Detection of atrial fibrillation episodes in long-term heart rhythm signals using a support vector machine

sensors Article Detection of Atrial Fibrillation Episodes in Long-Term Heart Rhythm Signals Using a Support Vector Machine Robert Czabanski 1, Krzysztof Horoba 2,*, Janusz Wrobel 2, Adam Matonia 2, Radek Martinek 3, Tomasz Kupka 2, Michal Jezewski 1, Radana Kahankova 3, Janusz Jezewski 2and Jacek M. Leski 1 1Department of Cybernetics, Nanotechnology and Data Processing, Silesian University of Technology, PL44100 Gliwice, Poland; [email protected] (R.C.); [email protected] (M.J.); [email protected] (J.L.) 2 Łukasiewicz Research Network–Institute of Medical Technology and Equipment, PL 41800 Zabrze, Poland; [email protected] (J.W.); [email protected] (A.M.); [email protected] (T.K.); [email protected] (J.J.) 3Department of Cybernetics and Biomedical Engineering, VSB–Technical University of Ostrava, 708 00 Ostrava-Poruba, Czech Republic; [email protected] (R.M.); [email protected] (R.K.) *Correspondence: krzysztof.hor[email protected] Received: 19 December 2019; Accepted: 27 January 2020; Published: 30 January 2020   Abstract: Atrial fibrillation (AF) is a serious heart arrhythmia leading to a significant increase of the risk for occurrence of ischemic stroke. Clinically, the AF episode is recognized in an electrocardiogram. However, detection of asymptomatic AF, which requires a long-term monitoring, is more efficient when based on irregularity of beat-to-beat intervals estimated by the heart rate (HR) features. Automated classification of heartbeats into AF and non-AF by means of the Lagrangian Support Vector Machine has been proposed. The classifier input vector consisted of sixteen features, including four coefficients very sensitive to beat-to-beat heart changes, taken from the fetal heart rate analysis in perinatal medicine. Effectiveness of the proposed classifier has been verified on the MIT-BIH Atrial Fibrillation Database. Designing of the LSVM classifier using very large number of feature vectors requires extreme computational efforts. Therefore, an original approach has been proposed to determine a training set of the smallest possible size that still would guarantee a high quality of AF detection. It enables to obtain satisfactory results using only 1.39% of all heartbeats as the training data. Post-processing stage based on aggregation of classified heartbeats into AF episodes has been applied to provide more reliable information on patient risk. Results obtained during the testing phase showed the sensitivity of 98.94%, positive predictive value of 98.39%, and classification accuracy of 98.86%. Keywords: support vector machine (SVM); heart rate variability (HRV); HRV features; atrial fibrillation (AF); AF detection 1. Introduction Atrial fibrillation (AF) is the most common heart arrhythmia, which occurs when the atria contracts quickly and irregularly at rates of 400 to 600 per minute. These contractions are independent from ventricles, which themselves operate at much lower rate. AF symptoms often include palpitations, irregular heartbeat, shortness of breath, chest pains and others, but they can be also asymptomatic and is then called silent AF. The frequency of AF occurrence is strictly correlated with the patient’s age [ 1 , 2 ]. The prognosis indicates that the AF occurrence within the period of the next 20–30 years will Sensors 2020,20, 765; doi:10.3390/s20030765 www.mdpi.com/journal/sensors Sensors 2020,20, 765 2 of 24 double, mainly due to the longer life span of the population. The AF detection is important, since this heart arrhythmia is a well-known risk factor for occurrence of ischemic stroke, even six times higher than among patients without the arrhythmia [3]. Figure 1presents the ECG signals from the MIT-BIH Atrial Fibrillation database (MIT-BIH AF) published on PhysioNet [ 4 – 6 ], comprising both segments with the AF episodes and non-AF segments. AF episodes occur irregularly and may last from a few heartbeats to hours, which significantly hinder the possibility to diagnose the silent AF by means of occasionally performed ambulatory ECG recordings. It implies that the longer the recording, the higher chance to detect the silent AF episodes [ 7 , 8 ]. The most efficient techniques of long-term monitoring are: Holter monitor, continuous telemetry [ 9 – 12 ], or implementable devices with internal memory [ 13 – 15 ]. However, visual analysis of long 24-h recording requires a lot of time and efforts from the cardiologists, thus the methods for automated detection of atrial fibrillation are needed to improve the objectivity of interpretation. When based on ECG, the efficient automated AF detection requires a high quality signal. It may not be ensured by the long-term