Spatio-temporal Aggregation for Visual Analysis of Movements
Gennady Andrienko, Natalia Andrienko
Fraunhofer Institute IAIS (Intelligent Analysis and Information Systems), Sankt Augustin, Germany
A
BSTRACT
Data about movements of various objects are collected in growing
amounts by means of current tracking technologies. Traditional
approaches to visualization and interactive exploration of
movement data cannot cope with data of such sizes. In this
research paper we investigate the ways of using aggregation for
visual analysis of movement data. We define aggregation methods
suitable for movement data and find visualization and interaction
techniques to represent results of aggregations and enable
comprehensive exploration of the data. We consider two possible
views of movement, traffic-oriented and trajectory-oriented. Each
view requires different methods of analysis and of data
aggregation. We illustrate our argument with example data
resulting from tracking multiple cars in Milan and example
analysis tasks from the domain of city traffic management.
CR Categories and Subject Descriptors: H.1.2 [User/Machine
Systems]: Human information processing – Visual Analytics;
I.6.9 [Visualization]: information visualization.
Additional Keywords: Movement data, spatio-temporal data,
aggregation, scalable visualization, geovisualization.
1 I
NTRODUCTION
One of the strengths of information visualization as an amplifier
of human cognition and ideation lies in supporting abstraction and
generalization [14]. Thus, appropriate positioning and/or
appearance of graphical elements representing data items can
stimulate holistic perception of multiple data items as a unit.
However, when the size and complexity of data increases, purely
visual approaches become insufficient and need to be combined
with computational generalization, which includes, among other
techniques (e.g. smoothing, filtering), data aggregation.
Aggregation is not only a tool to reduce the size of data but also a
way to distill general features out of fine-detail “noise”.
This paper considers the use of aggregation for visual analysis
of movement data, more specifically, data about multiple discrete
entities changing their spatial positions over time while preserving
their integrity and identity (i.e. the entities do not split or merge).
In our earlier papers we considered the structure and essential
properties of movement data and defined the possible general
analysis tasks [1] as well as the types of tools that could support
these tasks [3]. Among others, we discussed the use of data
aggregation and the possible ways of aggregating movement data.
In [2] we described a set of complementary tools for analysis of
movement data including database transformations, visualization,
interactive dynamic filtering, and clustering. We mentioned one
particular aggregation method, which was used for visualization
of clustering results. Unlike the previous publications, the current
paper primarily focuses on various possible ways of aggregating
movement data. The work has been done within an ongoing EU-
funded project GeoPKDD (http://www.geopkdd.eu).
In [1] and [3] we introduced a formal model of collective
movement of multiple entities as a function μ: E × T → S where E
is the set of moving entities, T (time) is the continuous set of time
moments and S (space) is the set of all possible positions. As a
function of two independent variables, μ can be viewed in two
complementary ways:
− as a set of trajectories of all entities: {μ
e
: T → S | e ∈ E}, where
the function μ
e
: T → S, called trajectory, describes the
movement of a single entity;
− as a temporal sequence of traffic situations: {μ
t
: E → S | t ∈ T},
where the function μ
t
: E → S, called traffic situation, describes
the spatial positions of all entities at a time moment t.
The first way will be further called trajectory-oriented view and
the second one will be called traffic-oriented view (we use the
term “traffic” in an abstract sense to denote collective movement
of any kind of entities). The view to take depends on the analysis
goals, as will be further demonstrated by examples. Each view
requires different analysis methods and, in particular, different
ways of aggregating movement data. In this paper, we investigate
what aggregation methods can be used for each of the views. For
the presentation purposes, we use an example dataset and example
analysis tasks from the domain of city traffic management.
However, our work is not specifically oriented to this domain and
these tasks; this is a more general research work on the use of
aggregation in analyzing massive movement data.
Before presenting the example dataset and discussing the
possible methods of aggregation, we shall briefly overview the
relevant works concerning aggregation of movement data.
2 R
ELATED WORK
Most software tools designed to support visual examination of
large sets of movement data involve data aggregation. There are
three basic types of aggregation, spatial (S), temporal (T), and
attributive (A), also called categorical [7]. These basic types are
used in various combinations.
Several aggregation techniques are described in a series of
papers written by D. Mountain and his colleagues (e.g. [6][10]).
