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Detection of Atrial fibrillation (AF) is more complex as compared to other cardiac diseases. It requires lengthy ECG signals and more time for visual inspection and analysis by the physicians. Automatic detection of AF using an expert system is essential for the investigation of ECG signals. In this study, the Physionet challenge 2017 dataset is used for the detection and classification of AF versus other signals. In this paper, ECG signals are segmented into a sample size of 250 samples for the detection of Wavelet Packet Decomposition (WPD) and approximate entropy (ApEn) features for classification. In addition to WPD and ApEn, statistical features were derived from ECG signals. The Principal Component Analysis (PCA) has been used to reduce the dimensionality of the features based on the rank. Ensemble classifiers such as AdaBoost, XGBoost and Random Forest (RF) are used for classification. The accuracy of 62.91%, 70.33% and 89% for the AdaBoost, XGBoost and Random Forest respectively. We found RF classifier is suitable for classifying AF, normal rhythm and other nonAF related abnormal heart rhythms.
atrial fibrillation, ECG, wavelet packet decomposition, approximate entropy, ensemble classifier, wavelet packet entropy
The Electrocardiogram is the most reliable method used to measure the electrical activity of the human heart. The ECG is used for the analysis and diagnosis of the cardiac condition of the patients. The morphological changes in ECG signal help us to detect and prediction of cardiac diseases in the patients and the most common disease is arrhythmia which is characterized by irregular heartbeats in the heart rhythm. Even minor changes in ECG pattern may lead to cardiac arrhythmias, as a result, change in irregularities in the heart rate, conduction of cardiac muscles leading to chest pain, tiredness, and loss of consciousness. Cardiac arrhythmias are classified into several types, some of them are life threatening and a few arrhythmias are not dangerous, but still, it requires the proper analysis to avoid future clinical problems.
Atrial fibrillation (AF) is a supraventricular tachyarrhythmia. The occurrence of AF is due to the disorder in the rhythm leading, the abnormal atrial foci beating [1], triggered rhythm [2], or there is atrial reentry in the atria [3, 4]. The diagnosis of AF is becoming a challenge in the modern world due to paroxistic behavior and the absence of symptoms in some cases. Atrial fibrillation (AF) is a cardiac pathology which is currently the most common cardiac rhythm disorder, characterized by the atrium chaotic contraction.A long electrocardiogram recording is required to detect the AF as appearing infrequently in the ECG signal. To analyze longer ECG recordings manually requires great time, as well as more effort, hence the automatic detection of ECG arrhythmias provides great support to physicians [5, 6].
Many research groups have been proposed for automatic detection and classification of various types of arrhythmias [713].
Clifford and Azuaje [14] emphases on physiology activity of the ECG signal. Several reseachers have classified arrhythmia based on heartbeats, fiducial points, QRS duration and RR intervals [1522] where the variation are predomaint for the classification. Principal Component Analysis (PCA) [2325], or Independent Component Analysis (ICA) were used to reduce the feature vector where heartbeat is represented by coefficients of the vector. Non linear structure Kernel Principal Component Analisys, Generalized Discriminant Analysis (GDA) [26] have better performance compared to PCA [25]. Few researchers have empolyed wavelet methods [2628] and found Daubechies [29] with the order 2 was suitable for high accuracy classification.
Ye et al. [30] proposed an algorithm based on morphology and dynamics of ECG to classify sixteen types of arrhythmias. Several methods are developed for automatic detection of arrhythmia and ECG classification. At present, there are several classification and regression methods, employed for automatic detection of ECG arrhythmia, like timedomain parameters, frequency analysis and nonlinear approaches [31], KNearest Neighbors [32], Artificial Neural Network [33], linear discriminant (LD) classifier [34] Support Vector Machine [35], Probabilistic Neural Network [36], multilayer perceptron [37], Genetic Algorithms and particle swarm optimization (PSO) [38] and path forest [39].
In this paper, Ensemble Classifiers with wavelet packet decomposition (WPD) coefficients and Approximate Entropy are used to classify the four classes of ECG signals. This paper includes methodology, results and discussions followed by the conclusion.
