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(a)
Figure 6.1 Visual representation of (a) a trajectory flock, (b) a sample result on a real data
set with all trajectories involved, and (c) a zoom on the segments that form the flock. (See
color plate.)
(b)
(c)
several hours, we can safely assume that they form a herd or that something is
happening that forces them to keep together.
The simplest form of trajectory pattern in literature that exactly answers the
question posed above is the trajectory flock . In one of its most common variants,
a flock is defined as a group of moving objects that satisfy three constraints as
follows:
A spatial proximity constraint: Within the whole duration of the flock, all its
members must be located within a disk of radius r - possibly a different one
at each time instant, that is, the disk moves to follow the flock;
A minimum duration constraint: The flock duration must be at least k time
units;
A frequency constraint: The flock must contain at least m members.
Figure 6.1 a shows an abstract example of flock, where three trajectories meet
at some point (at the fifth time unit), keep close to each other for some time
(four consecutive time units) and then separate (ninth time unit). If, for instance,
the constraints chosen by the user are the radius r used in the figure to draw
the circles, a minimum duration of four time units (or less), and a minimum
size of three members, then the common movement shown in the figure will be
recognized as a flock.
Figures 6.1 b-c show an example extracted from a real data set that contains
GPS tracks of tourists in a recreational park (Dwingelderveld National Park, in
the Netherlands). Figure 6.1 b depicts the three trajectories that were involved in
the flock, while Figure 6.1 c shows (a zoomwith) only the segments of trajectories
that create the flock. As we can see, in this example a flock is a local pattern,
both in the sense of involving only a small subset of trajectories (three, in our
case), and in the sense of describing an interesting yet relatively small segment
of the whole life of the trajectories involved.
The general concepts of moving together or forming a group are implemented
by the flocks framework in the simplest way possible: the objects are required
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