h ¼ h 1 ; h 2 ; . . .; h K
ð
Þ
h k ¼
X N
n¼1
a k;n j x n ; x
ð
Þþb k
8
> <
> :
ð1Þ
where jðx n ; xÞ is a kernel function, the parameters a k;n and b k are obtained by the SVM
optimization objective function. It is worth noting that h k k ¼ 1; 2; . . .; K
ð
Þ is not a one
dimensional by the structure of the algorithm and the specific formula and can be
defined. Next, the hidden layer feature h is taken as the input to the next nonlinear unit
(SVM unit), namely:
y ¼
X N
n¼1
b n Á jðh n ; hÞ þ c
h n ¼ h 1;n ; h 2;n ; . . .; h K;n
Â
Ã
h ¼ h 1 ; h 2 ; . . .; h K
½
Š
8
> > > > <
> > > > :
ð2Þ
where the parameters b n and c need to be learned, h n is the hidden layer feature of the
input x n , and h is the hidden layer feature of the input x.
2.2 Optimization Objective Function of the DSVM Algorithm
The optimization objective function is
min
h
JðhÞ ¼
1
N
X N
n¼1
^ y n À y n
k
k
2
2 þ kRðhÞ
ð 3Þ
Fig. 1. Module of a two-layer DSVM
Imbalanced Data Classification with Deep Support Vector Machines
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