Irregular Breathing Classification from Multiple Patient Datasets - Prediction and Classification of Respiratory Motion - page 113

Fig. 6.2 Reconstruction
error to detect the irregular
pattern using NN

Class m Datasets Neural Network

w ji w kj

o 1
m
o 2

m
e ˆ
m
e ˆ

Φ 1

+ m

δ

Φ 1
Φ 2

Σ

−

+

Φ 2

m
2

δ

Σ

−

Φ 3

Φ H -2

m
e 1

ˆ −
m

m
o −
m

+
+

δ
m
δ

m
N Φ N -1

Φ N

Σ

Φ H -1

ˆ

o

−

Σ

−

Φ H

m
ˆ

2

X

F

d i ¼ 1

x if o if

; ð 6 : 12 Þ

F

f ¼ 1

where i is the number of patient datasets in a class m, and f is the number of
features. After calculating the reconstruction error d ðÞ for each feature vector in
Fig. 6.2 , d m can be used to detect the irregular breathing pattern in the next section.

6.3.4 Detection of Irregularity Based on Reconstruction
Error

For the irregular breathing detection, we introduce the reconstruction error d ð ,
which can be used as the adaptive training value for anomaly pattern in a
class m. With the reconstruction error d ð , we can construct the distribution
model for each cluster m. That means the patient data with small reconstruction
error can have a much higher probability of becoming regular than the patient data
with many reconstruction errors in our approach. For class m, the probability b ð ,

class means m ðÞ and covariance P m can be determined as follows:

X

K

b m ¼ 1
K

Im j x i ð Þ; ð 6 : 13 Þ

i ¼ 1

P

K

Þ d i

Im j x i ð

X

K

1
b m K

i ¼ 1

Þ d i ; m m ¼ ¼ Im j x i ð ð 6 : 14 Þ

P

K

Im j x i

ð Þ

i ¼ 1

i ¼ 1