movement data

Transcription

1 A Primer on Visual Analytics Special focus: movement data Gennady Andrienko Natalia Andrienko

2 Outline 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary

3 Outline Visual Analytics 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary

4 Visual Analytics: the science of analytical reasoning facilitated by interactive visual interfaces People use visual analytics tools and techniques to Synthesize information and derive insight from massive, dynamic, ambiguous, and often conflicting data Detect the expected and discover the unexpected Provide timely, defensible, and understandable assessments Communicate assessment effectively for action The book (IEEE Computer Society 2005) is available at Analytical reasoning = data information knowledge explanation (interpreted data) (for myself) (for others)

5 Visual Analytics: divide the labor between the computers and humans to use the best of each Computers can store and process great amounts of information are very fast in searching information are very fast in processing data can extend their capacities by linking with other computers can efficiently render high quality graphics, both static and dynamic Humans are flexible and inventive, can deal with new situations and problems can solve problems that are hard to formalise can reasonably act in cases of incomplete and/or inconsistent information can simply see things that are hard to compute can employ their previous knowledge and experience

6 Visual Analytics: the importance of visualization Visualize = make perceptible to human s mind Visualisation offers a method for seeing the unseen. B. McCormick, T. DeFanti, and M. Brown. Definition of Visualization. ACM SIGGRAPH Computer Graphics, 21(6), November 1987, p.3 An estimated 50 percent of the brain's neurons are associated with vision. Visualization < > aims to put that neurological machinery to work. (ibid.) An abstractive grasp of structural features is the very basis of perception and the beginning of all cognition. R. Arnheim. Visual Thinking. University of California Press, Berkeley 1969, renewed 1997, p. 161 (in other words: seeing already includes analyzing) Visualization is essential for enabling human analysts to use their inherent cognitive capabilities

7 Visual Analytics technology: combining methods for visual and computational analysis Goal: enable synergistic work of humans and computers

8 Visual Analytics: a summary description Visual Analytics is meant to enable people to make sense from complex data and solve complex problems Complexities: massive amounts, high dimensionality, heterogeneity, multiple facets, time variance, incompleteness, uncertainty, inconsistency Visual Analytics combines interactive visual interfaces with algorithmic methods for data pre-processing, transformation, feature/pattern extraction,... Interactive visual interfaces help analysts to utilize their perceptual and cognitive capabilities fully and effectively Computer technologies compensate for the natural limitations in human skills and abilities and augment the discovery process The goal is to enable synergistic collaboration of humans and computers where each side can utilize its capabilities in the best possible way

9 Outline Data 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary

10 Types of components in data Types of values: Numeric Textual Predefined values (e.g., codes) Free text Spatial Coordinates Place names Addresses Temporal Other (image, video, audio,...) Scales of measurement*: Nominal ( order, distances) gender, nationality,... Ordinal (+ order, distances) evaluations: bad, fair, good, excellent Interval (+ order, + distances, ratios, meaningful zero) temperature, time,... Ratio (+ order, + distances, + ratios, + meaningful zero) any quantities * Stevens, S.S. (1946). "On the Theory of Scales of Measurement". Science 103 (2684):

11 Properties of data components Generalization of the scales of measurement Discrete or continuous Relations between the elements Mathematical relations Ordering (full or partial) Distances Ratios Semantic relations is-a part-of kinship... Examples: Statistical population (set of discrete entities): discrete, no relations Texts: discrete, no relations Evaluation scores: discrete, ordered Temperature values, times: continuous, ordered, have distances Amounts: continuous, ordered, have distances, have ratios Spatial locations (2D, 3D): continuous, have distances

12 Semantic roles of data components Reference: What is described? Object (physical or abstract) Place Time Object time Place time Generally: anything specified as a single element or combination Characteristic, or attribute: What is known about it?

13 Reference: time Reference: place Attributes......

14 Common classes of data structures Object-referenced data: attributes of objects Events: attributes include time of existence (moment or interval) Spatial objects: attributes include spatial location (point, area, or volume) Spatial events: attributes include existence time and location Time-referenced data, a.k.a. time series: attributes observed in different times (moments or intervals) Space-referenced data, a.k.a. spatial data: attributes observed in different places Object time series: attributes of objects observed in different times Trajectories of moving objects: time series of spatial locations Spatial time series: attributes observed in different places and times

15 Multidimensional data Data including multiple attributes May have various types of references: objects, places, times, combinations... Multiple attributes referring to times: multidimensional time series Multiple attributes referring to places: multidimensional spatial data Multiple attributes referring to places + times: multidimensional spatial time series

16 Classes of spatio-temporal data Include space and time as references or characteristics Reference: objects; attributes: existence time + location +... spatial events Earthquakes, mobile phone calls, public events,... References: places + times; attributes:... spatial time series Weather, population census data for different years, election results,... References: objects + times; attributes: location +... trajectories Trajectories of people, animals, vehicles, icebergs, hurricanes,...

