Database Reference
In-Depth Information
the other hand, in an
avoidance
relationship, the presence of one individual causes
the other to
move away
. So the individuals have a lower probability to be spatially
close than expected. Finally, with a
neutral
relationship, individuals
do not alter
their
movement patterns based on the presence (or the absence) of the other individual. So
the probability that they are being spatially close is what would be expected based
on independent movements.
The attraction relationship is commonly seen, for example, in animal herds or
human groups (e.g., colleague and family). In addition, the avoidance relationship
also naturally exists among moving objects. In animal movements, prey try to avoid
predators, and different animal groups of the same species tend to avoid each other.
Even in the same group, subordinate animals often avoid their more dominant group-
mates. In human movements, criminals in the city try to avoid the police, whereas
drug traffickers traveling on the sea try to avoid the patrol.
Intuitively, similar trajectories could be an indication of attraction relationship.
The similarity can be defined by the similarity measures mentioned in the previous
subsection. The assumption here is that the smaller the distance is or the higher the
meeting frequency is, the stronger the attraction relationship is. Unfortunately, such
assumption is often violated in real movement data. For example, two animals may
be observed to be spatially close for 10 out of 100 timestamps. But is this significant
enough to determine the attraction relationship? Further, another two animals are
within spatial proximity for 20 out of 100 timestamps. Does this mean that the latter
pair has a more significant attraction relationship than the former pair? Finally, if
two animals are never being spatially close, do they necessarily have an avoidance
relationship?
Li et al. [
25
] propose to mine significant attraction and avoidance relationships
by looking into the
background territories
. The relationships are detected through
the
comparison
between how frequent two objects are
expected
to meet and the
actual
meeting frequency they have. Intuitively, if the actual meeting frequency is
smaller (or larger) than the expectation, the relationship is likely to be avoidance (or
attraction).
Given two trajectories
R
and
S
, the probability for one point
r
i
in
R
to be spatially
close to any point in
S
is
n
j
=
1
τ
(
r
i
,
s
j
). Then the expected meeting frequency
between randomly shuffled
R
and
S
is:
1
⎛
⎞
n
n
n
n
1
n
1
n
⎝
⎠
=
E
[
freq
(
σ
(
R
),
σ
(
S
))]
=
τ
(
r
i
,
s
j
)
τ
(
r
i
,
s
j
),
i
=
1
j
=
1
i
=
1
j
=
1
where
σ
(
) denotes a random shuffled trajectory.
However, by comparing the actual meeting frequency with the expected meeting
frequency, one cannot determine a universal
degree
of the relationship. To further
measure the degree, let
·
be the multiset of all randomized
meeting frequencies. The significance value of attraction (or avoidance) between to
F
={
freq
(
R
,
σ
(
S
))
|
σ
}