2.1 Overview
In this study, the Physionet challenge 2017 dataset is used to classify Atrial Fibrillation, normal rhythm, noisy and other nonAF related abnormal heart rhythms. The range of cleaned ECG signals is between 0.05 Hz to 100 Hz. Raw ECG signal contains different types of highfrequency noises such as power line interference, Electromyogram/motion noises and lowfrequency noises such as baseline drift, electrode contact noise, which highly corrupts the ECG signal. Therefore, removing the noisy portions in the ECG signal is considered to be an important process before feature extraction and classification.
To eliminate lowfrequency noises and baseline wander, the FIR filter was implemented with cutoff frequency [0.5, 2] Hz and normalized frequency to Nyquist frequency (Fs/2). The filter order was taken as 5 as it work well with ECG signals and the attenuation at cutoff frequencies was fixed at 3dB. The notch filter is designed with a quality factor of 30, to remove power line interference of 50/60Hz and to obtain a cleaned ECG signal. After preprocessing the ECG signal were segmented into small segments with a duration of 800 to 1000 ms. The features were extracted from the segmented ECG, such as wavelet packet decomposition (WPD) coefficients, ApEn and statical features. These features were trained with ensemble classifiers to classify the arrhythmia. The structure of ECG classification is shown in Figure 1.
Figure 1. Block diagram of ECG classification
2.2 Feature extraction
For the classification of ECG signal, data feature extraction is the crucial step and it aims to extract the nonredundant and informative features from the raw ECG signal [35]. All the extracted features contain the relevant information of the input signal which can be used as an input to train the model to classify the signal.
2.2.1 Wavelet packet decomposition
Discrete Wavelet Transform (DWT) is the most powerful tool used for analyzing the signal in the timefrequency domain. DWT decomposes the original signal into approximation coefficients (ACs) and detail coefficients (DCs) in which the approximation coefficients (ACs) capture the high scale information and lowfrequency component of the input signal whereas, the detail coefficients (DCs) capture the low scale information and a highfrequency component of the input signal. In DWT, only approximation coefficients are further decomposed into new ACs and DCs but the DCs remains unchanged. As Discrete Wavelet Transform decomposes only ACs components in each layer and the extraction of information from DCs is very difficult. Wavelet Packet Decomposition (WPD) decomposes DCs in each level along with ACs simultaneously which provides additional highfrequency components of an ECG signal [4042]. The structure diagram of threelayer wavelet packet decomposition is shown in Figure 2. A threelevel WPD tree is sufficient for the classification of ECG signals.
Figure 3 shows the threelevel wavelet packet decomposition of ECG signal, where each node has both the DCs as well as ACs components which yield, more features. It is seen from Figure 3 first and second decomposition levels, decomposition of the approximate coefficients (lowpass filter) resembles the corresponding original signal, whereas the detail coefficient (highpass filter) decomposition varies with the original signal and this might be due to the lower cutoff frequency remains unchanged whereas higher cutoff frequency changes at these levels.
Figure 2. Structure diagram of threelayer wavelet packet decomposition
Figure 3. Three levels Wavelet packet decomposition of ECG signal
The decomposition of the wavelet packets is estimated recursively using Eq. (1):
$\left\{\begin{array}{c}d w_{0,0}(t)=E C G(t) \\ d w_{i, 2 j1}(t)=\sqrt{2} \sum_k h(x) d_{i1 . j}(2 tx) \\ d w_{i, 2 j}(t)=\sqrt{2} \sum_k g(x) d_{i1 . j}(2 tx)\end{array}\right.$ (1)
where, g(x) and h(x) are lowpass filter and highpass filter respectively, and at the i^{th} level for the j^{th} node, dw_{i,j} is the reconstruction signals (coefficients) from WPD.
2.2.2 Approximate entropy
Pincus first introduced the approximate entropy (ApEn) algorithm, which measures the complexity of a time series [43]. The approximate entropy depends on the length of the series, embedded dimension length and tolerance window M, n and r respectively. The lower and higher value of ApEn indicates the similarities and dissimilarities between the two cardiac cycles respectively. The ApEn of each ECG signal data set can be estimated. The ECG signal is segmented into 250 samples, which consists of at least one cardiac cycle. The ApEn is calculated between consecutive segments of ECG signals after threelevel WPD.