17 Outline Visualization 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary Interaction

18 Components of a visual display Display space (or visual space): set of positions Visual marks: points, geometric shapes, symbols positioned in the display space Types of marks: Points Lines Areas Surfaces Volumes Visual properties of marks: colour, shape, orientation, size, texture

19 Visual variables Jacques Bertin (1983): Semiology of Graphics. Diagrams, Networks, Maps. University of Wisconsin Press, Madison. Translated from Bertin, J.: Sémiologie graphique, Gauthier-Villars, Paris, Position in the display space (x, y) Size (length, area, volume) Shape Value, or degree of darkness (from light to dark) Colour (hue) Orientation Texture

20 Perceptual properties of visual variables Association: several marks with the same value of this visual variable can be easily grouped (perceived all together) despite differences in other visual variables Selection: easy to locate marks with a given value of the visual variable and perceive them separately from others Order: the values of the variable can be put in an order, e.g., from small to big, from light to dark,... Quantity: differences between two values of the variable can be interpreted numerically, e.g., how much bigger Perceptual length: number of different values of the variable that can be easily distinguished by an average human

21 Perceptual properties of visual variables Association Selection Order Quantity Length Position limited by display size Size Value (darkness) Texture + + +/- * Colour ** Orientation Shape * + : grain density or size; - : grain shape ** + for parts of the spectrum (e.g., cold hot)

22 The fundamental rule of visual mapping Visual mapping: the process of mapping data components to visual variables The fundamental rule: the perceptual properties of the visual variables must correspond to the properties of the data components they represent

23 Correspondence of visual variables to types of data components Nominal Ordinal Interval Ratio Spatial Temporal Position Size Value (darkness) Texture + + * Colour + + ** Orientation Shape * grain density or size ** parts of the spectrum (e.g., cold hot)

24 Common display types Scatter plot Bar chart Line chart Map Gantt chart Visual variables x-position y-position x- or y-position size (length) x-position y-position (x,y)-position other variables position size (length) Data components numeric attribute numeric attribute references (objects or times) numeric attribute references (typically times) numeric attribute spatial locations (references or attributes) space-referenced attributes event existence time (start, end) event duration

25 Visualization of relations The visual variables can represent mathematical relations between data elements: ordering, distances, ratios Semantic relations need to be represented explicitly by special marks and/or layouts Node-link diagram: objects are represented by nodes (point marks) and relations by links (linear marks) between nodes Matrix: objects are represented by horizontal and vertical positions and relations by marks in the cells Venn diagram: relations between sets Enclosing shapes: part-of relations...

26 Increasing the number of available visual variables Display space division (small multiples) Space embedding (e.g., diagram spaces within map space) Complementary displays

27 Additional variable: display time (animated displays)

28 Display time (animated displays) Theoretically suitable for representing a temporal component of data Problems: Does not support comparisons across times Change blindness Automatic animation: discouraged Interactive controlling of the display time: may be used

29 Basic interactions (video)

30 Purposes of interactive operations Access exact data values Link pieces of information from complementary displays Increase display expressiveness Decrease display clutter Focus on data portions Find particular pieces of information Compare...

31 Outline Tasks 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary

32 Types of data analysis tasks Data analysis task: find an answer to a question concerning the data Jacques Bertin: There are as many types of questions as components in the information (Jacques Bertin (1983): Semiology of Graphics. Diagrams, Networks, Maps. University of Wisconsin Press, Madison. Translated from Bertin, J.: Sémiologie graphique, Gauthier-Villars, Paris, 1967). Type focus of interest (what is to be characterized by what) Reference: time Reference: place Attributes Example: spatial time series...

33 Example: spatial time series Data structure S l May be multidimensional V Set of locations T t Set of time moments v Set of thematic attribute values S T V Data record: (l, t, v)

34 Task types (= foci) for spatial time series Peuquet, Donna J. (2002) Representations of Space and Time, New York: Guilford. S S T l t V? T l? v V Where + when what? S What + where when? T? t v V What + when where?

