Detection of electrocardiogram atrial fibrillation using modified multifractal detrended fluctuation analysis based on discrete transforms and fractional Fourier transform

Abstract

Cardiovascular diseases (CVD) are the most common cause of death. Electrocardiography (ECG) is a preferred non-invasive method for detecting heart diseases. Atrial fibrillation (AF) is a common cardiac disease. This results from improper functioning of the sinoatrial node. It can cause heart failure and stroke. AF can be detected using ECG. Several studies used artificial intelligence to classify normal and abnormal ECG signals, such as AF signals. Most of them failed to achieve optimal classification parameter rates and had a significant error factor. Therefore, it is necessary to create a new model to overcome the classification errors in ECG signals. In this study, a novel method was developed to extract ECG signals using a modified multifractal detrended fluctuation analysis (MMFDFA) based on machine learning. The used ECG signals were obtained from the training dataset of the Physionet 2017 Challenge, which comprised 5050 normal and 738 AF signals. MMFDFA was a new version of multifractal detrended fluctuation analysis (MFDFA) by modifying the fluctuation function using one of the next discrete transforms and fractional Fourier transforms (FRFT). These discrete transforms were discrete cosine transform, discrete sine transform, discrete tan transform, discrete sinc transform, discrete hyperbolic cosine transform, discrete hyperbolic sine transform, and discrete hyperbolic tan transform. All of them were decomposed from the discrete sine or cosine transform. Seven approaches of MMFDFA were compared with MFDFA as the first approach based on deep learning (DL) and a support vector machine (SVM) as the classification methods. The deep learning parameters were selected using a simulated annealing optimization method. After using MMFDFA based on the discrete hyperbolic cosine transform and FRFT, the obtained classification parameter rates, such as the accuracy rate and area under the curve (AUC), were 99.3% and 0.996, respectively. These classification parameter rates were the maximum based on the DL. Therefore, MMFDFA is the preferable method for extracting the features of ECG signals based on DL. The software platform used was MATLAB 2022a. The selected model can be programmed on a laptop to rapidly diagnose patients with cardiac disease. Therefore, cardiologists can easily classify the ECG signals.

Article Highlights

The main contribution of this paper is summarized in the following points:

ECG features are extracted using MMFDFA built on FRFT and discrete transforms. They were novel techniques extracted from MFDFA and DCT, respectively.

Detection of AF by comparing different classifiers, such as deep learning and support vector machines, for extracting features of ECG signals.

Selection of the MMFDFA_DCHT_FRFT_BILSTM model for extracting heart sound features for achieving the highest classification parameter rates.

Introduction

According to the World Health Organization (WHO), the number of deaths due to cardiovascular diseases is high. Electrocardiography (ECG) was used to measure the electrical activity of the heart. It is a popular method for the diagnosis of various heart diseases. This is an easy, comfortable, safe, and noninvasive method. It can be used for monitoring patients in the intensive care unit (ICU) and clinics. The normal ECG consists of 3 main waves. They are the p-wave, QRS complex, and T-wave. The p-wave refers to atrial contraction or depolarization. Depolarization propagates through the sinus node to the right atrium, then the left atrium. The normal length of the p-wave is 70–110 ms. It is used to measure the size of the atrium. The QRS complex refers to ventricular contraction or depolarization. The duration of the QRS complex is less than 110ms. T-wave comes after the QRS complex. T-wave refers to ventricular repolarization. The T-wave is wider and smaller than the QRS complex.

An ECG is used to detect various heart diseases, such as irregular heart rhythm due to tachycardia or bradycardia, absence of p-wave in atrial fibrillation (AF), prolonged QRS complex due to delayed electrical activation of the ventricles, and inverted T-wave in myocardial ischemia.

AF is a fast irregular heart rhythm that starts in the atria. The sinoatrial (SA) node does not work properly. The risk of AF increases with age and coronary artery disease. AF occurs due to hypertension and valvular heart diseases, but it may also occur without any underlying heart disease. The symptoms of AF are fatigue, dyspnea, and dizziness. AF must be treated early to restore sinus rhythm and preventing thromboembolism and restore sinus rhythm [1].

Several studies on the detection and classification of ECG signals have been conducted. K. Gupta et al. detected AF signals using the local mean decomposition and ensemble boosted trees classifier. The obtained accuracy rate was 92.33% [2]. S. Hao et al. classified ECG signals using a modified ResNeX structure. They obtained an accuracy rate of 96.16% [3]. D. Le and colleagues classified ECG arrhythmias using a self-supervised convolutional neural network (CNN) [4]. C.H. Lee et al. measured the ECG signals of different diseases and classified them using a support vector machine (SVM). The obtained accuracy rate was 84.24% [5]. S. Yang et al. used a multiscale multilevel neural network to classify ECG signals [6]. B. Wang et al. diagnosed arrhythmia using a conventional neural network (CNN). They achieved an accuracy rate of 99.43% [7]. E. Prabhakararao et al. detected heart failure by ECG signals using a deep residual neural network. They obtained an accuracy rate of 98.57% [8]. M.B. Abubaker et al. detected cardiovascular diseases in ECG images using DL. They obtained an accuracy rate of 99.79% [9]. F.S. Butt et al. classified ECG signals using DL [10]. These studies did not achieve the optimum performance rates. The obtained accuracy rate should be nearly 100% for better diagnosis of several heart diseases. Therefore, it is necessary to create a new computer technique to solve this problem. In this study, an MMFDFA method was applied in different approaches to achieve the best performance classification parameter rates.

