Aerospace and Electronic Systems Magazine July 2017 - 47
Lim, Gianelli, and Li
Figure 13.
Fermat's spiral problem. (a) There are two classes such as blue circles and red stars. A decision boundary is plotted from A to B. If one walks from A to B
~ at (26) onto the direcalong the boundary, at any point (ex. Point C), one could obtain a linear problem locally. (b) By projecting the transformed data u
i
tion specified by w, most samples have positive margins [11].
{
}
{
where i = q :1 ≤ q ≤ I , yq ≠ yi , i = q :1 ≤ q ≤ I , yq = yi , q ≠ i}
, and E q ~ i is the expectation computed with regard to i. The probabilities P x q = NM ( xi ) w and P x q = NH ( xi ) w are given by
(
)
(
)
P x q = NM ( xi ) w =
P (x q NH
( xi ) | w )
(
(
k x q − xi
z∈i
(
)
w
)
k x z − xi
k‖
( x q xi‖w )
zi
k‖
( x z xi‖w )
w
)
, ∀q ∈ i ,
, q i ,
(27)
where k (⋅) is a kernel function which denotes k(d) = exp (−d/σ).
Here, σ is a user parameter, which dictates the resolution where the
data is locally analyzed. In addition, (26) can be explained in detail
via an instance in Figure 13.
After obtaining the margin in (26), we find the optimized nonnegative vector w in the logistic regression formulation [19]:
I
(
(
))
arg min log 1 + exp − w T u i , s.t. w ≥ 0.
w
i =1
(28)
For the sparsity of w, we add an 1 penalty to (28). The relevant
cost function is given by
I
(
(
arg min log 1 + exp − w T u i
w
i =1
)) + λ w
, s.t. w ≥ 0,
1
(29)
where λ is a regularization parameter which determines the sparsity of w. Equation (29) cannot be solved directly with gradient
descent due to the nonnegative weight w. Thus we substitute the
following cost function for (29):
I
2
arg min log 1 + exp −bz2ui ( z ) + λ b 2 ,
b
i =1
z
JULY 2017
(30)
where bp2 = w p for 1 ≤ p ≤ P. Equation (30) can be solved easily via
gradient descent with the next update rule:
(
)
I
exp − zbz2ui ( z )
b ← b − τ λ1 −
2
i ( z )
i =1 1 + exp − bz u
z
(
)
⊗ b,
(31)
where τ denotes a learning rate which can be decided through a
standard line search, and ⊗ is the Hadamard operator. Both the
regularization parameter λ and the kernel width σ can be obtained
through cross-validation using the training data set.
After the optimized weight w is obtained, a class label of a test
sample can be estimated with the following cost function:
(
)
arg max ρ t ( w ) , s.t. yt ∈ {1, 2,3}
yt
(32)
ATR RESULTS
The ATR performance evaluation is carried out using the GOTCHA 2008 public data set [3]. We use three target types such as
sedan, SUV, and van in Table 1 of [3]. The vehicles are shown in
Figure 14. They were measured by a radar platform on 31 sensor
orbits. Throughout these orbits, the vehicles vary in their pose and
articulation [3].
Table 1.
Classification Performance of BP and Hybrid Method
with Full and Missing Data in Error Rate
BP
Hybrid
Full
38.58%
5.99%
30%
43.45%
7.87%
50%
44.19%
14.61%
IEEE A&E SYSTEMS MAGAZINE
47
Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine July 2017
No label
Aerospace and Electronic Systems Magazine July 2017 - No label
Aerospace and Electronic Systems Magazine July 2017 - Cover2
Aerospace and Electronic Systems Magazine July 2017 - 1
Aerospace and Electronic Systems Magazine July 2017 - 2
Aerospace and Electronic Systems Magazine July 2017 - 3
Aerospace and Electronic Systems Magazine July 2017 - 4
Aerospace and Electronic Systems Magazine July 2017 - 5
Aerospace and Electronic Systems Magazine July 2017 - 6
Aerospace and Electronic Systems Magazine July 2017 - 7
Aerospace and Electronic Systems Magazine July 2017 - 8
Aerospace and Electronic Systems Magazine July 2017 - 9
Aerospace and Electronic Systems Magazine July 2017 - 10
Aerospace and Electronic Systems Magazine July 2017 - 11
Aerospace and Electronic Systems Magazine July 2017 - 12
Aerospace and Electronic Systems Magazine July 2017 - 13
Aerospace and Electronic Systems Magazine July 2017 - 14
Aerospace and Electronic Systems Magazine July 2017 - 15
Aerospace and Electronic Systems Magazine July 2017 - 16
Aerospace and Electronic Systems Magazine July 2017 - 17
Aerospace and Electronic Systems Magazine July 2017 - 18
Aerospace and Electronic Systems Magazine July 2017 - 19