35 Comparison tasks = questions about relations T l2 S t2 l1 t1 V? How is the value at (l1, t1) related to that at (l2, t2)? Most typical comparison tasks Same time, different places: At the time t, how does the value at location l1 differ from that at l2? Same place, different times: How did the value at location l change from time t1 to time t2? Relation type: same, different, greater than, less than, Relation metrics, e.g. difference, ratio, distance

36 Task type = focus + target Task focus: Which data component is characterized by which data component(s)? Task target: values or relations? Lookup tasks: address values of data components Comparison tasks: address relations between values of data components

37 Examples of tasks What was the property crime rate in California in 2000? When did the property crime rate in California exceed 6,000 crimes/ 100,000 population? Where was the property crime rate in 2000 below 2,500? Was the property crime rate in California in 2000 higher or lower than in 1995? Which states had in 2000 higher crime rates than California? Lookup tasks Comparison tasks

38 Task levels Elementary tasks address one or several individual values of data components, i.e., elements of the sets The previous examples are elementary tasks Synoptic tasks address whole sets or subsets considered in their entirety. These tasks require abstraction from specific to general. Examples: How did the property rate in California change over the period ? How similar or different were the evolutions of the property crime rates in California and in Texas? How were the values of the property crime rate distributed over the territory of the USA in 2000? How similar or different were the spatial distributions in 1960 and in 2000? How are different temporal evolution patterns distributed over the territory? How did the spatial distribution pattern evolve over the whole time period?

39 Synoptic analysis level (1) Tasks may be synoptic with regard to one component and elementary with regard to another Space as a whole Spatial behaviour (value distribution over the space) Specific time Specific place t Synoptic with regard to space but elementary with regard to time Temporal behaviour (value variation over the time) Time as a whole Synoptic with regard to time but elementary with regard to space

40 Synoptic analysis level (2) + Time as a whole Space as a whole Synoptic with regard to both space and time Aspect 1: Temporal variation of the spatial behaviour Spatio-temporal behaviour Aspect 2: Spatial variation of the temporal behaviour t1 t2 t3 40

41 General formulations of synoptic tasks Synoptic tasks are about behaviours of attributes (analogy to behaviours of functions) Behaviour: a generalization of the concepts of distribution (statistical, spatial, temporal), temporal evolution, and other kinds of variation Behaviour characterization task: What is the behaviour of the attribute(s) over the set of references? Behaviour comparison tasks: Compare the behaviours of the attribute(s) over two or more subsets of the reference set. Compare the behaviours of attributes A and B over the reference set. Behaviour search task: On which subsets of the reference set do the attributes behave in the given way?

42 Decomposing a complex behaviour Data with 2 referential components: X Y A (e.g., S T A) The overall behaviour analysis task: What is the behaviour of A over the set X Y? B X Y (A(x,y)) What was the spatio-temporal behaviour of the crime rates in the USA over ? Slices of the overall behaviour: B Y (A(x,y) x = const); B X (A(x,y) y = const) For a selected element from X, what is the behaviour of A over the set Y? What was the temporal behaviour of the crime rates in California over ? For a selected element from Y, what is the behaviour of A over the set X? What was the spatial behaviour (distribution) of the crime rates over the USA in 2000? Aspects of the overall behaviour: B X (B Y (A(x,y))); B Y (B X (A(x,y))) How are the temporal behaviours of the crime rates over distributed over the territory of the USA? How did the spatial behaviour of the crime rates over the territory of the USA evolve over the period ?

43 Decomposing a complex behaviour: slices Space as a whole Spatial behaviour at this time Selected time t Selected place Temporal behaviour in this place Time as a whole

44 Decomposing a complex behaviour: aspects + Time as a whole Space as a whole Spatio-temporal behaviour Aspect 2: Spatial variation of the temporal behaviour Aspect 1: Temporal variation of the spatial behaviour t1 t2 t3

45 Task levels and types in visual analytics Elementary tasks play a secondary role in analysis (analysts may sometimes need to look up for specific values or compare one with another). Elementary tasks need to be supported (e.g., by basic interactions), but they are not of main concern in VA. VA primarily aims at supporting synoptic analysis tasks. Depending on the task focus and target, different visual, interactive, and computational techniques may be suitable. Spatial variation of the temporal behaviour B S (B T (A(s,t))) Temporal variation of the spatial behaviour B T (B S (A(s,t))) t1 t2 t3