Five steps were discussed in this study. First, a literature review was presented to discuss the shortage of previous studies and the need for this study to solve these problems. Then, the methods used in this study were introduced to apply them in the phases of feature extraction and classification methods. After that, the analysis and results were obtained to select the suitable model for feature extraction of ECG signals. After that, the discussions were presented to explain the results of the models used in this study. This study was used to certify its success in fulfilling the shortage of previous studies. Future works were introduced. Finally, conclusions about this study were presented.

Literature review

Many studies were conducted for extracting biomedical signals using different feature extraction methods. Embolic Doppler ultrasound signals were denoised using dual-tree complex discrete wavelet transform. It outperformed the denoising of these signals using conventional discrete wavelet transform [11]. Modified dual-tree complex wavelet transform (DTCWT) was used to reduce the complex analysis of quadrature Doppler signals from blood flow and stroke-prone patients [12, 13]. The DTCWT was used to extract features from Doppler ultrasound embolic signals. The classification phase was conducted for emboli detection using SVM and KNN. The DTCWT was better than FFT and DWT for detecting embolic signals [14]. Wheezes lung sounds features were extracted using rational dilation wavelet transform. It analyzed these signals in the time–frequency domain. Therefore, it was superior to the Fourier transform and wavelet transform [15]. The short-time Fourier transform (STFT), chaos Analysis, and principal component analysis (PCA) were used to detect QRS complex of ECG signals from the Physionet dataset and real-time dataset [16]. Tunable q-factor wavelet transform (TQWT) was used to localize crackles or wheezes in lung sounds. It had superiority over using empirical mode decomposition and independent component analysis [17]. Autoregressive (AR) modeling was used to process ECG signals using KNN for the classification method [18]. A novel fractional wavelet transform (FrWT), Yule–Walker Autoregressive Analysis (YWARA), and Principal Component Analysis (PCA) were used to detect arrhythmia in ECG [19]. Independent component analysis (ICA) and linear discriminant analysis (LDA) were used for preprocessing and classifying ECG signals [20]. The chaos analysis theory was used to extract features of ECG signals. Savitzky-Golay filtering (SGF) technique was used to preprocess ECG signals. Support vector machine (SVM) technique was applied for the classification phase [21]. The spider monkey optimization technique was used to extract features of ECG signals after filtering them with a digital band pass filter [22]. Independent Principal Component Analysis (IPCA), Fractional Fourier Transform (FRFT), and Fractional Wavelet Transform (FrWT) were used to extract features of ECG signals [23]. Wavelet transform (WT) and adaptive autoregressive modeling (AARM) were used to analyze and extract features from ECG signals. SVM and relevance vector machine (RVM) were used to classify ECG signals [24]. Wheezes lung sounds were detected using STFT. The classification phase was conducted using deep learning based on the CNN-BILSTM model [25]. TQWT was also used based on statistical calculations for feature extraction of lung diseases. The classification phase was conducted using an ensemble learning model [26]. Lung diseases were classified through electrical impedance tomography imaging and deep learning [27]. Extracellular neural recordings of the brain were extracted using dual-tree complex wavelet transform (DT-CWT). It was compared with Harr wavelet transform and principal component analysis. Results had lower average error rates based on using DT-CWT compared with Harr wavelet transform and principal component analysis [28].

In these studies, there were several techniques to extract and classify different biomedical signals. The shortage of previous studies for extracting ECG signals and classifying them as seen in the introduction section can be solved using new approaches that may be deduced from these studies.

Methods

Different methods are applied to obtain different approaches for extracting features of ECG signals. Most of these methods are novel for obtaining high-performance classification parameters. These methods are extracted from conventional methods, as described below.

Fractional Fourier transform

The Fourier transform (FT) is not suitable for nonstationary signals such as biomedical signals because it represents these signals in the frequency domain only [29]. However, these signals vary in both the time domain and the frequency domain. On the other hand, the fractional Fourier transform (FRFT) represents signals in the time–frequency domain using the fractional domain [30]. Therefore, it is suitable for nonstationary signals such as biomedical signals. In FRFT, if the input signal is x(t), the FRFT of x(t) is FR^α(u). The fractional domain is u. As shown in Eqs. (1–2), FR^α(u) can be computed by integration of the multiplication of x(t) and K_α(t,u). Where K_α(t,u) is the kernel function of the FRFT. Discrete FRFT of the discrete signal x(n) is shown in Eq. (3–4). Here, 0 <|α|< 2, where α is the order of the FRFT.

