Irregular Breathing Classification from Multiple Patient Datasets - Prediction and Classification of Respiratory Motion - page 115

threshold value (n m ). Accordingly, all the samples within the threshold value
highlighted with yellow in Fig. 6.3 can be the regular respiratory patterns, whereas
the other samples highlighted with gray in Fig. 6.3 can become the irregular
respiratory patterns.
Figure 6.3 shows that the threshold value (n m ) depicted by dotted lines can
divide the regular respiratory patterns (P m ) from the irregular respiratory patterns
(1 - P m ) for each class m. As shown in the upper left corner in Fig. 6.3 , we can
summarize the process of the regular/irregular breathing detection, and denote the
regular respiratory patterns highlighted with yellow as [ m ¼ 1 P ðÞ¼ P 1 [[
P m [[ P M and the irregular respiratory patterns highlighted with gray as
\ m ¼ 1 1 P ð Þ¼ 1 P ð Þ\\ 1 P ð Þ\\ 1 P ð Þ: We will use these
notations for the predicted regular/irregular patterns in the following section.

6.4 Evaluation Criteria for Irregular Breathing Classifier

6.4.1 Sensitivity and Specificity

We apply standard sensitivity and specificity criteria as statistical measures of the
performance of a binary classification test for irregularity detection. The classifier
result may be positive, indicating an irregular breathing pattern as the presence of
an anomaly. On the other hand, the classifier result may be negative, indicating a
regular breathing pattern as the absence of the anomaly. Sensitivity is defined as
the probability that the classifier result indicates a respiratory pattern has
the anomaly when in fact they do have the anomaly. Specificity is defined as the
probability that the classifier result indicates a respiratory pattern does not have
the anomaly when in fact they are anomaly-free, as follows [ 40 ]:

T ðÞ

True Positives

Sensitivity ¼

True Positives T ðÞþ False Negatives F ðÞ

True Negatives T ðÞ

Specificity ¼

True Negatives T ðÞþ False Positives F ðÞ

For the sensitivity and specificity, we can use Fig. 6.3 as the hypothesized class,
i.e., the predicted regular or irregular pattern, as follows:

FN þ TN ¼ S TP þ FP ¼ T

M M

P m ; ð 1 P m Þ : ð 6 : 18 Þ

m ¼ 1 m ¼ 1

The proposed classifier described in Sect. 6.3 should have high sensitivity and
high specificity. Meanwhile, the given patient data show that the breathing data
can be mixed up with the regular and irregular breathing patterns in Fig. 6.4 .
During the period of observation (T), we notice some irregular breathing pattern.
Let us define BC i as the breathing cycle range for the patient i as shown in