Database Reference
In-Depth Information
TR
4
TR
5
TR
3
A set of trajectories
(1) ParƟƟon
TR
2
TR
1
A representaƟve trajectory
A set of line segments
(2) Group
A cluster
Fig. 12.12
An example of trajectory clustering in the partition-and-group framework [
19
]
Given that an individual belongs to cluster
k
, there is a density function
f
k
(
y
j
|
θ
k
)
which generates observed data
y
i
for individual
j
.
From this generative model, the observed density on the
y
's should be be a mixture
model, i.e., a linear combination of the component models:
K
P
(
y
j
|
θ
)
=
f
k
(
y
j
|
θ
k
)
w
k
.
k
In Gaussian mixture model, we will assume the generative models
θ
k
as Gaussian
models. In Gaffney et al. [
12
], they assume the data is generated as mixtures of
regression models
, where we have measurements
y
which are a function of
x
and
the density function becomes
f
k
(
y
x
,
θ
k
). Here
x
represents time,
y
represents the
locations of object and
θ
k
is the regression model of
y
on
x
. The parameters in gener-
ative models can be estimated using the Expectation-Maximization (EM) algorithm.
Experimental results [
12
] show that the proposed linear regression model performs
slightly better than Gaussian mixture model. The difference becomes more obvi-
ous with higher standard deviation in data generation. Both mixture model methods
perform much better than K-means.
In some applications, people are interested in discovering
similar portions
of
trajectories. For example, meteorologists will be interested in the common behaviors
of hurricanes near the coastline (i.e., at the time of landing) or at sea (i.e., before
landing). To cluster sub-trajectories, Lee et al. [
19
] propose a partition-and-group
framework named as TRACLUS as shown in Fig.
12.12
. There are three steps in
TRACLUS.
1. Partitioning: in this step, each trajectory is partitioned into a set of line segment
based on characteristic points. A characteristic point is a point where the behavior
|
