# Interval-Based LDA Algorithm for Electrocardiograms for Individual Verification
## 3 Experiment and Results  
An experiment was carried out using a public open database, available on the PhysioNet website [34], to evaluate the proposed algorithm. The MIT-BIT arrhythmia database (MITDB) contains 48 records of heartbeats collected from 47 subjects (records 201 and 202 are from the same male subject). Each record is approximately 30 min long and was sampled at 360 Hz. The subjects are 25 men with ages between 32 and 89 years old and 22 women with ages between 23 to 89 years old. The data were obtained using a two-channel ambulatory Holter monitor at the Beth Israel Deaconess Medical Center from 1975 until 1979. This database is the most referred database related to arrhythmic studies. In this study, this database was used to evaluate the efficiency of the proposed algorithm. Two 2-min intervals were randomly selected for each data. The first 2-min interval of each data was used for training and the second data was used for verification. Only single lead data was used in the experiment. The error rate can be calculated for each subject, as shown in Figure 8. The FR (False Rejection) means that the subject was rejected despite being himself. The FA (False Acceptance) means that the subject was accepted despite being someone else. The distance threshold was chosen to be the intersection of FR (False Rejection) and FA (False Acceptance), depending on the subject. The threshold and EER for each subject are calculated based on the intersection of FR and FA. If there is only one intersection point, the threshold and EER are determined based on the intersection point, whereas if there are more than two points, the threshold is determined by the average value of the largest and smallest value, and certainly, EER is calculated as 0, as shown in Figure 8.  
Figure 9a shows an example of obtaining the EER for each individual. A histogram of the EER (Equal Error Rates) is shown in Figure 9b. The average EER is 0.143%, which indicates the efficiency of the overall algorithm, as shown in Equation (32). Only a single user was enrolled at any point in time. In other words, at any point in time, we had one client and 46 imposters. \[\text{Total efficiency of verification }=\frac{1}{\text{No. of subject }}\sum_{\text{Sub}=1}^{\text{No. of subject }}\text{EER}_{\text{Sub}} \tag{32}\]  
where Sub indicates the subject number. To demonstrate the efficiency of our proposed algorithm, we compared it with related works that used the same database (MIT-BIH), as shown in Table 1. Table 1 shows that the EER (Equal Error Rate) in Reference [48] is higher than the proposed algorithm despite using ECG data from two leads. Recently, most ECG wearable devices, such as smart watches, only use one lead; thus, the proposed algorithm is more suitable for real-life applications. In Reference [48], a fixed shifting size was used for the autocorrelation, while in the proposed algorithm, we used a flexible shifting size for the autocorrelation as the QRS width for the individual, which requires less computational effort. Although fused information from two ECG leads was used in Reference [49], their IDA (Identification Accuracy) is lower than the proposed algorithm; however, the enroll time is 5 min, which is longer than our algorithm. A fiducial point dependent method was used in References [28; 50; 51; 52] which is vulnerable to noise. Only 10-20 s data were used for enrollment and verification in References [53; 52]. However, we used two 2-min data for enrollment and verification to verify the stability of the proposed algorithm. Only a direct contact sensor was used in References [28; 48; 49; 50; 51; 52; 53] to verify the algorithms. In contrast, we used a non-contact single lead senor for real-life applications. In this paper, in the case of a fiducial dependent approach, although it has the advantage of being able to identify a subject in a relatively short time with less computational effort, it is easily affected by external noise.