46 Task foci and data structures Tasks may require changing the data structure Example: spatial event data E S T A E: set of events (objects), e.g., earthquakes; S: space, i.e., set of locations; T: time, i.e., set of moments; A: thematic attributes, e.g., magnitude, depth, radius,... Synoptic task focusing on E: what is the behaviour of S, T, and/or A over E? What are the distributions of the spatio-temporal positions and thematic attributes over the set of the earthquakes? Synoptic tasks focusing on S T: what is the behaviour of E and A over S T? How are the earthquakes and their thematic attributes distributed over the space and time? A meaningful change of the viewpoint: S T is a universal container of events and everything Requires considering data as spatial time series S T P(E) A

47 Possible task foci in movement analysis Multi-perspective view of movement Moving objects Trajectories M (T S) Spatial events Spatio-temporal positions E (T S) Space (locations) Presence dynamics S (T P(M E)) Time (time units) Spatial situations T (S P(M E)) Data transformations can bring available data to a suitable form depending on the task focus

48 Outline Transformations 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary

49 Transformations to support abstraction Simplification: reduce excessive detail and high-resolution fluctuations E.g., smoothing of time series, trajectories; spatial smoothing Generalization: transform to larger units E.g., time moments intervals; points in space areas; continuous range of numbers value intervals (discretization); individual nominal values semantic categories Grouping of similar and/or close items: elements subsets Close in space and/or in time Having similar values of thematic attributes Aggregation: summarize values by larger units or by groups of items E.g., mean, range, quartiles, percentiles; mode; centre and radius;...

50 Transformations for managing large data volumes Sampling Generalization and aggregation Grouping of similar and/or close items

51 Transformations for focusing on the relevant Filtering: spatial, temporal, attribute-based Extraction of features of interest From time series: increase/decrease, peaks/pits, values above/below a threshold,... events, spatial events From spatial distributions: peaks/pits, ridges, saddles,... static spatial objects, spatial events From trajectories: stops, slow movement, speed above a threshold,... spatial events

52 Transformations for adapting data structures to tasks Projection For example, spatial time series S T A: S (T A) set of local time series of A referring to different spatial locations T (S A) set (sequence) of spatial distributions of A referring to different times Aggregation For example, spatial events E S T A: Spatial time series S T P(E) A (obtained by aggregating the events by spatial and temporal units) Integration and disintegration For example, spatial events trajectories (O set of object identifiers): E O S T A O (T S A)

53 Transformations changing the data structure For example, spatio-temporal data: Spatial time series Projection Projection Local time series Spatial distributions Aggregation Extraction Extraction Aggregation Integration Spatial events Trajectories Extraction, disintegration

54 VA support to data transformations Example: generalization and spatio-temporal aggregation of trajectories

55 VA support to data transformations Example: extraction of spatial events from trajectories

56 Outline Example 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary

57 Transformations enable multi-perspective analysis of movement data Moving objects Trajectories Spatial events Movement data Locations Local time series Spatial event data Spatial time series Times Spatial distributions

58 Example dataset: trajectories of cars in Milan GPS-tracks of 17,241 cars in Milan, Italy Time period: from Sunday, the 1st of April, to Saturday, the 7th of April, 2007 Received from Comune di Milano (Municipality of Milan) Data structure: Car identifier Date and time Geographic coordinates Speed The trajectories from one day are drawn on a map with 5% opacity

59 Role of clustering in VA Grouping of similar or close items plays an essential role in VA as a tool supporting abstraction: elements subsets; the subsets may be considered as wholes as a tool to manage large data volumes as a tool to study the behaviour of attributes (i.e., distribution of attribute values) over the set of references, particularly, multiple attributes spatial and spatio-temporal positions of objects dynamic (time-variant) attributes, such as time series of numeric values trajectories of moving objects

60 Two major types of clustering Partition-based clustering: divide items into groups so that items within a group are similar (close) and items from different groups are less similar (more distant) Examples: k-means, self-organizing map Property of the result: each item belongs to some group Density-based clustering: find groups of highly similar (close) items and separate from them items that are less similar (more distant) to others Examples: DBScan, OPTICS Properties of the results: some items belong to groups, other items remain ungrouped and are treated as noise

61 Two major types of clustering: an example Partition-based: convex clusters including all objects Density-based: dense clusters of arbitrary shapes; many objects are treated as noise (gray)