1

$$F{R}^{\alpha }\left(u_{\mathrm{\varnothing }}\right)=\underset{-\infty }{\overset{\infty }{\int }}{K}_{\propto }\left(t,u_{\mathrm{\varnothing }}\right)x\left(t\right)dt$$

2

$$K_{\propto }\left(t,u_{\mathrm{\varnothing }}\right)=\left\{\begin{array}{cc}\sqrt{\frac{1-i.cot\left(\mathrm{\varnothing }\right)}{2\pi }}{e}^{i.\frac{(u_{\mathrm{\varnothing }}^2+t^2)\text{cot}\left(\mathrm{\varnothing }\right)}{2}-i.u_{\mathrm{\varnothing }}.t.csc\left(\mathrm{\varnothing }\right)}\hfill & \\ \delta \left(t-u_{\mathrm{\varnothing }}\right)if\mathrm{\varnothing }=2N\pi \hfill & if\mathrm{\varnothing }\ne N\pi \\ \delta \left(t+u_{\mathrm{\varnothing }}\right)if\mathrm{\varnothing }=\left(2N+1\right)\pi \hfill & \end{array}\right)$$

3

$$K_{\propto }\left(n,m\right)=\left\{\begin{array}{cc}\sqrt{\frac{1-i.cot\left(\mathrm{\varnothing }\right)}{2\pi }}{e}^{i.\frac{(m^2+n^2)\text{cot}\left(\mathrm{\varnothing }\right)}{2}-i.n.m.csc\left(\mathrm{\varnothing }\right)}\hfill & \\ \delta \left(n-m\right)if\mathrm{\varnothing }=2N\pi \hfill & if\mathrm{\varnothing }\ne N\pi \\ \delta \left(n+m\right)if\mathrm{\varnothing }=\left(2N+1\right)\pi \hfill & \end{array}\right)$$

4

$$F{R}_x^{\propto }\left(m\right)=\sum _{n=-N}^{N}x\left(n\right).K_{\propto }\left(n,m\right)$$

∅ = απ/2. Here, ∅ is the rotational angle of the FRFT. If it equals π/2, the FRFT will be converted to FT. In this study, α is selected to be 1.2.

Discrete cosine transform

The discrete cosine transform (DCT) is widely used in the feature extraction methods of biomedical signals. It can be used for feature selection in pattern recognition, noise reduction, and analyzing stationary and nonstationary signals. It has optimal performance and fast computation. Using DCT as a feature extraction method for signals is more accurate than using the FT. The highly correlated data energy can be compressed efficiently using DCT [31, 32–33]. Using DCT, a signal can be expressed as a sum of cosine functions at different frequencies. X(k) is the DCT of a discrete signal x(n). It can be calculated, as shown in Eqs. (5–6).

5

$$dct(x\left(n)\right)=X\left(k\right)=w\left(k\right)\sum _{n=1}^{N}x\left(n\right)cos\left(\frac{pi\left(2n-1\right)\left(k-1\right)}{2N}\right),1\le k\le N$$

6

$$w\left(1\right)=\sqrt{\frac{1}{N}},w\left(k\right)=\sqrt{\frac{2}{N}}2\le k\le N$$

Discrete sine transform

A signal can be expressed as a sum of sine functions at different frequencies using a discrete sine transform (DST). The DST algorithm is faster than the FFT and DCT algorithms. With the DST, the low-energy correlated data can be compressed efficiently. DST is widely used for image processing studies [32]. The calculation of the DST of digital signal x(n) is X(k), as shown in Eq. (7).

7

$$dst\left(x\left(n\right)\right)=X\left(k\right)=\sum _{n=1}^{N}x\left(n\right)sin\left(\frac{pi.n.k}{N+1}\right),1\le k\le N$$

Discrete tan transform

The discrete tan transform (DTT) is a novel discrete transform. The DTT is derived from the DCT. In this study, it is a step used to extract ECG signals. It is tested to achieve maximum accuracy. The DTT of the signal x(n) is X(k), as shown in Eqs. (6, 8).

8

$$dtt\left(x\left(n\right)\right)=X\left(k\right)=w\left(k\right)\sum _{n=1}^{N}x\left(n\right)tan\left(\frac{pi\left(2n-1\right)\left(k-1\right)}{2N}\right),1\le k\le N$$

Discrete Sinc transform

The discrete sinc transform (DSNT) is a novel discrete transform. It is derived from DCT. In this transform, the cosine function is replaced with sinc functions. The DSNT of a digital signal x(n) is X(k), as shown in Eqs. (6,9,10). DSNT is suggested because it may accurately classify ECG signals.

9

$$dsnt\left(x\left(n\right)\right)=X\left(k\right)=w\left(k\right)\sum _{n=1}^{N}x\left(n\right)\text{sinc}\left(\frac{pi\left(2n-1\right)\left(k-1\right)}{2N}\right),1\le k\le N$$

10

$$sinc\left(x\right)=\left\{\begin{array}{ccc}1\hfill & ifx=0& \\ \frac{sin\left(x\right)}{x}\hfill & \mathit{othewise}\end{array}\right)$$

Discrete hyperbolic cosine transform

The discrete hyperbolic cosine transform (DCHT) is a novel discrete transform. It is presented to find an approach to analyze biomedical signals correctly. It is derived from DCT by replacing the cosine function with the cosine hyperbolic function, as shown in Eqs. (6, 11). The DCHT of a digital signal x(n) is X(k), as presented in Eq. (11).

11

$$dcht\left(x\left(n\right)\right)=X\left(k\right)=w\left(k\right)\sum _{n=1}^{N}x\left(n\right)cosh\left(\frac{pi\left(2n-1\right)\left(k-1\right)}{2N}\right),1\le k\le N$$

Discrete hyperbolic sine transform

The discrete hyperbolic sine transform (DSHT) is a novel discrete transform. DSHT is derived from DCT by changing the cosine function to a hyperbolic sine function. It is created to extract features of ECG signals as an approach that may achieve high classification rates. The DSHT of a digital signal x(n) is X(k), as shown in Eq. (12). Where w(k) is defined in Eq. (6).

