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graph are similar to those that we observed for the presence (Figure
8.4
d,e).
However, we see that symmetric flows (i.e., flows between the same locations in
opposite directions) may have different patterns of temporal variation. Thus, on
the east and south of the city, symmetric flow symbols are coloured in blue and
in magenta, that is, the respective time series belong to different clusters. The
flows in the magenta cluster achieve higher magnitudes in the afternoons of all
days, except Friday (day 6).
Aggregation of movement data into transitions between locations does not
allow investigation of paths and movement behaviors where more than two
locations are visited. The visualization technique demonstrated in Figure
8.5
g
aggregates trajectories in such a way that movement behaviors can be traced
(
Bremm et al.
,
2011
). This is an abstract display where the horizontal axis
represents time and colors represent different locations. The map in Figure
8.5
f
shows the geographic regions of Milan filled in different colors. The same colors
are used in Figure
8.5
g.
In this example, we investigate the movements of 4,634 cars that spent at
least 6 hours on the territory under study on Wednesday (i.e., we have selected
the trajectories with a duration of at least 6 hours); the flow map in Figure
8.5
f
summarizes the movements of these cars. The trajectories have been aligned in
time to common start and end times, as mentioned in Section
8.2.3
. The resulting
time units are thousandths (also called “per mill”) of the total trajectory duration.
Then the transformed time has been divided into 50 intervals of the length 20 per
mills, or 2 percent. The temporal display in Figure
8.5
g represents time intervals
by vertical bars divided into colored segments proportionally to the number of
cars that visited the regions in these intervals. Aggregated transitions between
the regions are represented by bands drawn between the bars. The widths of the
bands are proportional to the counts of the objects that moved. Gradient coloring
is applied to the bands so that the left end is painted in the color of the origin
location and the right end in the color of the destination location.
The colored bars are shown not for all time intervals but for a subset of
intervals selected interactively or automatically. In our example, we have selected
the first 3 intervals, the last 3 intervals, and each 10th interval (i.e., 100 per mills,
200 per mills, and so on). The small rectangles at the bottom of the display
represent all time intervals. The greyscale shading encodes the amount of change
in each interval with respect to the previous interval, that is, how many objects
moved to different locations. We can observe that the most intensive movements
of the selected cars occurred in the first 2 percent and in the last 2 percent of
the total trajectory lifetime. Between the time intervals 100 and 900 the cars
mostly stayed in the same regions. The most visited region was center. There
were higher presence and more movements in the northern part of the city than
in the southern part. The most intensive flows at the beginning of the trips were
to the center and inner northeast and at the end to the outer northeast.
