Information Technology Reference
In-Depth Information
a
y
. Given a test point
q
∗
, we can calculate the posterior density
p
(
a
∗
|
q
∗
,q,a
)to
determine whether the point fits Gaussian univariate normal distribution with
mean
a
∗
(
q
∗
)andvariance
σ
(
q
∗
) [11] which are defined as
a
∗
a
∗
(
q
∗
)=
k
T
(
q
∗
)(
K
+
σ
2
I
)
−
1
a
(13)
σ
k
T
(
q
∗
)(
K
+
σ
2
I
)
−
1
k
(
q
∗
)
(
q
∗
)=
C
(
q
∗
,q
∗
)
−
(14)
a
∗
where,
K
ij
=
C
(
q
i
,q
j
),
k
(
q
∗
)=(
C
(
q
∗
,q
1
)
,C
(
q
∗
,q
2
)
,...,C
(
q
∗
,q
n
))
T
.
Key points for Gaussian Process Regression are the common covariance func-
tion and the calculation of their parameters. Main points of trajectories in classes
are used for training.
The following is covariance function
d
1
2
q
I
)
2
C
(
q,q
)=
v
0
exp
{−
w
I
(
q
I
−
}
+
v
1
(15)
I
=1
where
q
I
is the
I
th component of
q
. But the parameters
v
0
,v
1
,w
1
,...,w
d
in above
function are unknown.
The log likelihood
l
=log
P
(
q,a
|
φ
)
n
2
log 2
π
1
2
log
1
2
a
T
K
−
1
a
K
l
=
−
|
|−
−
(16)
where
K
=
K
+
σ
2
I
,
φ
= (log
v
0
,
log
v
1
,
log
w
1
,...,
log
w
d
).
In order to obtain a local maximum likelihood, we can figure out
φ
by partial
derivatives of
l
with respect to parameters.
2
tr
K
−
1
∂K
+
1
2
a
T
K
−
1
∂K
∂l
∂φ
i
=
1
∂φ
i
K
−
1
a
−
(17)
∂φ
i
In the end, the Gaussian mean and variance of each point in target trajectory are
calculated. And the possibility for target trajectory belonging to the trained class
are based on the number of points whose practical acceleration are in confidence
interval.
3Num lExp imen s
3.1 Trajectories Disposing and Clustering
Fig.1 is showing 9 raw trajectories which seemly have totally different position
and acceleration characters. After disposing, main features are shown clearly
in Fig.2. The final classification results are
{
Tra1,2,3,9
}
,
{
Tra4,5
}
,
{
Tra7,8
}
,
{
Tra6
}
.
Search WWH ::
Custom Search