ECG_S (n)=[ECG (1), ECG (2) ………. ECG (M)], where M is the total number of ECG segments.
(a) Form mvectors, ECG_V (1) to ECG_V (Mn+1) interpreted by:
$E C G_{V(i)}=\left[\begin{array}{c}E C G_{} S(i,:), E C G_{} S(i+1,:), \ldots \\ \ldots \ldots E C G_{} S(in+1,:)\end{array}\right]$ (2)
where, i=1, 2, …….., (Mn+1).
(b) Determine the distance between vectors ECG V I and ECG V (j) by calculating the absolute maximum difference between their scalar components.
$d\left[E C G_{V(i)}, E C G_{V(j)} \right]=_{k=0, m1}^{\max }\left[\mid\begin{array}{c}E C G_{} S(i+k) \\ E C G_{} S(j+k)\end{array} \mid\right]$ (3)
(c) Compute $\mathrm{C}_{\mathrm{r}}^{\mathrm{n}} \mathrm{(i)}$ for each i, for i=1, 2,………(Mn+1).
$\mathrm{C}_{\mathrm{r}}^{\mathrm{n}}(\mathrm{i})=\frac{\mathrm{v}^{\mathrm{n}}(\mathrm{i})}{\mathrm{M}\mathrm{n}+1}$ (4)
where, V^{n} (i)=number of d[ECG_V(i), ECG_V(j)]<r.
(d) Compute $\Phi^{\mathrm{n}}(\mathrm{r})$ by taking the natural logarithm of each $\mathrm{C}_{\mathrm{r}}^{\mathrm{n}} \mathrm{(i)}$ and average it over i as defined in step (b).
$\Phi^n(r)=\frac{1}{Mn+1} \sum_{i=1}^{Mn+1} \ln \left(C_r^n\right)$ (5)
Increment the embedded dimension to n+1 and repeat the steps ad.
(e) Evaluate ApEn values for a finite data length.
$A p E n(M, n, r)=\Phi^n(r)\Phi^{n+1}(r)$ (6)
In this analysis, the values were chosen as n=1 or n=2 and tolerance window r=0.20 times the standard deviation of the time series.
2.2.3 The procedure for feature extraction
From the ECG signals, the features were extracted by performing the following steps as depicted in the Figure 4.
2.3 Random Forest
Random Forest (RF), is an ensemble supervised machine learning algorithm proposed by Breiman [44]. With the strategy of bagging the RF builds many classification trees by selecting some random features from randomly selected samples and finally employing voting it selects the best solution. The RF classifiers handle large data scales, both numeric and categorical variables more efficiently. It uses fewer features, and also it provides minimum classification error for unbalanced datasets. The normalization of variables is not necessary for RF and also reduces the overfitting of the data, hence it provides superior performance in classification. Figure 5 depicts the Random Forest Classifier algorithm's flowchart.
Figure 4. Procedure for feature extraction
Figure 5. Flowchart of random forest classifier algorithm
Algorithm:
The basic working flow of Random Forest classifiers is depicted as
Step a−Select the samples randomly from the given dataset.
Step b–Create a decision tree for each randomly selected sample using the bagging strategy, and then use the decision tree to predict the outcome.
Step c–Every predicted result is based on the voting performance.
Step d–The prediction result with the most votes is chosen as the final prediction result.