62 Use of two types of clustering Partition-based: unites elements into subsets for abstraction reduction of analytical workload data aggregation integrates multiple attributes, allows comparison of items in terms of multiple attributes Density-based: separates what is common, frequent from what is specific, infrequent may be a tool for studying attribute behaviours (distributions) concentrations of close/similar objects may have special meanings e.g., spatio-temporal cluster of low speed events traffic jam

63 Outline Trajectories 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary Movers Trajectories Movement data Spatial events Spatial event data Spatial time series Locations Local time series Times Spatial distributions

64 Diverse distance functions for trajectories Trajectories are time series of spatial positions and other movement attributes Trajectories are complex objects with heterogeneous properties: positions in space and in time, shape, dynamics of speed,... A single distance measure accounting for all properties would be hard to implement and results would be hard to interpret Trajectories can be explored using diverse distance measures addressing different properties Simple, easily interpretable, computationally efficient Allowing to answer different types of questions concerning trajectories

65 Interactive progressive clustering Applying different distance measures Data: trajectories of cars in Milan Step 1: clustering according to the spatial proximity of the end points Distance function: common ends Question: what are the most frequent destinations of car trips?

66 Interactive progressive clustering Applying different distance measures (2) Data: one (or more) selected cluster(s) from the previous step Step 2: clustering according to the similarity of the routes (shapes) Distance function: route similarity Question: what routes are usually taken to get to the selected destination?

67 Interactive progressive clustering Purposes Controlled refinement of previously obtained clusters for reducing internal variation more detailed investigation of data subsets of interest Study of a set of complex objects with heterogeneous properties application of diverse distance measures addressing different properties incremental construction of multifaceted knowledge by progressively considering different properties

68 Where to read more S.Rinzivillo, D.Pedreschi, M.Nanni, F.Giannotti, N.Andrienko, G.Andrienko Visually driven analysis of movement data by progressive clustering Information Visualization, 2008, v.7 (3/4), pp

69 Clustering of very large sets of trajectories Problem: clustering of complex objects (such as trajectories) involving nontrivial distance functions (such as route similarity ) can only be done in RAM, i.e. for a relatively small dataset Our approach: 1. Take a subset (sample) of the objects suitable for processing in RAM. 2. Discover clusters in the subset. 3. Load the remaining objects into RAM by portions. Classify each object = identify to which of the discovered clusters the object belongs. Store the result of the classification in the database. 4. Take the objects that remained unclassified and apply steps 1 to 3 to them. Repeat the procedure until no meaningful new clusters can be discovered. Question: how to identify the cluster where an object belongs?

70 Classifier, the main idea From each cluster C i select one or more representative objects (prototypes) and respective distance thresholds: { (pt 1, d 1 ),, (pt n, d n ) } such that o C i k, 1 k n: distance (o, pt k ) < d k The set of all cluster prototypes with the respective distance thresholds defines the classifier A new object o may be ascribed to the cluster if the same condition holds for it. For each object from a large database: measure the distances to all prototypes; take the closest prototype among those with the distances below the thresholds and ascribe the object to the respective cluster; if no such prototypes found, label the object as unclassified. To select prototypes: Divide the cluster into round subclusters Take the medoid of each subcluster as one of the prototypes Take the maximum of the distances from the subcluster medoid to the subcluster members as the distance threshold for this prototype

71 Dividing a cluster into round sub-clusters: an illustration using points This can be done by a variant of the K-medoids clustering algorithm where the desired maximum radius of a subcluster is a parameter.

72 Division of a cluster of trajectories into round subclusters

73 To obtain meaningful results, the analyst may needs to review and, possibly, edit the classifier Some trajectories are not very similar to the others. Should such trajectories be in the cluster? Should I keep the three branches in one cluster? Or should I divide the cluster into two or three clusters? Is it good to have this prototype? This is not a core trajectory of the cluster.

74 Example of interactive editing

75 What are the most frequent routes on Wednesday? Result of clustering of single-day trajectories by route similarity

76 How frequent are these routes during the whole week? Result of building a classifier and applying it to the whole set of trajectories

77 Further analysis of the trajectories The analysis is continued by loading a subset of the unclassified trajectories ( noise ) to RAM, applying clustering to it, building a new classifier, and applying the classifier to the whole set of unclassified trajectories. Empirical experience: With each new iteration step, the number and the sizes of discovered clusters substantially decrease in comparison to the previous step. After 4-5 steps of the procedure, only very small clusters can be discovered. The analyst s effort needed for editing of the classifier also decreases. The editing effort is high for big clusters with high internal variation, which mostly appear in the first step; the following clusters are smaller and cleaner. Unfortunately, no formal criterion for terminating the procedure.