T-aggregation appears in the form of temporal histogram where
the bars correspond to time intervals and their heights are
proportional e.g. to the number of locations visited or the distance
traveled. S-aggregation is done by imposing a regular grid over
the territory and counting trajectory points fitting in each cell. The
resulting density counts are represented by coloring or shading of
the grid cells on a map display. In S×T-aggregation the densities
are computed for consecutive time intervals and shown on an
animated map display. Similar to densities, other aggregated
characteristics can be computed and visualized. Thus, in [8] the
total number of person/minutes spent in each cell is computed. A
sophisticated S×T×A-aggregation is suggested in [17]: position
records are grouped spatially by cells of a regular grid and then
temporal (e.g. by days of the week) and attributive (e.g. by vehicle
types) aggregation is applied to each group. The results are
represented by multiple treemaps [13] placed inside each cell.
Essentially, all these aggregations do not differ from what was
suggested in [7] for aggregating spatially distributed discrete
http://geoanalytics.net/and
51
IEEE Symposium on Visual Analytics Science and Technology
October 21 - 23, Columbus, Ohio, USA
978-1-4244-2935-6/08/$25.00 ©2008 IEEE
events: each record from the movement data is, in fact, treated as
an independent event. Hence, these ways of aggregation do not
capture the specific nature of movement data. The results of the
aggregation show the presence of entities in different places at
different times but not the movement of the entities from place to
place. S×T- and S×T×A-aggregations can be helpful where the
traffic-oriented view of movement data is required but do not
support the trajectory-oriented view.
A different way of aggregating movement data is counting for
each pair of places in space how many entities moved from the
first to the second place between two time moments. This kind of
aggregation may be represented by the formula S×S×T×T (start
place, end place, start time, and end time). The resulting counts
may be visualized as a transition matrix where the rows and
columns correspond to the places and symbols in the cells or cell
coloring or shading encode the counts [9]. For more than one pair
of time moments, one would need to build several transition
matrices, which could then be compared. However, the limitations
of this approach with respect to the length of the time series of
movement data are evident. Another problem is that such
visualization lacks the spatial context. Tobler [15][16] visualizes
aggregated moves on a map by bands or arrows connecting pairs
of locations with the widths proportional to the volumes moved
between these locations. Unfortunately, such a map may be
illegible because of intersecting and overlapping symbols.
Therefore, Tobler suggest a specific method for spatial smoothing
of aggregated moves and generation of continuous flow maps.
Intersections and overlaps between movement symbols may be
reduced by involving the third spatial dimension, as in the
visualization of the movement of tourists in New Zealand [5]
(discussed in [3]). Irrespective of the visualization, S×S×T×T-
aggregation does not fully support the trajectory-oriented view
since it hides essential information about the routes of the entities.
In all aggregations discussed so far the results are numeric
values such as counts, sums, statistical means, etc. In [4] a kind of
geometric summary of several trajectories is derived. The authors
use functions of ArcGIS to build a convex hull containing the
trajectories, compute the central tendency and dispersion of the
paths, and represent the results on a map as the averaged path.
Such geometric summarization works well only when the
trajectories are similar in shape and close in space. It can be
applied, for example, to groups of similar trajectories resulting
from clustering. Grouping of trajectories by similarity and/or
closeness of the routes followed by geometric and/or numeric
summarization may be called R- (route-based) aggregation.
Our earlier paper [2] contains examples of combining route-
based grouping of trajectories with S×S×T×T-aggregation; all
together may be called R×S×S×T×T-aggregation. It can support
the trajectory-oriented view of movement, as will be shown later.
3 E
XAMPLE DATA AND ANALYSIS TASKS
To present our work, we shall use an example dataset collected by
GPS-tracking of 17,241 cars in Milan (Italy) during one week
from Sunday to Saturday. Figure 1 shows the variation of the
numbers of simultaneously moving cars from the tracked sample
over the period of the observation. The numbers have been
counted by hourly intervals and range between 80 and 3173. The
vertical lines on the graph correspond to 0 o’clock.
The dataset consists of more than 2 million records each
including car identifier, time stamp (date and time of the day),
geographical coordinates, and speed. The time intervals between
the records of the same car are irregular, mostly ranging from 30
to 45 seconds while there are also larger intervals ranging from
several minutes to several days. The data have been kindly
provided by Comune di Milano (Municipality of Milan) for the
use within the project GeoPKDD.
Figure 1. Variation of the number of simultaneously moving cars.