monitoring techniques which usually comprise periods of daily physical activity of the patient which distort the ECG signal. Sensors 2020, 20, 765 2 of 24 is important, since this heart arrhythmia is a well-known risk factor for occurrence of ischemic stroke, even six times higher than among patients without the arrhythmia [3]. Figure 1 presents the ECG signals from the MIT-BIH Atrial Fibrillation database (MIT-BIH AF) published on PhysioNet [4–6], comprising both segments with the AF episodes and non-AF segments. AF episodes occur irregularly and may last from a few heartbeats to hours, which significantly hinder the possibility to diagnose the silent AF by means of occasionally performed ambulatory ECG recordings. It implies that the longer the recording, the higher chance to detect the silent AF episodes [7,8]. The most efficient techniques of long-term monitoring are: Holter monitor, continuous telemetry [9–12], or implementable devices with internal memory [13–15]. However, visual analysis of long 24-h recording requires a lot of time and efforts from the cardiologists, thus the methods for automated detection of atrial fibrillation are needed to improve the objectivity of interpretation. When based on ECG, the efficient automated AF detection requires a high quality signal. It may not be ensured by the long-term monitoring techniques which usually comprise periods of daily physical activity of the patient which distort the ECG signal. Figure 1. ECG signals (04043 and 04045) taken from the MIT-BIH AF database, with recognized segments of atrial fibrillation and the non-AF ones. The AF episode is manifested in ECG by significant changes of duration of the beat-to-beat (RR) intervals [16–19], see Figure 1. However, the RR intervals irregularity caused by AF occurrences is much more easy to observe after converting RR intervals into the instantaneous heart rate (HR) signal (Figure 2). The presented HR signals confirm that AF episodes occur very accidentally, and they can last a few seconds (signal 04048), but also expand to long lasting episodes (signal 04936). In the light of above facts an efficient automated method for AF detection should be based on estimation of RR irregularity or equivalent i.e., HR irregularity observed in long-term recording [20,21]. Moreover, such approach enables to involve the various recording methods which can provide signals in which the heartbeats can be detected. Beside electrocardiogram, such signals include photoplethysmogram [22–24] or seismocardiogram [25]. Using a photoelectric sensor is attractive in case of home telecare as long-term recording should be accomplished by instrumentations being minimally troublesome and inconvenient to the patient [26,27]. It may be a smart monitor in a form of a wrist bracelet with a specialized reflective optical sensor to perform the heart rate monitoring using the method previously developed by the authors [28]. The general concept of the methods most commonly used for automated detection of AF episodes relies on determination of features estimating the RR interval changes, and then application of the statistical analysis or more advanced classifier to differentiate between AF episode and normal sinus rhythm segments, basing on the information on RR irregularity. The feature set is composed most commonly of different statistical measures (mean or median HR, root mean square of successive RR differences, turning point ratio). It can also include normalized RR intervals [29,30] or normalized RR differences [31], Shannon entropy [19] or coefficient of sample entropy [15,32]. Other Figure 1. ECG signals (04043 and 04045) taken from the MIT-BIH AF database, with recognized segments of atrial fibrillation and the non-AF ones. The AF episode is manifested in ECG by significant changes of duration of the beat-to-beat (RR) intervals [ 16 – 19 ], see Figure 1. However, the RR intervals irregularity caused by AF occurrences is much more easy to observe after converting RR intervals into the instantaneous heart rate (HR) signal (Figure 2). The presented HR signals confirm that AF episodes occur very accidentally, and they can last a few seconds (signal 04048), but also expand to long lasting episodes (signal 04936). In the light of above facts an efficient automated method for AF detection should be based on estimation of RR irregularity or equivalent i.e., HR irregularity observed in long-term recording [ 20 , 21 ]. Moreover, such approach enables to involve the various recording methods which can provide signals in which the heartbeats can be detected. Beside electrocardiogram, such signals include photoplethysmogram [ 22 – 24 ] or seismocardiogram [ 25 ]. Using a photoelectric sensor is attractive in case of home telecare as long-term recording