Customized Prediction of Respiratory Motion - Prediction and Classification of Respiratory Motion - page 93

patterns, we show feature selection metrics in Table 5.1 . Murthy et al. showed that
the breathing stability can be quantified by autocorrelation coefficient and delay
time [ 31 ]. Respiratory motion signal may be represented by sinusoidal curve [ 32 ]
so that each breathing pattern can have variable measurements of breathing signal
amplitude including acceleration, velocity, and standard deviation [ 33 ]. The typ-
ical vector-oriented feature extraction, exemplified by Principal component anal-
ysis (PCA) and Multiple linear regressions (MLR), has been widely used [ 5 , 26 ].
Table 5.1 shows the feature selection metrics for the clustering of breathing pat-
terns. Breathing frequency also showed diversity in individuals [ 34 ]. We create
Table 5.1 based on previous existences of breathing features, so that the table can
be variable. We randomly selected 7800 sampling frames (5 minutes) for the
feature extraction with three marker breathing datasets of each patient.
We pick up feature extraction criteria that are currently available for the
breathing patterns in the previous works [ 5 , 26 , 31 - 33 ]. The feature extraction
criteria listed in Table 5.1 may be duplicated, but we introduce the following
discriminant criteria to find out the most reliable feature set, e.g. dominant feature
vector I = (I x , I y , I z ), as three coordinate combinations selected from 10 feature
metrics, where I x , I y and I z correspond to each of the 10 feature metric values
indexed in Table 5.1 , so that we can have 10 C 3 (= 120) feature combination
vectors. The feature metrics for the appropriate clustering of breathing patterns
have yet to be determined. The objective of this section is to select the effective
feature combination metric (Î) from the candidate feature combination vector (I).
For the selection of the estimated feature metrics, we use the objective function
based on clustered degree using within-class scatter (S W ) and between-class scatter
(S B )[ 35 ]. Here, the S W is proportional to the number of class (c) and the covariance
matrix of feature samples based on each class. Accordingly, the S W can be

expressed as S W ¼ c P i ¼ 1 S ðÞ , where c is the number of class and S i is the
covariance matrix based on feature combination vectors in the ith class. The S B is
proportional to the covariance matrix of the mean (m i ) for the feature combination
vector and can be expressed as S B ¼ P i ¼ 1 ð n i m i ð Þ 2 Þ , where n i is the sample
number of the feature combination vector in the ith class. m i and m are means of

Table 5.1 Feature selection metrics with description
Index (x, y, z) Name Description

1 AMV Autocorrelation MAX value

2 ADT Autocorrelation delay time

3 ACC Acceleration variance value

4 VEL Velocity variance value

5 BRF Breathing frequency

6 FTP Max power of fourier transform

7 PCA Principal component analysis coefficient

8 MLR Multiple linear regression coefficient

9 STD Standard deviation of time series data

10 MLE Maximum likelihood estimates