12

$$dsht\left(x,\left(n\right)\right)=X(k)=w\left(k\right)\sum _{n=1}^{N}x(n)\text{sinh}\left(\frac{pi\left(2,n,-,1\right)(k-1)}{2N}\right),1\le k\le N$$

Discrete hyperbolic tan transform

The discrete hyperbolic tan transform (DTHT) is a novel discrete transform that is derived from DCT by changing the cosine function into a hyperbolic tan function. An approach consisting of DTHT to achieve a high accuracy rate may be obtained. The DTHT of a signal x(n) is X(k), as presented in Eqs. (6, 13).

13

$$dtht\left(x,\left(n\right)\right)=X(k)=w\left(k\right)\sum _{n=1}^{N}x(n)\text{tanh}\left(\frac{pi\left(2,n,-,1\right)(k-1)}{2N}\right),1\le k\le N$$

Multifractal detrended fluctuational analysis

In this study, the features of ECG signals are extracted using a multifractal detrended fluctuation analysis (MFDFA) [34]. The MFDFA is suitable for analyzing nonstationary signals such as ECG signals by calculating the time series multifractal spectrum [35]. The multifractal spectrum determines the fractal structure derivatives in the large and small fluctuations of periods. The MFDFA is derived from the detrended fluctuation analysis (DFA) [36]. The MFDFA is constructed in 5 steps. The first 3 steps of the MFDFA are the steps of the DFA. In step 1, the profile Y(j) is detrended and calculated from the input signal x(i) and its average (µ), as shown in Eq. (14). In step 2, Y(j) is divided into nonoverlapping segments (N_s = N/s) of equal length s (scale). The N_s series’ length is not a multiple of length s. The same procedure is repeated at the end. Therefore, the number of segments is 2N_s.

14

$$Y\left(j\right)=\sum _{i=1}^{j}x\left(i\right)-\mu ,j=1\cdots \cdots .N$$

In step 3, the local trend for each of the 2N_s segments is computed using the least squares fit of the segment, and a variance (square of the fluctuation function) $F^2\left(s,,,v\right)$ is subsequently obtained, as shown in Eq. (15).

15

$$F^2\left(s,,,v\right)=\frac{1}{s}\sum _{i=1}^s{\{Y\left[\left(v,-,1\right),s,+,i\right]-y_v\left(i\right)]\}}^2$$where y_v(i) is the fitting polynomial of segment v. Here v = 1···N_s for each segment. When v = N_s + 1···2N_s, $F^2\left(s,,,v\right)$ will be modified, as shown in Eq. (16).

16

$$F^2\left(s,,,v\right)=\frac{1}{s}\sum _{i=1}^s{\{Y\left[N,-,\left(v,-,N_s\right),s,+,i\right]-y_v\left(i\right)]\}}^2$$

First, second, third, or higher-order polynomials can be obtained in the fitting procedure. The order m of the MFDFA is determined as MFDFA(m).

In step 4, all the segments of $F^2\left(s,,,v\right)$ are raised to the power q/2 and averaged at q ≠ 0, then raised to the q-th order to calculate the fluctuation function F_q, as shown in Eq. (17). If q = 0, the exponential of the half-average for the natural logarithmic of $F^2\left(s,,,v\right)$ is F_q. The value of q is a real number. F_q(s) is calculated for values of s ≥ m + 2.

17

$$F_q\left(s\right)=\left\{\begin{array}{c}{\left\{\frac{1}{{2N}_s},{\sum }_{v=1}^{2N_s},{{[F}^2(s,v)]}^{\frac{q}{2}}\right\}}^{\frac{1}{q}}ifq\ne 0\\ \text{exp}\left[\frac{1}{4N_s},{\sum }_{v=1}^{2N_s},\mathit{ln},\left(F^2,\left(s,,,v\right)\right)\right]ifq=0\end{array}\right)$$

In step 5, the scaling behavior of the F_q function is obtained by calculating a log–log plot of F_q(s) for each value of q versus s, as shown in Eq. (18).

18

$$F_q\left(s\right)\propto s^{h(q)}$$

Here, the Hurst exponent is h(q). Where h(q) is independent of q for the monofractal time series with compact support.

Modified multifractal detrended fluctuation analysis

Modified multifractal detrended fluctuation analysis (MMFDFA) is derived from MFDFA. It is used to construct approaches for extracting features of ECG signals. These features will be classified to be compared with the obtained features using MFDFA. The steps of the MMFDFA look like the steps of the MFDFA except that the q-th order fluctuation function $F_q\left(s\right)$ at q = 0 in Eq. (17) is changed. As shown in Eq. (19), the exponential function is replaced with a discrete transform such as DCT, DST, DSNT, DTT, DCHT, DSHT, or DTHT. The logarithmic function is replaced with FRFT. ${\mathit{FR}}^{1.2}$ is the FRFT of the square of the fluctuation function $F^2\left(s,,,v\right)$, where the order of FRFT α equaled 1.2.

19

$$F_q\left(s\right)=\left\{\text{discrete transform},\left[\frac{1}{4N_s},\sum _{v=1}^{2N_s},{\mathit{FR}}^{1.2},\left(F^2,\left(s,,,v\right)\right)\right],i,f,,q,=,0\right)$$

Classification methods

The suggested classification methods are deep learning and SVM. They are compared to obtain the maximum classification rates.