should be accomplished by instrumentations being minimally troublesome and inconvenient to the patient [ 26 , 27 ]. It may be a smart monitor in a form of a wrist bracelet with a specialized reflective optical sensor to perform the heart rate monitoring using the method previously developed by the authors [28]. The general concept of the methods most commonly used for automated detection of AF episodes relies on determination of features estimating the RR interval changes, and then application of the statistical analysis or more advanced classifier to differentiate between AF episode and normal sinus rhythm segments, basing on the information on RR irregularity. The feature set is composed most commonly of different statistical measures (mean or median HR, root mean square of successive RR Sensors 2020,20, 765 3 of 24 differences, turning point ratio). It can also include normalized RR intervals [ 29 , 30 ] or normalized RR differences [ 31 ], Shannon entropy [ 19 ] or coefficient of sample entropy [ 15 , 32 ]. Other form to present the RR irregularity are: the density histogram of the difference between successive RR intervals [ 33 , 34 ], map that plots RR intervals versus change of RR intervals [ 35 ], mapping the RR-interval time series to binary symbolic sequences [36,37] or Markov score of RR interval [16]. Sensors 2020, 20, 765 3 of 24 form to present the RR irregularity are: the density histogram of the difference between successive RR intervals [33,34], map that plots RR intervals versus change of RR intervals [35], mapping the RR-interval time series to binary symbolic sequences [36,37] or Markov score of RR interval [16]. Figure 2. Two HR signals expressed in beats per minute (bpm) with clinically recognized AF segments of different characteristics of HR changes in relation to normal sinus rhythm (non-AF). The AF segments are marked using the experts’ annotations provided for particular records in the MIT-BIH AF database. In the simplest approach to AF classification the Receiver Operating Characteristics (ROC) curve has been used to find the optimal threshold values for the input features providing the best classification performance [30,35,36,38]. The statistical test (Kolmogorov-Smirnov) was used in [33] to check if the density histograms of the test data differ from the standard density ones prepared as a template of AF episodes. In order to differentiate between AF and non-AF patterns the various classification methods have been applied: Neyman-Pearson detector [31], Random Forest (RF) model and k-nearest neighbors classifier [32], Support Vector Machine (SVM) with promising results reported in [39–41], as well as artificial neural network [42], also with interval transition matrices as an input [43]. In [39] SVM approach was used for classification of the 30-s segments of ECG and 300-beat sequences of RR intervals. Two parameters of Stationary Wavelet Transform (peak-to-average power ratio and log-energy entropy) were used for raw ECG-based approach, while five features were extracted from HR signal. The efficiency of AF detection achieved by the feature-based classification of the RR sequences was tested against the algorithm based on raw ECG. Higher sensitivity was ensured by the HR-based approach, while ECG-based algorithm provided improved specificity and classification accuracy. The classifier based on SVM with radial basis function was proposed in [40], with two features as the inputs: the average of RR differences and the standard deviation of differences in a defined duration. The same SVM classifier was employed in [41]. The input set comprised more RR interval features: median heart rate, minimum RR interval, mean RR interval, various entropy measures, and difference irregularity measure. The features estimating the RR variability are calculated in a sliding window comprising an established number of consecutive RR intervals (or HR values). Since there is no standard for the window length, many works have aimed to find the optimal length, providing the best classification performance. Some works assumed that AF episodes of less than 30 s duration are not clinically significant, which led to higher optimal number of heartbeats: 100 [33], 128 [35] and 150 [37]. Other authors claim that longer windows tend to miss short AF episodes, and thus they applied significantly shorter windows: 30 [32], 12 [15] or even 8 beats [44]. It is obvious that different Figure 2. Two HR signals expressed in beats per minute (bpm) with clinically recognized AF segments of different characteristics of HR changes in relation to normal sinus rhythm (non-AF). The AF segments are marked using the experts’ annotations provided for particular records in the MIT-BIH AF database. In the simplest approach to