In [2] we have described how we preprocess raw movement
data in the database and integrate individual position records into
trajectories. There is no unique way of combining position records
into trajectories. In [2] we discuss several possible methods. In
this paper we shall use trajectories obtained by one of the
methods; the details are irrelevant to the topic of the paper. The
number of the trajectories is about 176,000.
It should be noted that the whole dataset is too big for loading
and processing in the computer’s main memory and for interactive
exploration with the use of dynamic querying, brushing, and other
techniques addressing individual objects, i.e. points or trajectories.
Therefore, it is necessary either to aggregate the data inside the
database and explore the resulting aggregates or to divide the data
into manageable subsets and explore them separately. The results
then need to be compared and somehow integrated.
Example analysis tasks related to city traffic management come
from the interviews with specialists from mobility agencies and
traffic departments of several Italian cities. The interviews have
been conducted by our GeoPKDD partners from the Italian
telecommunication company WIND and its business school.
According to the interviews, city traffic managers need to cope
with the following tasks: (1) estimate the average flows (number
of people) between regions of interest and their variation in
different time periods and in presence of extraordinary events
such as football games, concerts, strikes, etc.; (2) estimate the
average travel times between regions and their variation; (3)
estimate the “impedance” of a street (obstruction to movement)
and its variation; (4) estimate the proportions of the cars leaving a
main road on different exits; (5) understand the actual paths used
by people to get from one point or region of interest to another.
At the present time, traffic managers do not use data resulting
from tracking the movement of vehicles or people. Although such
data become widely available, there are no appropriate tools for
their analysis. A common practice is to use results of public
surveys and traffic monitoring data coming from stationary video
cameras or other sensors. Such data are not well suited to the
tasks. While methods for reconstructing traffic flows from
stationary sensor data are devised in data mining [11], analysis of
tracking data could significantly help in coping with the tasks as
well as in verifying traffic models built on the basis of data from
stationary sensors.
Assuming that the tasks of traffic managers are to be carried out
with the use of car tracking data like in our example dataset, we
can say that tasks 1, 2, and 5 require the trajectory-oriented view
and task 3 requires the traffic-oriented view of the car movement.
We shall discuss later which view is more appropriate for task 4.
In the following sections we investigate what aggregation
methods can support the two different views of movement data
and what visualization techniques are suitable for viewing and
exploring the outcomes of the aggregation. We would like to
stress that the data and tasks described in this section serve only as
examples for illustrating the suggested general framework for
analysis of massive movement data with the use of aggregation.
4 S
UPPORTING THE TRAFFIC-ORIENTED VIEW
We use the term “traffic situation” to denote the spatial positions
of all moving entities and the values of the movement-related
attributes including speed, direction, acceleration (change of
52
speed) and turn (change of direction) at some time moment. In the
traffic-oriented view, an analyst looks at traffic situations at
different time moments and considers the evolution of the traffic
situation over time. For practical reasons, the analyst cannot
analyze the traffic situation of each second. On the one hand, this
would require too much time and effort; on the other hand, the
available data may not allow this because of larger time intervals
between the measurements. A reasonable approach is to aggregate
the data by time intervals of appropriate lengths. Thus, in
analyzing city traffic it may be sufficient to use time intervals of
the length of one hour or, if this is too coarse, half an hour or
quarter of an hour.
S×T-aggregation can adequately support the consideration of
aggregate traffic situations on time intervals. Besides dividing the
time into intervals, the space (i.e. the territory where the entities
move) is divided into appropriate compartments. In our
experimental implementation, compartments are defined by
building a regular rectangular grid of a desired resolution, but it is
possible, in principle, to use other divisions. Then, various
aggregates are computed for each pair of space compartment and
time interval from the track records fitting in this compartment
and this interval: number of different entities, number of visits,
total time spent, statistics of the movement-related attributes
(minimum, maximum, average, median, etc.). The aggregation
can be done in the database. The results are loaded in the main
memory and can be visualized in various ways including static
and animated maps and non-cartographic displays.
Figure 2. Temporal variation of the median speeds in different
places of Milan (grid cells) computed by hourly time intervals.
For example, Figure 2 shows the variation of the frequency
distribution of the median speeds throughout the territory of Milan
(divided into compartments by a regular grid) over the whole
period of the observation from Sunday to Saturday. The data have
been aggregated by hourly intervals; the segmented bars represent
these intervals. The colors of the bar segments correspond to
intervals of the values of the aggregate attribute “median speed”.