The classifier’s performance is evaluated using the statistical indices namely sensitivity (recall), positive predictivity (precision), F_{1} score, and accuracy (ACC) which provides clairvoyance of the algorithm. These performance metrics were derived from true positive (TP), true negative (TN), false positive (FP), and falsenegative (FN). In the classification of ECG signal, TP stands for the number of outcomes that the model predicted correctly of all the positive classes, while TN stands for the number of outcomes that the model predicted correctly of all the negative classes, and FP is the number of outcomes from all positive classes that model predicted incorrectly, while FN denotes the number of outcomes from all negative classes that model predicted incorrectly. The performance metric of the classifier is given below:
$Accuracy=\frac{\mathrm{TP}+\mathrm{TN}}{(\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN})} * 100 \%$ (7)
$\mathrm{F}_1=\frac{\mathrm{TP}}{\mathrm{TP}+0.5(\mathrm{FP}+\mathrm{TP})} * 100 \%$ (8)
Predictivity $=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}} 100 \%$ (9)
Sensitivity $=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}} * 100 \%$ (10)
An ideal ECG classifier should achieve high recall, precision, F_{1} score and accuracy.
An ensemble approach for the categorization of AF and other arrhythmias from brief segments of ECG signals was given in this study. The detection of atrial fibrillation from ECG signals is the most difficult task due to the high variability of the signals between different patients. In addition to the advantages of WPD and RF, we have also faced some important issues while choosing the appropriate mother wavelet for WPD. In the present study, we used three mother wavelets db6, db8 and db16 from the Daubechies wavelets family. Threelevel decomposition was performed on the original ECG signal for the analysis and extraction of features from WPD. In addition to approximate and detail coefficients, approximate entropy, higherorder statistical features were also estimated from the threelevel decomposition. The features extracted from the dataset are shown in Table 1. The ANOVA test was performed to determine the significance of the features and was found to be statistically more significant. From Table 1, it was observed that extracted features show a significant difference between atrial fibrillation and other classes. It is observed that the mean value was high for AF when compared with other classes and also the entropy and kurtosis values were low for AF than the other remaining classes. All these variations in the statistical features of AF, when compared with other classes, might be due to the disorganized atrial activity and contraction leading to a typical electrical transmission to the AV node and ventricles. Hence all these features have a significant contribution to training the model.
The accuracy results of each wavelet family are represented in below Table 2. The Db6 wavelet from the Daubechies family with threelevel decomposition achieves the high accuracy of 89% when compared to the other Daubechies wavelets after using the Principal Component Analysis technique which speeds up the computation by reducing the dimension of the larger dataset which is slightly better when compared to the other Daubechies wavelets. The wavelets from the Daubechies family are more effective for ECG classification than any other wavelet family. Usually, the threelevel decomposition achieves effective results for all mother wavelets.
Table 1. List of extracted features

AF 
Normal 