AF classification the Receiver Operating Characteristics (ROC) curve has been used to find the optimal threshold values for the input features providing the best classification performance [ 30 , 35 , 36 , 38 ]. The statistical test (Kolmogorov-Smirnov) was used in [ 33 ] to check if the density histograms of the test data differ from the standard density ones prepared as a template of AF episodes. In order to differentiate between AF and non-AF patterns the various classification methods have been applied: Neyman-Pearson detector [ 31 ], Random Forest (RF) model and k-nearest neighbors classifier [ 32 ], Support Vector Machine (SVM) with promising results reported in [ 39 – 41 ], as well as artificial neural network [42], also with interval transition matrices as an input [43]. In [ 39 ] SVM approach was used for classification of the 30-s segments of ECG and 300-beat sequences of RR intervals. Two parameters of Stationary Wavelet Transform (peak-to-average power ratio and log-energy entropy) were used for raw ECG-based approach, while five features were extracted from HR signal. The efficiency of AF detection achieved by the feature-based classification of the RR sequences was tested against the algorithm based on raw ECG. Higher sensitivity was ensured by the HR-based approach, while ECG-based algorithm provided improved specificity and classification accuracy. The classifier based on SVM with radial basis function was proposed in [ 40 ], with two features as the inputs: the average of RR differences and the standard deviation of differences in a defined duration. The same SVM classifier was employed in [ 41 ]. The input set comprised more RR interval features: median heart rate, minimum RR interval, mean RR interval, various entropy measures, and difference irregularity measure. The features estimating the RR variability are calculated in a sliding window comprising an established number of consecutive RR intervals (or HR values). Since there is no standard for the window length, many works have aimed to find the optimal length, providing the best classification performance. Some works assumed that AF episodes of less than 30 s duration are not clinically significant, which led to higher optimal number of heartbeats: 100 [ 33 ], 128 [ 35 ] and 150 [ 37 ]. Other authors claim that longer windows tend to miss short AF episodes, and thus they applied significantly Sensors 2020,20, 765 4 of 24 shorter windows: 30 [ 32 ], 12 [ 15 ] or even 8 beats [ 44 ]. It is obvious that different window length reported as the optimal value depends on the method used for automated AF detection. Another important aspect of using the sliding window for AF detection is how many beats it is shifted. Shifting the window every heartbeat results in one beat resolution of the AF classification. Then each heartbeat (RR interval), usually corresponding to the middle of the window, is classified as AF or non-AF. In such case, determination of classification performance is evident as each automatically classified beat can be related to the reference one, basing on the expert annotations. Otherwise, additional condition has to be applied—the window is labeled as AF episode only if the number of clinically annotated AF beats within the window exceeds a predefined threshold, usually 0.5 like in [ 35 , 45 ]. However, it is obvious that the threshold value affects the classification performance. The threshold has been included into the input feature set and tuned for optimum sensitivity and specificity in [ 38 ]. However, it should be noted that in such approach, the reference information is modified to achieve the best classification performance of the automated method tested, which seems to be rather doubtful. In order to avoid short false positive AF episodes or short artifact of classified AF the post-processing correction was applied, like dedicated mechanism called AF alarm enhancer [ 16 ]. It is the hysteresis counter that begins (or ends) an episode if established number of consecutive analyzed RR segments have been classified as AF (or non-AF). Other post-processing method was based on median filtering [45]. In [ 16 ], after combining R-R interval Markov score with two P-wave measurements: the location expressed by P-R interval duration, and the morphology defined as similarity between two consecutive P-waves, the sensitivity did not change, whereas specificity and positive predictive values increased slightly. A novel deep learning has been adopted for automated detection of AF in the long-term ECG recordings. This classifier learns directly from the RR intervals and therefore there is no need to extract the features. The model based on deep Recurrent Neural Network (RNN) with Long Short-Term Memory (LSTM) was used in [ 46 ], and combining with the Convolutionaland Recurrent-Neural Networks to extract high level features was proposed in [ 45 ]. Although a high classification performance has been reported, the computational complexity of deep learning model is much higher than traditional feature-based classifier. In this paper, we describe the method for automated AF detection which assigns the vector of parameters quantitatively describing the HR signal into two classes representing the absence or presence of atrial fibrillation. As estimation of HR variability is also important part of the Fetal Heart Rate (FHR) analysis [ 47 – 49 ], the indices widely used for FHR variability description have been considered as potentially useful for AF detection. The detection method presented in this paper was derived from the machine learning principles. Our classification routine was performed by means of the Lagrangian Support Vector Machine (LSVM) [ 50 ]—the state-of-the-art classifier based on the linearly convergent learning algorithm. The efficient LSVM learning procedure was obtained from the reformulation of the Quadratic Programing (QP) optimization problem of the Support Vector Machine (SVM) [ 51 ]. Additional aggregation stage has been applied to provide more reliable information on risk for the patient. The performance of the proposed AF detection method was examined using the MIT-BIH Atrial Fibrillation database, which includes 25 ten-hour long ECG recordings. 2. Materials and Methods Automated detection of the atrial fibrillation episodes proposed in this work starts with extraction of sixteen HR irregularity features composing the classifier input vector. Then the LSVM classifier is applied to mark a given heartbeat as AF or non-AF one. Final step is aggregation of the classified beats into AF episodes. 2.1. HR Irregularity Features Considering on-line detection of AF and limited computational power of the developed mobile monitor, we applied a simple linear classifier which recognizes the AF heartbeats basing on easily accessible information about heart rhythm and HR features [ 52 , 53 ]. Apart from the HR value, other Sensors 2020,20, 765 5 of 24 four input features have been selected in a series of preliminary investigations carried out among larger feature set [ 54 ]. Having the information on heartbeats detected, the instantaneous heart rate values HRi(expressed in beats per minute) are calculated according to the formula: HRi[bpm]=60000 RRi[ms], (1) where: RRiis the i-th interval between two consecutive heart beats expressed in milliseconds. Next, the features are determined in symmetrical moving window comprising 21 of HRivalues: •MEDi=median{HRi−k,. . . ,HRi+k}; •MADi=median{xi−k,. . . ,xi+k}, where xi= |HRi−MEDi|; •QNTi—represents the quantile of order 0.7 estimated over 21 values of heart rate; • PRP i —is the ratio of number of HR values between thresholds level of 120 to 160 bpm, to total number. where: iis the number of consecutive heartbeats to be classified, and k=1. . . 10. The values of the additional parameters: window width Nset to 21, quantile order set to 0.7 and HR thresholds of 120 and 160 were determined as a result of previously performed experiments [54]. For the new classification method, the input vector has been significantly expanded. It additionally comprises seven measures obtained from classical analysis of HR variability used in adults’ electrocardiography. This analysis includes exclusively sinus excitation, i.e., generated by the sinus-atrial node. Thus, it concerns only sinus rhythm variability, and any other types of excitation are excluded and replaced with artificially generated beats. Corrected in this way the series of changes in the subsequent RR intervals become the basis for the determination of heart rate variability measures. The most commonly used quantitative analysis methods can be divided into time, frequency, time-frequency and non-linear methods. In the presented work, the indices describing the HR variability were used in an unusual way as a set of features allowing the detection of atrial fibrillation episodes. The four selected features, obtained in statistical analysis in time domain within the same moving window, are as follows: •The mean heart rate: HR[bpm]=1 N N X i=1 HRi. (2) •Standard deviation of instantaneous heart rate values: STD_HR [bpm]=v u t1 N−1 N X i=1HR −HRi2. (3) • Root Mean Square of Successive Differences (RMSSD) which measures the variability within a data set—RR intervals—according to the following equation: RMSSD[ms]=v u t1 N−1 N−1 X i=1 (RRi+1−RRi)2. (4) • Percentage of differences between the RR intervals that exceed the value of 50 ms, denoted as pNN50 [%]: pNN50 =PN−1 i=1Ai N−1∗100%, (5) Sensors 2020,20, 765 6 of 24 where: Ai=(1 when