Deep learning

Deep learning (DL) has been used recently as a classification method in many studies. DL is a subclass of machine learning. Machine learning is a subclass of artificial intelligence. The word deep indicates that DL has many hidden layers. DL is used for many applications such as the classification of biomedical signals. Two types of DLs are convolutional neural network (CNN) and recurrent neural network (RNN). CNN is widely used in the classification of images. RNN is widely used in the classification of nonlinear time series. RNN is updated using backpropagation. An RNN can model biomedical signals, but it cannot address long time intervals because the gradient of the RNN vanishes through backpropagation.

The long short-term memory (LSTM) is a new version of the RNN architecture. It can avoid the defects of RNN. LSTM can cope perfectly with tasks of long-time intervals.

The hidden layer is the only difference between the architectures of RNN and LSTM. The cell of LSTM is the hidden layer of the LSTM. The cell of the LSTM consists of three gates (input, output, and forget). The information is fed to the input gate. The forget gate is used to remove redundant information from the input gate. BILSTM is a bidirectional LSTM layer, which is another new version of an RNN. BILSTM consists of two layers of LSTM, one in the forward time series and the other in the backward time series, with two separate hidden layers. BILSTM outperforms LSTM based on information from the past and future. It can also be used to solve the vanishing gradient problem of the classical RNN. It has a better accuracy rate than LSTM if it is used in a classification phase.

DL has many advantages over other machine learning methods. It can deal with large datasets, achieving the highest accuracy rates. It can extract and classify complex raw data such as images directly without extracting their features. It avoids redundancy from the input dataset. It can handle missing labels. DL can be used as supervised, semi-supervised, unsupervised, or reinforcement learning [37].

In this study, DL was used as supervised learning. It was used based on the BILSTM. There were six layers in the DL training process, as shown in Fig. 1. The first layer was the sequence input layer. Its size was the number of extracted features of the ECG signals. The second layer was the BILSTM layer. The number of BILSTM hidden units was 100. The BILSTM output mode was the sequence mode. The third layer was fully connected. Its size was two, which indicated that the output of the classification method was normal or AF ECG signals. The fourth layer was the Softmax layer, which converted numbers into a probability distribution. The fifth layer was the dropout layer, which was used to avoid overfitting. At the final classification layer, the classification process was obtained by identifying the label of the related features normal or AF ECG signal.

[See PDF for image]

Fig. 1

Deep Learning BILSTM Steps

Support vector machine

The support vector machine (SVM) has been used as a classification method for a long time. V. Vapnik and C. Cortes used it as a classification method in 1995 [38]. It can be used in binary or multinomial classification. It is used for supervised learning only. Steps of the SVM algorithm were shown in Fig. 2. The input layer of the SVM was the extracted features of the ECG signals using the MMFDFA. The kernel function of the SVM may be linear, quadratic, cubic, or n^th order. In this study, a linear kernel function was used for the classification process. After that, the training process of the SVM model was obtained using a labelled training dataset. Then the optimal hyperplane was selected to determine the best decision boundary. Finally, the untrained normal or AF ECG signals were determined in the classification step.

[See PDF for image]

Fig. 2

SVM Steps

Performance evaluation

The performance evaluation parameters are used to judge the quality of the used classifier. The predicted values of the classifiers are compared with the expected values. If the binary classifier is used, there will be two types of values, such as positive values and negative values. In this research, the positive value is the number of AF patients. The negative value is the number of normal patients. The number of positive patients correctly predicted is Tp. The number of negative patients correctly predicted is Tn. The number of positive patients incorrectly predicted is Fp. The number of negative patients incorrectly predicted Fn. The most common performance evaluation parameters are accuracy, sensitivity (recall), specificity, F1_score, G_mean, and area under the curve (AUC). They can be calculated based on Tpr, Tnr, Fpr, Tp, Tn, Fp, and Fn, as shown in Eqs. (20–28). Where Tpr, Tnr, and Fpr are the true positive rate, true negative rate, and false positive rate, respectively. The most famous classification parameter is accuracy. It is calculated by dividing the number of correctly classified samples by the total number of samples. If the accuracy rate is high and near 100%, then the used model can classify samples correctly. AUC is used to analyze the classification process in detail. Whenever AUC is near unity, the performance of the used classifier is perfect.

20

$$T_{\mathit{pr}}=\frac{\mathit{Tp}}{Fn+Tp}$$

21

$$T_{\mathit{nr}}=\frac{\mathit{Tn}}{Fp+Tn}$$

22

$$F_{\mathit{pr}}=\frac{\mathit{Fp}}{Fp+Tn}$$

23

$$Accuracy=\frac{Tp+Tn}{Fp+Fn+Tp+Tn}$$

24

$$Sensitivity=recall=\frac{\mathit{Tp}}{Fn+Tp}$$

25

$$Specificity=\frac{\mathit{Tn}}{Fp+Tn}$$

26

$$F1\_\text{score}=2·\frac{precision·recall}{precision+recall}$$

27

$$G\_mean=\sqrt{T_{\mathit{pr}}.T_{\mathit{nr}}}$$

28

$$AUC={\int }_0^1{T}_{\mathit{pr}}d{F}_{\mathit{pr}}$$

Receiver operating characteristic (ROC) curve

The receiver operating characteristic (ROC) curve is used to qualify the performance of the model. In ROC, the y-axis is the true probability of detection (Tpr or sensitivity), and the x-axis is the false alarm (Fpr or 1-specificity). The area under this curve is AUC. ROC is used to compare the performance of different models. When the slope of the ROC of the used model is infinity, this model is selected. And vice versa, when the slope of the ROC of a model is unity, this model is excluded.

