Trajectories and Their Representations - Mobility Data - page 8

Figure 1.3 Two trajectories extracted from the movement of an object.
Collecting information on daily travels of tourists enables extracting knowl-
edge on their favorite places, in which order places are visited, how much time
tourists spend at each attraction, etc. This can be used to tune the facilities to
better match tourist expectations and regulate the flow of tourists to avoid large
waiting lines. It can also be used to build tourist profiles, propose personalized
tours and services, and suggest to tourists on the move their next preferred des-
tination. Similar kinds of moving persons' scenarios are used in many research
papers to illustrate various kinds of analysis. We will use it throughout this
chapter for illustrating the concepts.
1.2.2 Trajectory Definition
As stated in Section 1.1 , while some applications keep and analyze whole
movement tracks, many other applications are interested in specific segments
of the movement. We call trajectories the segments of the object's movement
that are of interest for a given application. Obviously the whole movement is a
particular case of trajectory.
Definition 1.2. A trajectory is the part of the movement of an object that is
delimited by a given time interval [ t Begin ,t End ]. It is a continuous function from
the time interval [ t Begin ,t End ] to Space. The spatio-temporal position of the object
at t Begin (resp. t End ) is called the Begin (resp. End) of the trajectory.
Figure 1.3 shows (as a dotted line) a section of the movement of an object
and, superimposed as continuous lines, two segments identified as relevant
trajectories.
The criterion to identify trajectories within movement is application depen-
dent. For instance, in the tourists scenario, to globally analyze the activities
performed by a tourist during his/her stay in Paris, the whole track left by the
tourist will generate a single trajectory (spatial criterion “inside Paris”). On the
other hand, in order to analyze what tourists do in one day in Paris (whatever
the length of their stay), or what they do on specific days (e.g., on Sundays, on
December 25), each daily track of each tourist in Paris will generate a separate
trajectory as in Figure 1.1 .
In the real world, time, movements, and trajectories are continuous, but in the
digital world, where applications are implemented, we can only store discrete