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k
=1
|
n
d
a
=
1
n
(
S
a
)
k
−
(
S
b
)
k
|
(12)
where
P
a
and
P
b
are main points sets of two trajectories a and b,
S
a
and
S
b
are
main segments sequences of them.
Fine classification also uses modified k-means method to subdivide classes.
Position distance
d
p
and acceleration distance
d
a
are constrains of this fine clas-
sification. The more specific algorithm is shown in Algorithm 3.
Algorithm 3.
Fine classification (
d
p
+
d
a
)
Input:
Class
: Trajectories belong to this class
Output:
List of subclasses
Processing:
Find out trajectories whose
d
p
+
d
a
are the most large ones to be K centroid.
for
T
a
∈ Class
do
TempDis
=
d
p
(
T
a
,Cid
1
)+
d
a
(
T
a
,Cid
1
);
for
i
=2;
i ≤ K
;
i
++
do
if
TempDis>d
p
(
T
a
,Cid
i
)+
d
a
(
T
a
,Cid
i
)
then
TempDis
=
d
p
(
H
a
,Cid
i
)+
d
a
(
T
a
,Cid
i
);
C
a
=
i
;
end if
end for
if
TempDis>d
pamin
then
K
=
K
+1;
H
a
belongs to the new
K
th subclass;
else
Then
T
a
belongs to the
C
a
th subclass,
m
C
a
is the number of trajectories belongs
to the
C
a
th subclass;
position centroid:
CidP
C
a
=
m
C
a
m
C
a
+1
1
m
C
a
+1
CidP
C
a
+
P
La
acceleration centroid:
CidA
C
a
=
m
C
a
m
C
a
+1
1
m
C
a
+1
CidA
C
a
+
S
Aa
m
C
a
=
m
C
a
+1;
end if
end for
2.3 Gaussian Process Regression for Matching
In order to find out similar ones for all kinds of trajectories, we adopt Gaus-
sian Process Regression method [3] to build the model
a
=
f
(
q
)+
τ
,where
τ
∼ℵ
(
μ,σ
2
).
q
denotes the position of point (
q
x
,q
y
). The position sequence is
q
=
.
a
is the acceleration of the point, that includes
a
x
and
a
y
in different direction. The acceleration sequence is
a
=
{
q
1
,q
2
,...,q
n
}
.Inthis
part,we train Gaussian Progress Regression model for both acceleration
a
x
and
{
a
1
,a
2
,...,a
n
}
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