Dataset

ECG signals using a single short lead were collected from the Physionet challenge in 2017 [39]. The recorded time of ECG signals was between 30 and 60 s. The Physionet challenge dataset was divided into normal, AF, noisy, and other ECG signals. The selected signals were AF and normal ECG signals. Noisy and other signals were excluded. These data were collected from the training dataset. There was no need to perform preprocessing for the ECG signals because the dataset in this challenge was filtered with a bandpass filter ranging from 0.5 to 40 Hz. The dataset was measured using an AliveCor device. This device was used to monitor the ECG easily. It was a handheld device with a single channel. The used sampling frequency was 300 Hz. An expert identified the labels of this dataset.

The number of selected normal ECG signals was 5050. The number of AF ECG signals was 738. All of them were collected from the training set of this 2017 dataset challenge. In the training process of the DL and SVM methods, there were two methods to distribute the dataset between testing and training, i.e. k-fold cross-validation method and the train-validation-test split. The value of k was 10 in the k-fold cross-validation method. In the train-validation-test split, the percentages of training, validation, and testing ratios were 60%, 10%, and 30%, respectively. The validation was used to avoid overfitting and was not a part of the testing process.

ECG artifacts

The ECG artifacts are signals that appear on the ECG but do not reflect the electrical activity of the heart. They can cause misdiagnosing of the patient’s heart. There are two types of artifacts such as external artifacts and internal artifacts. The internal artifacts occur mainly due to motion artifacts. The external artifacts mainly occur due to electromagnetic interference of the neighboring devices (i.e. mobile phones), power lines interference, deposits of previously used gel on the surface of electrodes, and malfunctions of ECG electrodes and ECG cables [40]. Filters must be used to remove all these artifacts from ECG signals. In the Physionet Challenge 2017, a bandpass filter was applied with bandwidth from 0.5 to 40 Hz.

Analysis and results

The previously discussed methods were used to extract features of ECG signals and classify them. The obtained results were compared to select the best model, where the highest performance classification parameters were achieved, as shown below.

The feature extraction model was obtained from the ECG signals by comparing eight approaches. The approach 1 was the MFDFA of ECG signals. The MMFDFA of ECG signals was applied as a new method. It was obtained by inserting a discrete transform instead of a natural exponential function and inserting a fractional Fourier transform instead of the natural logarithmic function, when F_q was calculated at q = 0. The discrete transform in approach 2, approach 3 approach 4, approach 5, approach 6, approach 7, and approach 8, was DCT, DST, DTT, DSNT, DCHT, DSHT, and DTHT, respectively. Therefore, approaches 1, 2, 3, 4, 5, 6, 7, and 8 are MFDFA, MMFDA_FRFT_DCT, MMFDA_FRFT_DST, MMFDA_FRFT_DTT, MMFDA_FRFT_DSNT, MMFDA_FRFT_DCHT, MMFDA_FRFT_DSHT, and MMFDA_FRFT_DTHT, respectively.

As shown in Fig. 3, eight models were used to obtain the features of ECG signals. Then, feature extraction methods were compared using 8 approaches until the highest classification rate was obtained. Otherwise, another approach would be used.

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Fig. 3

Flow chart of feature extraction model

The simulated annealing method (SAM) was used to optimize the hyperparameters of deep learning. The lower values for this optimization method were the maximum number of epochs, the hidden layer size, the minimum patch size, and the initial learning rate. They were 50, 50, 50, and 0.001, respectively. The upper values were 200, 200, 200, and 0.1, respectively. After applying SAM, the hyperparameter values of the minimum error rate were 100, 100, 150, and 0.01, respectively.

As shown in Table 1, the classification parameter rates were compared between the training-validation-testing and k-fold cross-validation methods for approach 1 and approach 6. In this study, the value of k was 10. The accuracy rates and AUC values of approaches 1 and 6 using the training-validation-testing method were greater than the same values using the tenfold cross-validation method. Therefore, the training-validation-testing method was used to compare the classification parameter rates for all approaches.

Table 1. Classification parameter rates of DL using training-validation-testing and tenfold cross-validation at m = 1

	Classification parameters	Accuracy	Sensitivity	Specificity	Precision	G_mean	F1_score	AUC
Approach 1	k-fold cross validation	93.3%	92.3%	100%	100%	96.1%	0.96	0.83
	Training–validating testing	94.2%	100%	54.7%	93.8%	74	0.97	0.97
Approach 6	k-fold cross validation	93.8	92.9%	100%	100%	96.4%	0.96	0.84
	Training–validating testing	99.3%	100%	94.1	99.1%	97%	0.996	0.996

Bold values indicate the maximum value

As shown in Table 2, the classification parameter rates of the DL and SVM methods at different polynomial orders for the detrending process (m). When m was equal to one and DL was used, the accuracy rate was 94.2% and the AUC was 0.97. When m equaled two at DL, the accuracy rate was 88.2% and the AUC was 0.76. When m was equal to 3, the accuracy rate was 86.6% and the AUC was 0.74 for DL. When m was equal to one and SVM was used, the accuracy rate was 63.7%, and the AUC was 0.5. When m was equal to two for the SVM, the accuracy rate was 64.5%, and the AUC was 0.61. When m was equal to three at the SVM, the accuracy rate was 87.3%. The accuracy rates and AUC of SVM as a classification method were lower than those of DL. When m was 1, the classification method using DL achieved a higher accuracy rate than using SVM for other values of m. Therefore, DL was chosen as a classification method when m was equal to 1 for comparing different approaches.