Others 
Noisy 
AAA3_mean 
15.5259 ± 1.2357 
1.1075 ± 12.4976 
0.0771 ± 26.3460 
3.3604± 35.6352 
AAA3_entropy 
0.0582 ± 0.4530 
0.4190 ± 0.07088 
0.4093 ± 0.0712 
0.3651± 0.0443 
AAA3_skew 
1.9136 ± 1.9019 
2.1367 ± 2.3240 
1.8855 ± 2.1764 
0.2655± 0.6850 
AAA3_kurtosis 
7.5245 ± 14.0300 
18.6347 ± 6.3132 
16.2710 ± 7.3401 
3.1582± 2.2595 
DAA3_mean 
0.0067 ± 0.0003 
0.0001 ± 0.0032 
0.0002 ± 0.0093 
0.0031± 0.0193 
DAA3_entropy 
0.0496 ± 0.2858 
0.2927 ± 0.0573 
0.2829 ± 0.0618 
0.3447± 0.0417 
DAA3_skew 
0.3291 ± 0.18285 
0.3456 ± 0.3215 
0.2607± 0.3727 
0.0525± 0.4063 
DAA3_kurtosis 
2.2443 ± 9.47851 
10.5032 ± 2.3772 
9.9987 ± 2.6886 
7.7612± 1.6298 
ADA3_mean 
0.1076 ± 0.0048 
0.0005 ± 0.0408 
0.0006 ± 0.1289 
0.0369± 0.2973 
ADA3_entropy 
0.0546 ± 0.3269 
0.3395 ± 0.0575 
0.3260 ± 0.0618 
0.3662± 0.0369 
ADA3_skew 
0.2876 ± 0.1123 
0.1871 ± 0.2297 
0.1381 ± 0.3323 
0.0862± 0.3155 
ADA3_kurtosis 
2.2762 ± 8.5390 
9.1337 ± 2.2197 
8.8927 ± 2.5922 
7.0703± 1.8062 
DDA3_mean 
0.0576 ± 0.0001 
0.0004 ± 0.0244 
0.0010± 0.0882 
0.0225± 0.1824 
DDA3_entropy 
0.0310± 0.1015 
0.1315± 0.0333 
0.1168± 0.0382 
0.0641± 0.0119 
DDA3_skew 
0.4169 ± 0.05200 
0.0580± 0.6653 
0.0391± 0.6365 
0.0154± 0.3627 
DDA3_kurtosis 
0.9160 ± 11.5430 
10.8351± 0.9293 
11.2004± 1.1166 
11.5943± 0.8606 
AAD3_mean 
2.7645 ± 2.05276 
2.0084± 2.6989 
1.9753± 3.0284 
1.6370± 6.5957 
AAD3_entropy 
0.0870 ± 0.3859 
0.3769± 0.0966 
0.3746± 0.0954 
0.4212± 0.0328 
AAD3_skew 
1.2503 ± 0.8280 
1.2359± 1.7212 
1.0673± 1.5287 
0.0871± 0.4093 
AAD3_kurtosis 
5.5347 ± 12.6153 
17.1078± 4.5010 
14.9455± 5.4853 
4.6292± 2.5807 
DAD3_mean 
0.0988 ± 0.0207 
0.0066± 0.0969 
0.0111± 0.1129 
0.1405± 0.3058 
DAD3_entropy 
0.0775 ± 0.3884 
0.3783± 0.0868 
0.3783± 0.0852 
0.4309± 0.0445 
DAD3_skew 
1.7973 ± 0.5931 
0.6267± 2.5976 
0.5486± 2.2961 
0.1664± 0.6753 
DAD3_kurtosis 
5.3591 ± 13.3725 
17.6765± 5.0416 
15.7190± 5.6784 
6.1239± 2.5699 
ADD3_mean 
0.0961 ± 0.4069 
0.3846± 0.1097 
0.3891± 0.1061 
0.4474± 0.0469 
ADD3_entropy 
1.6404 ± 0.8587 
1.1866± 1.8812 
1.0534± 2.0010 
4.1070± 7.5698 
ADD3_skew 
1.8183± 0.1174 
0.5141± 2.4720 
0.3672± 2.2022 
0.3515± 0.4955 
ADD3_kurtosis 
6.2192± 15.11690 
19.7330± 5.1231 
17.4770± 6.0586 
6.4727± 2.7591 
DDD3_mean 
0.1296± 0.1039 
0.1128± 0.1287 
0.1070± 0.1510 
0.1500± 0.3558 
DDD3_entropy 
0.0578± 0.3280 
0.3464± 0.0581 
0.3332± 0.0623 
0.3547± 0.0359 
DDD3_skew 
1.1310± 0.7079 
1.4027± 1.5522 
1.0537± 1.4589 
0.0052± 0.8782 
DDD3_kurtosis 
3.3965± 11.5120 
10.6422± 2.3881 
11.0627± 3.4925 
11.5731± 3.7693 
Table 2. Accuracy results of each wavelet family
Classifier 
Db6 
Db8 
Db16 
Random Forest 
89.00 
88.84 
88.99 
XGBoost 
70.33 
71.39 
70.45 
AdaBoost 
62.51 
57.83 
62.56 
In this paper, a comparative study of feature extraction and analysis of ECG signals was carried out with Wavelet Packet Decomposition using Daubechies wavelet family. The significance of features and the problem of imbalanced datasets were examined. The refinement of ECG signals using preprocessing methods and feature extraction using statistical measurements has proven to be an accurate and efficient method for ECG signal classification. The proposed method yields better results regardless of signal duration, whether complete ECG signals, parameters derived from signalsbased ECG data, or downsampled ECG signals. With Db6 wavelets, this approach based on feature extraction using multicumulants produces 89 percent accurate results for ECG signals. In future work, deep learning algorithms maybe improve classification accuracy.
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