78 Where to read more G.Andrienko, N.Andrienko, S.Rinzivillo, M.Nanni, D.Pedreschi, F.Giannotti Interactive Visual Clustering of Large Collections of Trajectories IEEE Visual Analytics Science and Technology (VAST 2009) Proceedings, IEEE Computer Society Press, 2009, pp.3-10

79 Outline Events 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary Movers Trajectories Movement data Spatial events Spatial event data Spatial time series Locations Local time series Times Spatial distributions

80 Example of analysis focusing on movement events Data: trajectories of cars in Milan Task: find places of traffic congestions and determine their characteristics (times of the congestions, durations, numbers of cars involved,...) Traffic congestion dense spatio-temporal cluster of low speed movement events Movement direction must be taken into account Places of interest: areas where at least one traffic congestion occurred areas containing the clusters Characteristics of places: time series of event counts, vehicle counts,... Data transformations: Trajectories Events Places Spatial time series

81 Step 1: extract low speed events from the trajectories Low speed := speed 10 km/h

82 Vertical dimension time

83 Step 2: density-based clustering of events by spatio-temporal positions and directions Distance function: neighbourhood defined as a cube neighbourhood defined as a sphere D s spatial distance threshold; D 0,D 1,,D N - distance thresholds for other attributes d s,d 0,d 1,,d N distances; d s distance in space Distance in time (t 1, t 2 are intervals): Distance for a cyclic attribute (V is the cycle length): E.g., direction: V = 360 ; d(5,355, 360 ) = 10

84 The result of the densitybased clustering of the slow movement events by their spatial positions, temporal positions, and movement directions (STD) with the distance thresholds 100 meters, 10 minutes, and 20 degrees and the minimum number of neighbors 5.

85 The STD-clusters, noise hidden

86 Step 3: unite STD-clusters in SD-clusters Cluster the events from the STD-clusters by the spatial positions and directions The result of the density-based clustering with the spatial distance threshold of 100 m and direction distance threshold of 20

87 Events that occurred in same or close places but in different times were formerly in different clusters, but now they are in the same clusters. One SD-cluster includes one or several STD-clusters.

88 Step 4: outline the places of interest Build spatial buffers around the SD-clusters of events The places are painted according to the prevailing movement directions of the respective events.

89 Belt road north-south on the east of the city (A50) Extended areas of congested traffic directed to the south and southeast Smaller areas of obstructed movement directed to the north and northwest Belt road west-east on the north of the city (A4) Very long area of congested traffic directed to the east Long area of congested movements directed to the west

90 Step 5: aggregate data by the places and by suitable time intervals, e.g., hourly Place-referenced time series of the counts of slow movement events

91 The temporal diagrams show the variation of the attribute value (vertical dimension) over time (horizontal dimension).

92 Map fragment (northwest) enlarged Congested traffic in the afternoon in the direction out of the city (northwest) Congested traffic in the morning in the direction to the south

93 Other map fragments enlarged East Northeast morning morning and midday morning and afternoon afternoon morning and afternoon morning afternoon morning

94 Where to read more IEEE VAST 2011 paper (best paper award) G.Andrienko, N.Andrienko, C.Hurter, S.Rinzivillo, S.Wrobel From Movement Tracks through Events to Places: Extracting and Characterizing Significant Places from Mobility Data IEEE Visual Analytics Science and Technology (VAST 2011), Proceedings, IEEE Computer Society Press, Extended version, covering also scalable clustering of events G.Andrienko, N.Andrienko, C.Hurter, S.Rinzivillo, S.Wrobel Scalable Analysis of Movement Data for Extracting and Exploring Significant Places IEEE Transactions on Visualization and Computer Graphics, 2013, 19(7),

95 Outline Situations 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary Movers Trajectories Movement data Spatial events Spatial event data Spatial time series Locations Local time series Times Spatial distributions

96 Spatio-temporal aggregation of trajectories

97 Division of the territory Characteristic points from the trajectories Spatial clusters of characteristic points Cluster centres seeds for Voronoi tessellation Details: Natalia Andrienko, Gennady Andrienko Spatial Generalization and Aggregation of Massive Movement Data IEEE Transactions on Visualization and Computer Graphics (TVCG), 2011, v.17 (2), pp