Table 2. Classification parameter rates of SVM & DL approach 1 for training-validation-testing method

Classification parameters	Accuracy	Sensitivity	Specificity	Precision	G_mean	F1_score	AUC
DL m = 1	94.2%	100%	54.7%	93.8%	74%	0.97	0.97
SVM m = 1	63.7%	68.4%	30.8%	87.1%	45.9%	0.77	0.5
DL m = 2	88.2%	86.5%	100%	100%	93%	0.93	0.76
SVM m = 2	64.5%	69.9%	27.6%	86.9%	43.9%	0.77	0.61
DL m = 3	86.6%	84.7%	100%	100%	92%	0.92	0.74
SVM m = 3	87.3%	100%	0	87.3	0	0.93	NA

Bold values indicate the maximum value

The classification parameter rates of approaches 1, 2, 3, 5, 6, 7, and 8 were presented in Table 3 using DL as a classification method for m equaled 1. For approach 6, the accuracy rate was 99.3%. The sensitivity rate was 100%. The G-mean rate is 97%. The F1_score was 0.996. The AUC was 0.996. All these parameters were the highest compared with the calculated parameters of the other approaches. Therefore, approach 6 was selected.

Table 3. Rates of the DL classification parameters of the proposed approaches when m = 1

Classification parameters	Accuracy	Sensitivity	Specificity	Precision	G_mean	F1_score	AUC
Approach 1	94.2%	100%	54.7%	93.8%	74%	0.97	0.97
Approach 2	98.5%	100%	88.2%	98.3%	93.9%	0.99	0.992
Approach 3	88.9%	100%	13.1%	88.8%	36.2%	0.94	0.94
Approach 4	91.6%	90.4%	100%	100%	95.1%	0.94	0.8
Approach 5	98.4%	100%	87.8%	98.2%	93.7%	0.99	0.991
Approach 6	99.3%	100%	94.1%	99.1%	97%	0.996	0.996
Approach 7	76.7%	73.3%	100%	100%	85.6%	0.85	0.68
Approach 8	98.6%	99.3%	93.7%	99.1%	96.4%	0.992	0.97

Bold values indicate the maximum value

As shown in Fig. 4, the ROC curves were introduced for m = 1, 2, and 3 of approach 1 using DL or SVM as classification methods. The ROC curve of DL at m was equal to one that was closer to 1 than the other curves were. Therefore, DL was selected as a classification method for the other approaches at m was equal to 1.

[See PDF for image]

Fig. 4

ROC curve of DL & SVM of approach 1 for different values of m

As shown in Fig. 5, ROC curves of the DL for the other approaches when m was equal to 1 were presented. The ROC curve of approach 6 was much closer to 1 than those of the other approaches. The ROC curves of the other approaches were far from 1. Therefore, Approach 6 was the most stable method. It was preferred for extracting ECG signals using DL at m = 1.

[See PDF for image]

Fig. 5

DL ROC curves of different approaches when m = 1

Selected model

As shown in Fig. 6, the selected model was applied using MMFDFA (FRFT at α = 1.2, and DCHT) in the feature extraction phase. First, ECG signals were detrended. The fit polynomial function at m = 1 was obtained from the detrended signal. The variance of the subtraction of detrended ECG signals and the fitted 1st order polynomial was calculated. Then, it was shifted and divided into non-overlapping segments. Finally stage in the feature extraction method was calculating the fluctuation function of the scale s and order q values. These seven values of both s and q were stated above. If q ≠ 0, it was calculated from the average qth order. If q = 0, the FRFT was calculated and its order was 1.2. Then, half the average of DCHT was obtained. The output features from this stage were seven features. They were fed to the classification stage, where DL was used based on BILSTM. AF or normal ECG signals were detected using this classification stage.

[See PDF for image]

Fig. 6

Selected model using approach 6

Discussion

AF is a heart arrhythmia that can lead to stroke and heart failure. AF is a direct cause of death. Many studies applied computer-aided diagnosis (CAD) to facilitate the detection of AF. As shown in Table 4, previous studies were introduced [41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57–59]. All these studies used the same ECG signals of the Physionet 2017 challenge. Andreotti et al. used a feature-based approach to classify ECG signals. F1_score was 0.91 [41]. Behar et al. used SVM as a classification method. The obtained F1_score was 0.9 [42]. The least-square SVM was applied as a classification method with an F1_score of 0.94 [43]. The decision tree was used as a classification method with an F1_score of 0.93 [44]. Deep learning was chosen as a classification method with an F1_score of 0.94 [45]. CNN was used as a classification method with an F1_score of 0.86 [46]. Linear discriminant Analysis (LDA) was applied as the classification method with an F1_score of 0.89 [47]. A hierarchical classification model was applied as a classification method with an F1_score of 0.86 [48]. A multi-layer cascaded binary classifier was used as a classification method with an F1_score of 0.99 [49]. SVM was used as a classification method with an F1_score of 0.85 [50]. CNN was applied as a classification method with an F1_score of 0.88 [51]. Gliner and Y. Yaniv used quadratic SVM as a classification method of an F1_score of 0.9 [52]. Goodfellow et al. applied gradient boosting as a classification method with an F1_score of 0.91, a precision of 88%, and a sensitivity of 94% [53]. Jekova et al. used a decision tree as a classification method with an F1_score of 0.82 [54]. Ahmed et al. used a combination of CNN and LSTM as a classification method with an accuracy rate of 91.2% [55]. Nguyen et al. used stacking SVM as a classification method with an F1_score of 0.84 [56]. LSTM was used as a classification method with an accuracy of 98.7% [57]. DL was applied as a classification method with an F1_score of 0.87 [58]. A combination of ShuffleNet and AlexNet DL was used as a classification method with an accuracy of 93.7% [59].

