Trajectories and Their Representations - Mobility Data - page 19

cranes, involves two trajectories with the same role. Another example is the
Pursuit behavior that also involves two trajectories, but with opposite roles.
A trajectory representation is inherently a temporally ordered list of ele-
ments, be they raw tuples (spatio-temporal positions) or annotated episodes. The
predicate used to define a behavior can involve any number of elements. The
simplest behaviors will only require a predicate on a single element. Examples
include behaviors such as “starting from a given geo-object” (whose predicate
only constrains the Begin element) and “passing by a given geo-object” (whose
predicate is satisfied as soon as one of the trajectory elements is located inside or
equal to the geo-object). More advanced behaviors rely on complex predicates
that involve several elements so that each element has to satisfy the condition
associated to it. A simple example is the HomeToWork behavior, whose predi-
cate is composed of two component predicates: one on the Begin element and
another one on the End element.
Complex predicates may require that their component predicates be satis-
fied by a sequence of elements that complies with a specified temporal order.
Consider, for example, the predicate “starting at a given point P1, later crossing
the area A1, 2 hours later crossing the line L1, and ending up inside the area
A2.” This predicate on the one hand constrains the Begin and End elements
(Begin must be point P1, End must be inside A2), and on the other hand imposes
two additional constraints that have to be satisfied by some elements. Which
elements satisfy the two constraints is not relevant, but the element crossing the
A1 area has to come before the element crossing the L1 line. Complex predi-
cates where a temporal order is specified define behaviors denoted as Sequence
behaviors.
Definition 1.11. A trajectory sequence behavior is a trajectory behavior whose
predicate is composed of several conditions, each condition being coupled with
a temporal constraint, such that the constraints enforce a specific temporal order
on the elements satisfying the conditions.
As sequence behaviors may be quite complex, a language is defined for
expressing the various sequence operators that link the component conditions.
The most usual operators are:
AND_THEN_NEXT[N] : the next element (or the N next elements) of the
trajectory must comply with the predicate;
AND_THEN_LATER[d] : there must be later (or at least/exactly some duration
d later) within the trajectory, an element that complies with the predicate.
The definition of the Tourist behavior given in the previous section is a
complex behavior, but not a sequence one, because the two component predicates
“it makes at least one stop in a place of kind Museum or TouristAttraction” and