Database Reference
In-Depth Information
Fig. 12.4
Front region defined in [
2
]
moving objects
R
and
S
is defined as:
sig
attract
=
Pr
[
freq
(
R
,
S
)
>freq
(
R
,
σ
(
S
))]
+
1
2
Pr
[
freq
(
R
,
S
)
=
freq
(
R
,
σ
(
S
))],
sig
avoid
=
Pr
[
freq
(
R
,
S
)
<freq
(
R
,
σ
(
S
))]
+
1
2
Pr
[
freq
(
R
,
S
)
=
freq
(
R
,
σ
(
S
))]
.
. Permutation test is a popular
non-parametric approach, to performing hypothesis tests and constructing confi-
dence intervals. The null hypothesis is that the movement sequences of two objects
are independent. Since the total number of permutations is factorial, Monte Carlo
sampling is used to approximate the significance value.
Permutation test is conduced to get the multiset
F
4.3
Behavioral Pattern
The behavioral patterns describe certain behaviors within a (short) period of time,
such as pursuit, evasion, fighting, and play [
7
]. Following/leading is one interesting
behavioral pattern between two moving objects. For example, animal scientists study
which individual animal leads the group when animals move in order to determine
the social hierarchy, whereas police and security officers look suspicious movements
of a criminal who is following a victim.
Intuitively, a follower has similar trajectories as its leader but always arrives at a
location with some time lag. The challenges lay in three aspects: (1) the following
time lag is usually unknown and varying; (2) The follower may not have exactly the
same trajectory as the leader; and (3) the following relationship could be subtle and
always happens in a short period of time.
Andersson et al. [
2
] propose the concept of
front region
. A point
s
i
in the front
region of
r
i
is defined by an apex angle
α
, a radius
r
, and an angle
β
restricting their
difference in direction
. Figure
12.4
shows an illustration of the front
region. In [
2
], a leader should appear in the front region of the follower(s) for at least
k
consecutive timestamps.
In real scenario, a leader does not necessarily appear in the
front region
of the
followers for
consecutive
timestamps. Figure
12.5
illustrates a counter example. In
d
i
−
d
j