The breaks are 15, 30, 45, 60, 80, and 100 km/h. Yellow is
assigned to the interval from 45 to 60, the shades of red represent
median speeds below 45, and the shades of green are used for
median speeds over 60 km/h (the color legend can be seen on the
left of Figure 3). The heights of the bar segments are proportional
to the numbers of the compartments where the median speeds
fitted in the respective intervals. Gray segments show the numbers
of the compartments with no occurrences of tracked cars during
the corresponding time intervals.
Figure 3. The mosaic diagrams show the variation of the median speeds in spatial compartments by days of the week (columns of the
diagrams) and hours of the day (rows of the diagrams). The cells are colored according to the speeds. The breaks and colors for the
speed intervals are the same as in Figure 2. Slow speeds are shown in shades of red and fast speeds in shades of green.
53
Figure 4. Focusing on selected spatial compartments along a particular road.
Figure 5. The directional bar diagrams show movement data aggregated by compass directions. The lengths of the bars are proportional to
the numbers of the cars that moved in the respective directions during a selected time interval. The radii of the circles are proportional to
the numbers of the cars with the speeds below a selected threshold (here 5km/h). On the right, only dominant directions are shown,
specifically, where values are at least 25% higher than the next highest value (25% is a selected threshold).
Since time is not only a linearly ordered sequence of moments
but also has a cyclical organization, it is possible to aggregate
time-related data by dividing their time span according to one or
more temporal cycles. Thus, Figure 3 represents aggregates
obtained with the use of two temporal divisions: according to the
days of the week and according to the hours of the day. The first
division groups together data referring to the same day of the
week irrespective of the date. The second division groups together
data from different days referring to the same hour of the day. As
a result, aggregated values have been computed for each
combination of space compartment, day of the week, and hour of
the day. Each “mosaic” diagram summarizes the daily and weekly
patterns of the traffic in a particular place.
A traffic analyst can use this aggregation to explore the
impedance of a street (task 3). For this purpose, the analyst can
select the space compartments covering the street and look only at
the data in these compartments (Figure 4). It should be noted that
regular rectangular compartments may not ideally suit the
geometry of a particular street. In this case arbitrarily specified
compartments are preferable.
The aggregation discussed so far is not specific to movement
but can be applied to other kinds of spatio-temporal data, e.g.
point events. In fact, this is the same type of aggregation as used
for traffic incidents in [7]. To capture the specifics of movement
data, we suggest another aggregation method where the data are
aggregated not only by space and time but also by the direction
(course) of movement. This aggregation can be denoted by the
formula S×T×D, where D stands for “direction”. Movement
directions are often indicated in the original track records. If this
is not the case, they can be computed from pairs of consecutive
positions of the same entity.
The directions are specified in movement data as numeric
values typically representing angular degrees from 0 to 359. For
S×T×D-aggregation we suggest to divide this range into intervals
54
corresponding either to four main compass directions (north, east,
south, and west) or to four main and four intermediate directions.
Track records fitting in the same spatial compartment and
temporal partition are additionally grouped by the movement
directions. A separate group is made from records where the
speed is below a chosen threshold. This is treated as the absence
of movement. Then, various counts and statistics of attribute
values are computed for the groups.
To visualize the resulting aggregate data, we suggest a special
technique in which the data are represented on a map by
directional bar diagrams. Analogously to the wind rose used in
meteorology, the bars are oriented in four or eight compass
directions and their lengths are proportional to the values of the
currently selected aggregate attribute corresponding to the
respective directions. Thus, the diagrams in Figure 5 (left) portray
the numbers of the cars that moved in different directions on
Monday between 7 and 8 AM. The bars are colored depending on
their orientation; a particular color is assigned to each direction.
This helps in gaining an overall view of the prevailing movement
directions throughout the whole territory. Besides the directional
bars, some diagrams include gray circles representing the groups
of records with the speeds below the chosen threshold. The radii
of the circles are proportional to the values of the currently
selected aggregate attribute computed for these groups of records.
The radii can be easily compared with the lengths of the bars. In
Figure 5 the circles represent the numbers of the distinct cars that
had the speeds below the chosen threshold of 5km/h. Such speeds
occur predominantly in the central part of the city but also on the
northeast, where the circles located on a segment of a motorway
may indicate its congestion.