98 Spatial situations: presence

99 Spatial situations: flows

100 Clustering of spatial (flow) situations by similarity

101 Comparison of clusters of spatial situations Values for cluster 9 have been subtracted from values for all other clusters

102 Where to read more N.Andrienko, G.Andrienko, H.Stange, T.Liebig, D.Hecker Visual Analytics for Understanding Spatial Situations from Episodic Movement Data Künstliche Intelligenz, 2012, v.26 (3), pp

103 Outline Local time series 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary Movers Trajectories Movement data Spatial events Spatial event data Spatial time series Locations Local time series Times Spatial distributions

104 An alternative view of spatial time series: a set of local time series

105 An alternative view of spatial time series : a set of local time series We wish to represent the essential characteristics of the ST-variation explicitly by a formal model or a set of models.

106 Methods for spatio-temporal modelling (e.g. STARIMA) Account for spatial and temporal dependencies Require prior specification of multiple weight matrices expressing impacts among locations for different temporal lags may be difficult (the impacts are not easy to quantify) Build a single global model of the entire spatio-temporal variation It does not necessarily perform better than a set of local temporal models Assume spatial smoothness of the modelled phenomenon, i.e., closer places are more similar than more distant ones May be not very suitable for spatially abrupt phenomena

107 Existing techniques for time series modelling + Widely available in numerous statistical packages and libraries can be applied to spatially referenced time series - The modelling methods are designed to deal with singular time series hard to use for a large number of time series - Separate consideration of each time series ignores the phenomenon of spatial dependence (relatedness and similarities among spatial locations or objects) - Separate consideration of each time series does not allow data abstraction and generalisation over space

108 Combination of spatial and temporal modelling Approach 1: 1. Model the temporal variation independently for each location 2. Model the spatial variation of the parameters of the temporal models, e.g., as a random field Assumes that the character of the temporal variation is the same everywhere and only the parameters differ Approach 2: Model the spatial variation independently for each time step, e.g., as a random field Model the temporal variation of the parameters of the spatial models at each location Both approaches assume spatial smoothness of the phenomenon

109 Our approach Step 0: Prepare data Step 1: Group time series Details: Natalia Andrienko, Gennady Andrienko A Visual Analytics Framework for Spatio-temporal Analysis and Modelling Data Mining and Knowledge Discovery, 27(1), 55-83, Clustering Progressive clustering Interactive re-grouping For each group: Step 2: Analyse and model Select method Set parameters Compute and view model Step 4: Store model set Step 3: Evaluate model Predict values and compute residuals Visualise and analyse residuals

110 Step 1: Clustering of local TS Here: k-means (Weka) but may be another partition-based method Tried different k from 5 to 15 Immediate visual response facilitates choosing the most suitable k

111 Step 1: Re-grouping by progressive clustering

112 Step 2: Analysis and modelling A) Check automatically detected time cycles in the data. B) Select the current class (cluster) for the analysis and modelling. C) Build the representative TS. D) Select the modelling method. E) View and modify model parameters (this section changes depending on the selected modelling method).

113 Step 2: Analysis and modelling

114 Step 2: Analysis and modelling

115 Step 2: Analysis and modelling

116 Step 3: Model evaluation (analysis of residuals) The goal is not to minimise the residuals The model should not reproduce all fluctuations and outliers present in the data This should be an abstraction capturing the characteristic features of the temporal variation High values of the residuals do not mean low model quality The goal is to have the residuals randomly distributed in space and time (no detectable patterns) This means that the model correctly captures the characteristic, nonrandom features of the temporal variation

117 Analysis of residuals (example) No systematic bias: approximately equal numbers of positive and negative errors in each time step No periodic increases and decreases at the level of the whole group However, we are not sure about individual objects

118 More detailed analysis by subgroups Periodic drops It may be reasonable to consider this subgroup separately -> back to re-grouping

119 Use of a model for prediction We obtain a common model for a group (cluster) of time series Predicts the same values for all objects/places of the group The statistical properties of the distribution of the predicted values in each place differ from the distribution of the original values Adjustment of the prediction for individual objects/places: Compute and store the basic statistics (quartiles) of the original values for each object/place i: Q1 i, M i, Q3 i Compute the statistics of the model-predicted values for the same time steps as the original values: Q1, M, Q3 (common for the cluster) Shift (level adjustment): S = M i M M i Q1 i Scale factors (amplitude adjustment): F low = F high = M Q1 Let v t be the model-predicted value for an arbitrary time step t and v t i the individually adjusted value for the place/object i v t i = Q3 i M i Q3 M M + F low (v t M) + S, if v t < M M + F high (v t M) + S, otherwise