Aerospace and Electronic Systems Magazine July 2017 - 20
Aerospace and Electronic Systems Magazine July 2017 - 21
Aerospace and Electronic Systems Magazine July 2017 - 22
Aerospace and Electronic Systems Magazine July 2017 - 23
Aerospace and Electronic Systems Magazine July 2017 - 24
Aerospace and Electronic Systems Magazine July 2017 - 25
Aerospace and Electronic Systems Magazine July 2017 - 26
Aerospace and Electronic Systems Magazine July 2017 - 27
Aerospace and Electronic Systems Magazine July 2017 - 28
Aerospace and Electronic Systems Magazine July 2017 - 29
Aerospace and Electronic Systems Magazine July 2017 - 30
Aerospace and Electronic Systems Magazine July 2017 - 31
Aerospace and Electronic Systems Magazine July 2017 - 32
Aerospace and Electronic Systems Magazine July 2017 - 33
Aerospace and Electronic Systems Magazine July 2017 - 34
Aerospace and Electronic Systems Magazine July 2017 - 35
Aerospace and Electronic Systems Magazine July 2017 - 36
Aerospace and Electronic Systems Magazine July 2017 - 37
Aerospace and Electronic Systems Magazine July 2017 - 38
Aerospace and Electronic Systems Magazine July 2017 - 39
Aerospace and Electronic Systems Magazine July 2017 - 40
Aerospace and Electronic Systems Magazine July 2017 - 41
Aerospace and Electronic Systems Magazine July 2017 - 42
Aerospace and Electronic Systems Magazine July 2017 - 43
Aerospace and Electronic Systems Magazine July 2017 - 44
Aerospace and Electronic Systems Magazine July 2017 - 45
Aerospace and Electronic Systems Magazine July 2017 - 46
Aerospace and Electronic Systems Magazine July 2017 - 47
Aerospace and Electronic Systems Magazine July 2017 - 48
Aerospace and Electronic Systems Magazine July 2017 - 49
Aerospace and Electronic Systems Magazine July 2017 - 50
Aerospace and Electronic Systems Magazine July 2017 - 51
Aerospace and Electronic Systems Magazine July 2017 - 52
Aerospace and Electronic Systems Magazine July 2017 - 53
Aerospace and Electronic Systems Magazine July 2017 - 54
Aerospace and Electronic Systems Magazine July 2017 - 55
Aerospace and Electronic Systems Magazine July 2017 - 56
Aerospace and Electronic Systems Magazine July 2017 - 57
Aerospace and Electronic Systems Magazine July 2017 - 58
Aerospace and Electronic Systems Magazine July 2017 - 59
Aerospace and Electronic Systems Magazine July 2017 - 60
Aerospace and Electronic Systems Magazine July 2017 - 61
Aerospace and Electronic Systems Magazine July 2017 - 62
Aerospace and Electronic Systems Magazine July 2017 - 63
Aerospace and Electronic Systems Magazine July 2017 - 64
Aerospace and Electronic Systems Magazine July 2017 - Cover3
Aerospace and Electronic Systems Magazine July 2017 - Cover4
http://www.brightcopy.net/allen/aesm/34-2s
http://www.brightcopy.net/allen/aesm/34-2
http://www.brightcopy.net/allen/aesm/34-1
http://www.brightcopy.net/allen/aesm/33-12
http://www.brightcopy.net/allen/aesm/33-11
http://www.brightcopy.net/allen/aesm/33-10
http://www.brightcopy.net/allen/aesm/33-09
http://www.brightcopy.net/allen/aesm/33-8
http://www.brightcopy.net/allen/aesm/33-7
http://www.brightcopy.net/allen/aesm/33-5
http://www.brightcopy.net/allen/aesm/33-4
http://www.brightcopy.net/allen/aesm/33-3
http://www.brightcopy.net/allen/aesm/33-2
http://www.brightcopy.net/allen/aesm/33-1
http://www.brightcopy.net/allen/aesm/32-10
http://www.brightcopy.net/allen/aesm/32-12
http://www.brightcopy.net/allen/aesm/32-9
http://www.brightcopy.net/allen/aesm/32-11
http://www.brightcopy.net/allen/aesm/32-8
http://www.brightcopy.net/allen/aesm/32-7s
http://www.brightcopy.net/allen/aesm/32-7
http://www.brightcopy.net/allen/aesm/32-6
http://www.brightcopy.net/allen/aesm/32-5
http://www.brightcopy.net/allen/aesm/32-4
http://www.brightcopy.net/allen/aesm/32-3
http://www.brightcopy.net/allen/aesm/32-2
http://www.brightcopy.net/allen/aesm/32-1
http://www.brightcopy.net/allen/aesm/31-12
http://www.brightcopy.net/allen/aesm/31-11s
http://www.brightcopy.net/allen/aesm/31-11
http://www.brightcopy.net/allen/aesm/31-10
http://www.brightcopy.net/allen/aesm/31-9
http://www.brightcopy.net/allen/aesm/31-8
http://www.brightcopy.net/allen/aesm/31-7
https://www.nxtbookmedia.com