Visual exploration of traffic with the use of this kind of display
can be supported by a number of interactive facilities:
− switch from one aggregate attribute to another, e.g. from the
number of entities to the average or median speed;
− select another temporal partition, i.e. another interval, day of
the week, time of the day, etc., depending on how the data have
been aggregated;
− hide some directions in order to focus on the remaining
direction(s), e.g. to see where northward movement occurs;
− choose presenting only the dominant direction(s) in each
spatial compartment. A direction is treated as dominant when the
corresponding value of the current aggregate attribute exceeds the
highest value among the remaining directions by a chosen
threshold, which may be either absolute (i.e. minimum difference
between the values) or relative (i.e. minimum ratio).
The screenshot on the right of Figure 5 shows the dominant
movement directions defined by the relative threshold of 25%. It
may be seen that movements towards the center prevail on most
radial streets and that movements to the east (green bars)
dominate on the motorway on the south. In some compartments
there are two or more dominant directions. This means that the
respective attribute values differ by less than 25%.
The S×T×D-aggregation together with the visualization can
support a more refined exploration of street impedance than it is
possible with the S×T-aggregation. An example is shown in
Figure 6. To explore the traffic on a particular road, only the space
compartments (grid cells) covering this road have been selected.
The data have been aggregated according to the four main
compass directions. The bar diagrams represent the median speeds
in the eastern (green) and western (purple) directions. The
diagrams are substantially asymmetric, meaning different speeds
of the movement in the eastern and in the western directions.
Lower speeds, in turn, signify higher obstruction to the
movement. In this way, the impedance of a street to the movement
in the different directions can be explored.
Figure 6. The bars represent the median speeds of the movement
toward the east (green) and west (purple) between 11 and 12
AM on Wednesday along a motorway on the north of Milan.
It may seem that the S×T×D-aggregation and directional bar
diagrams can also support task 4 – estimation of the proportions
of cars leaving a road on its exits. Indeed, some diagrams in
Figure 5 (left) show the proportions of the movements in different
directions on road exits and crossings. However, these data are not
very reliable. The course of the movement in a particular point is
determined using the next measured position of the same car.
Depending on the temporal spacing between the measurements
and the speed of the movement, the next measurement may be
taken on another road, somewhere on a curved exit, or on another
lane of the same road just in a few meters from the previous
measurement. The computed course of a car leaving the road may
occasionally coincide with the direction of this road, and on the
opposite, the course of a car staying on the road but changing the
lane may significantly differ from the road direction. For a more
reliable estimation of the proportion of the cars leaving the road,
the further routes of the cars need to be taken into account. This
means that task 4 requires the trajectory-oriented view of the car
movement, like tasks 1, 2, and 5.
5 S
UPPORTING THE TRAJECTORY-ORIENTED VIEW
In the trajectory-oriented view, collective movement of multiple
entities is considered as a set of trajectories of the entities. In
practical tasks, the entire trajectory of each entity made during the
whole period of the observation is usually divided into parts
representing different trips of this entity; the term “trajectory” is
also applied to such a part.
In analyzing trajectories, one may be interested in the origins
and destinations of the trips, routes, start and end times, durations,
distances, variation of the speeds along the routes, intermediate
stops, etc. When trajectories are numerous, it is impracticable to
examine each of them in detail. They need to be aggregated in
such a way that the distribution of the relevant properties over the
set of trajectories could be seen. For certain properties, the
aggregation may be quite traditional. Thus, a frequency histogram
can appropriately represent the distribution of the trip durations or
distances. More specific aggregation and visualization techniques
are required for the spatial properties (origins, destinations, and
routes) and for the spatio-temporal properties (speed variation and
intermediate stops).
The general approach is to group the trajectories by similarity in
terms of the properties relevant to the goals of the analysis. Then,
the groups need to be represented in a summarized way, which
appropriately conveys the relevant properties. The easiest case is
when the analyst is interested only in the origins and destinations
of the trips but not in the routes and spatio-temporal properties.
This is the case in tasks 1 and 2. To support such tasks, the
trajectories need to be grouped by the origins and destinations.
5.1 Aggregation by origins and destinations
In this method, which may be called S×S-aggregation, two
approaches are possible. One is to refer the starts and ends of the
trajectories to predefined areas of interest, for example, city
districts. Then, for each pair of areas, the trajectories starting in
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