Biomedical Engineering Reference
In-Depth Information
where M and K are the total cluster number and the total number of patient
datasets, respectively. Given an initial estimation
, E-step in the EM
a
0
;
l
0
;
P
0
algorithm calculates the posterior probability pmx
k
ð
j
Þ
as follows:
!,
X
!
Þ¼
a
ð
m
/ x
k
j
l
ð
m
;
X
ðÞ
a
ð
m
/ x
k
j
l
ð
m
;
X
ðÞ
M
pm
j
x
k
ð
;
ð
6
:
9
Þ
m
m
¼
1
m
and then M-step is as follows:
X
K
¼
1
K
a
t
þ
1
ð
Þ
pm
j
x
k
ð
Þ
m
k
¼
1
P
K
pm
j
x
k
ð
Þ
x
k
X
K
1
a
m
K
k
¼
1
l
t
þ
1
ð
Þ
¼
¼
pm
j
x
k
ð
Þ
x
k
ð
6
:
10
Þ
m
P
K
pm
j
x
k
ð
Þ
k
¼
1
k
¼
1
:
x
k
l
t
þ
1
T
ð
X
t
þ
1
Þ
a
m
K
X
K
1
x
k
l
t
þ
1
ð
Þ
ð
Þ
¼
pm
j
x
k
ð
Þ
k
k
m
k
¼
1
With Eq. (
6.9
) in the E-step, we can estimate the tth posterior probability
pmx
k
jð Þ
. Based on this estimate result the prior probability (a
m
), the mean (l
m
) and
the covariance (R
m
) in the (t ? 1)th iteration can be calculated using Eq. (
6.10
)in
the M-step. Based on clustering of respiratory patterns, we can make a class for
each breathing feature with the corresponding feature vector x
ðÞ
of class m. With
the classified feature combination vector x
ð
, we can get the reconstruction error
for the preliminary step to detect the irregular breathing pattern.
6.3.3 Reconstruction Error for Each Cluster Using NN
Using the classification based on EM, we can get M class of respiratory patterns, as
shown in Fig.
6.1
. With the classified feature vectors x
ð
, we can reconstruct the
corresponding feature vectors (o
m
) with the neural networks in Fig.
6.2
and get the
following output value,
!
!
o
m
¼
U
X
w
kj
U
X
H
N
x
i
w
ji
þ
w
j0
þ
w
k0
;
ð
6
:
11
Þ
j
¼
1
i
¼
1
where U is the nonlinear activation function, and N and H denote the total neuron
number of input and hidden layers, respectively. The neural weights (w) are
determined by training samples of multiple patient datasets for each class M. Then,
the neural networks calculate the reconstruction error d
ðÞ
for each feature vector
x
i
using a multilayer perceptron for each class in Fig.
6.2
, as follows [
34
]:
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