# Interval-Based LDA Algorithm for Electrocardiograms for Individual Verification
## 1 Introduction  
Since the invention of electrocardiogram (ECG) recording in 1903 [1], a considerable number of studies using the electrocardiogram have been performed in the fields of diagnosing cardiac-related diseases [2; 3; 4; 5], detecting sleep apnea [6], monitoring driver drowsiness [7], and measuring blood pressure [8], because of its advantage of noninvasive convenience. Recently, researchers started to use the ECG biometrics to verify individual identity [9]. The ECG is a suitable tool because the signal itself constantly changes depending on the sympathetic/parasympathetic activities and it is resistant to attacks and duplication [10; 11; 12]. According to the latest US Federal Trade Commission report published in March 2019 [13], identity theft and cybercrime ranked third among the issues most complained about. Such kinds of identity fraud and hacking are becoming seriously dangerous. Unfortunately, they are unavoidable as long as we use password-based identity authentication systems. Therefore, new types of biometrics such as facial characteristics [14], gait [15], fingerprints and iris scans [16], vein pattern [17], etc., have been developed. Nevertheless, References [18; 19] show that they are still vulnerable to a replay/falsification attack even though they perform better with very low identification errors. To avoid problems related to such attacks, the biometrics should be a variable, so that they cannot be stolen, duplicated, or shared. Thus, many studies are showing a great interest in the ECG signal as a promising alternative biometric [20; 21; 22; 23]. The ECG signal is non-stationary and thus continuously changes over time. The two limbs of the autonomic nervous system (i.e., sympathetic and parasympathetic nerves) are the most important factors determining the changes in the heart rate. This type of variability is called intra-subjectvariability [24; 25; 26], that is, the changes occur for the same individual over time. There is also inter-subject variability found in the ECG's waveform that depends on the position, size, and anatomy of the heart, age, gender, relative body weight, chest configuration, and various other factors [27; 28]. Therefore, the ECG signal varies from person to person, implying that we can use it as a biometric for the verification of an individual's identity. There have been numerous attempts at applying ECG inter-subject variation for individual verification/identification [20; 21; 22; 23; 29; 30; 31; 32], which can be classified into two categories: the fiducial dependent approach [20; 21; 22; 23] and the fiducial independent approach [29; 30; 31; 32]. The fiducial dependent approach relies on local features, such as time duration and amplitude differences between specific points of interest in an ECG, so it is less affected by heart rate variations. However, it has the possibility of missing the overall morphological information that might be useful in identifying individuals. Many studies have focused on fiducial dependent features such as time intervals, angles, and amplitudes between specific fiducial points on the QRS complex [20; 33; 34; 35]. On the contrary, the fiducial independent approach is to find the feature of the ECG signal in the frequency domain rather than the time domain, or to extract the whole morphological features that appear to offer excellent discrimination information among individuals. Many algorithms based on frequency transformation have been proposed for extracting fiducial independent features from ECG signals, in which they use wavelet transform or DCT (Discrete Cosine Transform) to convert ECG signals in the time domain to the frequency domain [36; 37; 38; 39; 40]. The autocorrelation method also has been gaining considerable attention because of its excellent performances reported in many studies. It eliminates the need for fiducial point localization in the ECG signal by using an autocorrelation (AC) of the segmented ECG signal followed by DCT or LDA [41; 42; 43].