Table 4. Comparison between previous studies and this study

References	Classification method	Classification parameters for the normal signals of training data
Andreotti et al. [41]	Feature-based approach (no segmentation)	F1_score 0.91
Behar et al. [42]	SVM	F1_score 0.9
Billeci et al. [43]	Least square SVM	F1_score 0.94
Bin et al. [44]	Decision tree	F1_Score 0.93
Bonizzi et al. [45]	Deep learning	F1_score 0.94
Chandra et al. [46]	CNN	F1_score 0.86
Christov et al. [47]	Linear discriminant Analysis (LDA)	F1_score 0.89
Coppola et al. [48]	Hierarchical	F1_score 0.86
Datta et al. [49]	series of multi-layer cascaded	F1_score 0.99
García et al. [50]	SVM	F1_score 0.85
Ghiasi et al. [51]	CNN	F1_score 0.88
Gliner [52]	Quadratic SVM + Neural network	F1_score 0.9
Goodfellow et al. [53]	Gradient boosting	F1_score 0.91 Precision 88% Sensitivity 94
Jekova et al. [54]	Decision tree	F1_score 0.82
Ahmed et al. [55]	CNN + LSTM	Accuracy 91.2%
Nguyen el al. [56]	CNN SVM	F1_score 0.84
Malik el al. [57]	DL + LSTM	Accuracy 98.7%
Pham el al. [58]	DL	F1_score 0.87
Anbalagan el al. [59]	ShuffleNet-AlexNet DL	Accuracy 93.7%
This study	DL-BILSTM	Accuracy 99.3% Sensitivity100% Specificity 94.1% Precision 99.1% G-mean 97% F1_score 0.996 AUC 0.996

All these studies achieved low evaluation parameter rates compared to those in this study. There were two classification methods used in this study, such as SVM and deep learning. The evaluation parameters of deep learning were higher than those of SVM. There are two reasons for these results. First, SVM is suitable for small datasets, but DL is suitable for large datasets. Second, DL is more complicated than SVM. The DL consists of multiple layers, whereas the SVM consists of one layer.

In this study, features of ECG signals were obtained using MMFDFA based on novel discrete transform (DCHT) and FRFT as the approach 6. DL was chosen in the classification step. The obtained classification parameter rates were the highest. Therefore, this approach was selected to extract ECG signals for obtaining the best computer technique for aiding cardiologists in classifying ECG signals. The shortage of this study was the absence of a segmentation technique. The dataset of ECG should be larger. In the future, several datasets of ECG will be compared. The detection of heart diseases will be applied using ECG data in real-time. Segmentation of ECG signals will be presented. Novel feature extraction methods can be applied to achieve higher classification parameter rates based on the fractional wavelet transform and discrete wavelet transforms. Novel classification techniques will be applied.

Conclusions

In this study, the MMFDFA was used as a method for extracting the characteristics of ECG signals using eight approaches. MMFDFA was derived from MFDFA by changing the content of the q-th order fluctuation function using FRFT and a different discrete transform. Each approach from 2 to 8 referred to a certain discrete transform of the q-th order fluctuation function. DL and SVM were compared as classification methods for MFDFA as approach 1 at different values of m (i.e., 1, 2, and 3). The accuracy rate obtained using DL was the highest when m was equal to 1 compared with the other values of m and SVM. Therefore, approaches 1 to 8 were compared at m equaled 1. The accuracy rate and AUC of DL for classifying ECG signals using approach 6 were the highest. Therefore, approach 6 and the DL technique were selected for extracting features and classifying ECG signals. Cardiologists can use this model as an application of artificial intelligence to detect AF or any other heart disease onsite or remotely. This model can also be generalized to be used for extracting different biomedical signals.

Author contributions

MMA made all the paper.

Data availability

The used dataset of ECG signals [39] is available at the website https://physionet.org/content/challenge-2017/1.0.0/.

Declarations

Ethics approval and consent to participate

Not available. The used dataset is from the site of Physionet.

Consent for publication

The author gives his consent for the publication of identifiable details, which can include details within the text (“Material”) to be published in the Journal of DISCOVER APPLIED SCIENCES to be available in both print and on the Internet, and will be available to a broader audience through marketing channels and other third parties. Therefore, anyone can read material published in the Journal. I understand that readers may include not only medical professionals and scholarly researchers but also journalists and general members of the public.

Competing interests

The authors declare no competing interests.

Publisher's Note

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