Trajectories and Their Representations - Mobility Data - page 13

representation does not implement a continuous function: the moving object
jumps (so to speak) from one episode and annotation value to the next. It corre-
sponds to a step function as shown in Figure 1.4 c.
According to their needs, applications may use the continuous representation,
a segmented one, or both superimposed. For example, Figure 1.1 shows for a
tourist's trajectory the superimposition of the continuous representation and a
Stop/Move segmented representation.
Definition 1.5. A segmented representation of a trajectory (or segmented tra-
jectory in short) is the implementation of a step function that maps the time
interval [ t Begin ,t End ] to a finite set of values, D. Each step of the function is
called an episode, and its corresponding D-value the defining annotation of the
episode.
Practically, a segmented trajectory representation is a temporally ordered sub-
sequence of tuples (time interval, defining annotation value, annotation values),
where the time intervals are all disjointed.
Another example of segmentation of human trajectories is the transportation
means. Chapter 2 shows how this information can be computed automatically by
combining the raw trajectory data with the data on the public transport system
and some common sense rules about transportation modes. Often a human
trajectory starts with a first “walk” segment (at least to get out of the building
and into the first transportation means), and this segment is followed by, say,
a “metro” segment, then again a “walk” segment, and so on. In this case the
segmenting expression is a procedure call whose result is the corresponding
defining annotation, for example, “walk,” “metro,” “bus,” “car,” or “boat.”
A given trajectory may be structured into episodes in many different ways,
that is, using different expressions. For example, the tourists' trajectories may
be alternatively segmented into episodes based on (1) stops and moves, (2) the
time period corresponding to the instant of the spatio-temporal position (e.g.,
morning, noon, afternoon, evening, night), and (3) the category of the area
of the city corresponding to the location of the spatio-temporal position (e.g.,
residential, touristic, commercial, recreational, services, special). There is no
limit to the number of episode segmentations that can be applied to a set of
trajectories. Each segmentation into episodes provides a new interpretation of
the trajectory that can be superimposed as needed.
Moreover, while episodes are created via their defining annotation, episodes,
like every other component (especially spatio-temporal positions) of a trajectory,
can be further annotated using other annotations. For instance, assuming that
the tourists' trajectories have been segmented into Stop and Move episodes,
the Stop episodes may be further annotated with the nearest point of interest
that is the most likely to have been visited by the tourist during this stop. The
Move episodes may be annotated with the transportation means. It is the case