120 Use of a model for prediction: example Common prediction for a cluster: Set of individually adjusted predictions for this cluster: median

121 Prediction based on the models

122 Predicted: Monday Saturday Original:

123 Comparison of actual values with predicted (e.g., in monitoring) Absolute differences Normalized differences

124 Analysis and modelling of relationships between two time-variant attributes flow magnitudes mean speeds

125 Data transformation and clustering Dependency of attribute A(t) on attribute B(t): Divide the value range of B into intervals For each interval, collect all values of A that cooccur with the values of B from this interval Compute statistics of the values of A: minimum, maximum, median, mean, percentiles For each of these, there is a series B A, or A(B) Dependencies of maximal mean speed on flow magnitude Dependencies of maximal flow magnitude on mean speed

126 Dependency modelling: flow maximal mean speed

127 Dependency modelling: mean speed maximal flow

128 Graphical representation of the models built

129 Use of the models: simulation of extraordinary traffic from given places

130 The bottlenecks can be revealed even before the simulation

131 Simulated trajectories Some traffic re-routed to the south:

132 The speeds on the northern motorway

133 Animation of simulation results

134 Presence and flows for selected time intervals 20:00 20:10 21:00 21:10 21:30 21:40 00:00 00:10 22:00 Analyse- und Informationssysteme 22:10 IAIS 23:00 23:10

135 Multi-perspective analysis of movement Trip destinations, routes... Spatial events Moving objects Trajectories Movement data Periodic variation of flow volumes; Dependencies volume vs. speed Locations Local time series Spatial event data Spatial time series Times Spatial distributions Low speed events traffic jams Periodic (daily and weekly) variation of spatial situations

136 Movers Trajectories Spatial events Movement data Locations Local time series Spatial event data Spatial time series Times Spatial distributions Springer, June 2013 ISBN p. 200 illus., 178 in colour Ch.1. Introduction Ch.2. Conceptual framework Ch.3. Transformations of movement data Ch.4. Visual analytics infrastructure Ch.5. Visual analytics focusing on movers Ch.6. Visual analytics focusing on spatial events Ch.7. Visual analytics focusing on space Ch.8. Visual analytics focusing on time Ch.9. Discussion and outlook

137 Outline Summary 1. Introduction to visual analytics 2. Data types and structures; spatio-temporal data 3. Fundamentals of visualization and interaction 4. Types of tasks in data analysis 5. Data transformations 6. Multi-perspective analysis of movement by example a) Trajectories b) Movement events c) Spatial situations d) Local time series 7. Concluding summary

138 Concluding summary Visual analytics tools and techniques support human analysts in performing data analysis: Data Information Knowledge Explanation VA tools and techniques enable analysts to exploit effectively their visionbased cognitive capabilities Abstraction, grasping general, characteristic features, pattern detection and interpretation,... VA tools and techniques divide the analytical labour between humans and computers Use computer processing where human judgement is not needed Use computers to prepare data to human analysis Use computers to present data to analysts in the most suitable form

139 Design and use of VA techniques is based on data and task analysis Analyze data structure (components, types, references, attributes) Analyze the analysis task(s): what needs to be characterized in terms of what E.g., places in terms of traffic congestions Does the data structure correspond to the task(s)? Does it include necessary components? If no, find/design data transformations to obtain the structure needed E.g., extract events, find dense event clusters, outline places,... VA tools designer: provide support to analysts for performing the transformations Choose/design visual representations enabling the analyst to explore the data, fulfil the tasks, and thus obtain the required information and knowledge

140 Design of visual representations Following the rules of visual representation, select appropriate visual variables for representing data components Give primary attention to enabling synoptic analysis level Choose/design representations stimulating holistic perception and perceptual abstraction When necessary, involve computational data transformations supporting abstraction: generalization, aggregation, clustering,... Provide the possibility of focusing and obtaining details on demand through interactive operations: zoom, filter, drill down, get additional views,...

141 Enable effective use of computing power Support the use of algorithmic methods by visualizations and interactions Allow the analyst to investigate and understand the impact of algorithm parameters Support iterative analysis, returns to previous steps, trying alternative paths Support progressive refinement of analysis results Support progressive enrichment of obtained results by new facets and features

142 Thank you!