Irregular Breathing Classification from Multiple Patient Datasets - Prediction and Classification of Respiratory Motion - page 119

combination vector (x), whereas the black and the blue spots represent the aver-
aged objective function and the standard deviation of the objective function with
respect to the feature metrics number. In Fig. 6.6 b we notice that two feature
combination vector can have a minimal feature combination vector. Even though
z = 9 has the minimum standard deviation in Fig. 6.6 a, a minimum objective
function (J)ofz= 9 is much bigger than those in z = 3, 4, 5 and 6 shown in
Fig. 6.6 b. The interesting result is that the combinations of BRF, PCA, MLR, and
STD have minimum objective functions in z = 3 and 4. Therefore, we would like
to use these four feature extraction metrics, i.e., BRF, PCA, MLR, and STD as the
estimated

feature vector (x) for the rest of modules for breathing patterns

classification.

6.5.3 Clustering of Respiratory Patterns Based on EM

In this section, the breathing patterns will be arranged into groups with the esti-
mated feature vector ðÞ for the analysis of breathing patterns. For the quantitative
analysis of the cluster models we used two criteria for model selection, i.e., Akaike
information criterion (AIC) and Bayesian information criterion (BIC), among a
class of parametric models with different cluster numbers [ 41 ]. Both criteria
measure the relative goodness of fit of a statistical model. In general, the AIC and
BIC are defined as follows:

AIC ¼ 2k 2ln ðÞ; BIC ¼ 2 lnL þ k ln ðÞ;

where n is the number of patient datasets, k is the number of parameters to be
estimated, and L is the maximized log-likelihood function for the estimated model
that can be derived from Eq. ( 6.8 ).
In Fig. 6.7 , we can notice that both criteria have selected the identical clustering
number; M = 5. Therefore, we can arrange the whole pattern datasets into five
different clusters of breathing patterns based on the simulation results.

6.5.4 Breathing Pattern Analysis to Detect Irregular Pattern

We have shown that breathing patterns are a mixture of regular and irregular
patterns for a patient in Fig. 6.4 . Before predicting irregular breathing, we analyze
the breathing pattern to extract the ratio c ðÞ with the true positive and true neg-
ative ranges for each patient. For the breathing cycle (BC i ) we search the breathing
curves to detect the local maxima and minima. After detecting the first extrema,
we set up the searching range for the next extrema as 3-3.5 s [ 13 ]. Accordingly,
we can detect the next extrema within half a breathing cycle because one breathing
cycle is around 4 s [ 7 ]. The BC i is the mean value of the consecutive maxima or