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The qualitative features selection (QFS) is performed
after obtaining the PQRST complex features. Let Ri,j denote
the feature value range of the ith PQRST complex feature
for the jth heartbeat case. The sub-index i is defined as the
same as that of Fi. The sub-index j = 1, 2, 3, 4,5 denotes the
case of ‘‘NORM”, ‘‘LBBB”, ‘‘RBBB”, ‘‘VPC” and ‘‘APC”, respectively
(see Fig. 4). For instance, R1,1 = [0.695,2.69] mV,
R1,2 = [0.205,2.06] mV, R1,3 = [0.695,2.24] mV, R1,4 = [0.105,
3.095] mV, and R1,5 = [0.275,1.870] mV in Fig. 4a.
The following procedure is run to perform QFS:
Step 2-1: Obtain feature Fi using the following algorithm:
If eR
¼ 1, then feature Fi (see Fig. 3) is obtained
for 1 6 i 6 9, 1 6 k 6 5, 1 6 j 6 5, k – j, where eR
¼
Ri;k \ Ri;j, and the index i, j (or k) is defined as the same
as that of Ri,j. Remark 2-1: Let eR
¼ Ri;k \ Ri;j ¼ 1 if the
two feature value ranges Ri,k and Ri,j do not overlap.
Thus, feature Fi is obtained to discriminate heartbeats
case-k and case-j, and NFi is increased by 1, where NFi
denotes the total number of cases in which feature
Fi can discriminate two disjoint heartbeats case-k
and case-j. For instance, if R3,1 = [33,79] ms, R3,2 = [86,
153] ms (see Fig. 4c), then eR
¼ R3;1 \ R3;2 ¼ 1, meaning
that feature F3 (‘‘QRS-dur”) can discriminate heartbeats
case-1 (NORM case) and case-2 (LBBB case). Similarly,
let eR
¼ Ri;k \ Ri;j ¼ 0 if Ri,k and Ri,j overlap, that is, feature
Fi is not obtained and heartbeats case-k and case-j cannot
be discriminated. In this case, the value of NFi
remains unchanged. For instance, if R1,1 = [0.695,
2.69] mV, R1,2 = [0.205,2.06] mV (see Fig. 4a), then
eR
¼ R1;1 \ R1;2 ¼ 0, meaning that feature F1 (‘‘H-QR”)
cannot discriminate heartbeats case-1 (NORM case)
and case-2 (LBBB case).
Step 2-2: Sort NFi, i = 1,2,. . ., 9, with the order of
decreasing values, and then select the index with the
highest value, that is,
i ¼ argðmaxfNFig; i ¼ 1; 2; . . . ; 9Þ: ð3Þ
For instance, suppose that NF1 = 6, NF2 = 1, NF3 = 3, the
sorted sequence becomes NF1, NF3 and NF2. Thus, the
index with the biggest value is NF1 and the sequence
of sub-indexes NFi with the order of decreasing values
of NFi is 1, 3, and 2.
Step 2-3: Obtain qualitative feature Fi. A feature Fi is
selected as a qualitative feature if it satisfies both the
following conditions:
Condition 1: Feature Fi can discriminate heartbeats
case-k and case-j, where sub-indexes i are obtained
from Step 2-2.
Condition 2: The qualitative feature for discriminate
between heartbeats case-k and case-j is not found
yet, where k, j = 1,2,3,4,5, and k – j.
If the feature Fi is selected as qualitative feature, then
both heartbeat cases k and j are recorded in data items
for the feature Fi and OUT Fi (that is, Fi is a qualitative
feature). If the feature Fi cannot be selected as qualitative
feature, then go to Step 2-4. Fig. 5 shows the flowchart
of Step 2-3. Remark 2-3: Index k and
j = 1, 2, 3, 4,5 denote the heartbeat cases of ‘‘NORM”,
‘‘LBBB”, ‘‘RBBB”, ‘‘VPC” and ‘‘APC”, respectively.
Step 2-4: Obtain the next qualitative feature.If the
qualitative features obtained from Step 2-3 are
enough to discriminate each heartbeat case, then
go to Step 2-5, otherwise go to Step 2-3.
Step 2-5: End.Four qualitative features QRS-dur,
QTP-int, Ratio-RR, and Area-R0ST0 were selected after
performing the above procedure QFS. Each heartbeat
case had its own range of values for each qualitative
feature, as shown in Fig. 4c–e and i. Thus, these specific
value ranges can be adopted to determine
whether the patient has the case of cardiac arrhythmia
by the LDA method.