RRi+1−RRi>50 0 when RRi+1−RRi≤50 (6) In addition, three non-linear features of HRV analysis were applied in the form of: • Poincare graph, which is a graphical representation of the current interval RR i plotted against subsequent one RR i+1 . Using the ellipse fitting technique, in each moving window comprising 21 heartbeats, two standard deviations are determined from the points: perpendicular to the regression line (SD1) and along the line (SD2). The SD1 describes the short-term variability of the heart rhythm, while the SD2 refers to the long-term HR variability. • Turning Points Ratio (TPR) measures the randomness of fluctuations within a data set, by calculating the ratio of the number of turning points to the maximum number of possible turning points. Turning point is found if both the preceding and succeeding points are either greater or lower. It is expected in random data set of arbitrary length N, that the number of possible turning points is (2N−4)/3, with a standard deviation of p(16N−29)/90. A separate group of features used for the detection of AF episodes are parameters commonly used in fetal heart rate analysis [ 55 , 56 ]. It turns out that in perinatal medicine quite different features are used to describe the FHR variability, mainly short-term (beat-to-beat) [ 57 ]. For the detection of AF episodes, four widely known short-term coefficients (indices) have been selected [ 58 , 59 ]. They are characterized by high sensitivity to changes in subsequent values of RR intervals and thus they potentially may be useful for AF detection [60–62]: • The Yeh’s index (DI_Yeh) whose determination starts with calculation of the auxiliary values d i representing the ratio of the difference between two successive RR intervals to their sum: di=RRi−RRi+1 RRi+RRi+1 . (7) Then, for the analyzed signal fragment, the DI_Yeh index is defined as the standard deviation from the obtained coefficients di: DI_Yeh [ms]=v u t1 N−2 N−1 X i=1di−d2, (8) where: d =1 N−1 N−1 P i=1 di,N—number of beats set to 21. • The Zugaib’s variability index (STV_Zug) has been defined as an average of the absolute values of the differences between successive Divalues and their median value: STV_Zug[ms]=1 N−1 N−1 X i=1 |Di−Med|, (9) where: Med—median value for the D i series, N—number of beats set to 21. The D i value represents the ratio of the absolute value of the difference between the heart intervals RR to their sum: Di=RRi+1−RRi RRi+1+RRi , (10) Sensors 2020,20, 765 7 of 24 • The Huey’s index (STV_Huey) was defined as the sum of absolute values of differences of subsequent instantaneous HR values for which the sign of difference was changed: STV_Huey [bpm]= N−1 X i=2 k·HRi+1−HRi. (11) where: k=(1 for (HRi−1−HRi)·(HRi−HRi+1)<0 0 for (HRi−1−HRi)·(HRi−HRi+1)≥0. (12) • The definition of de Haan’s index (STI_Haan) is based on a polar coordinate system whose both axes refer to RR intervals expressed in milliseconds, and points represent the pairs of subsequent intervals (RR i−1 , RR i ), as shown in Figure 3. STI_Haan is determined as the interquartile range of the angles ϕi between the lines connecting the point with origin of the coordinate system, and the X axis, designated for subsequent periods RRi: STI_Haan =IQR(ϕi), (13) where: i =1, 2 . . . N,N—number of beats. Sensors 2020, 20, 765 7 of 24 • The definition of de Haan’s index (STI_Haan) is based on a polar coordinate system whose both axes refer to RR intervals expressed in milliseconds, and points represent the pairs of subsequent intervals (RRi-1, RRi), as shown in Figure 3. STI_Haan is determined as the interquartile range of the angles ϕi between the lines connecting the point with origin of the coordinate system, and the X axis, designated for subsequent periods RRi: STI_Haan=IQR(), (13) where: i = 1, 2…N,N – number of beats. Figure 3. Distribution of successive RRi intervals in the polar coordinate system, illustrating the definitions of the de Haan’s index describing the short-term HR variability. 2.2. LSVM Classifier The proposed method for automated recognition of AF episodes is based on a machine learning approach. To achieve high accuracy of AF detection, we applied the classification routine that originates from the Statistical Learning Theory (SLT) [63]. The SLT is the base for the machine learning methods which are characterized by a high generalization ability, meaning the high efficiency when evaluating previously unknown data i.e., data that have not been used when designing the classifier (also called as classifier training or learning). One of the major achievements of SLT is the Structural Risk Minimization (SRM) principle, which states that the quality of machine learning depends both on the empirical data and the complexity of the model. The most-known practical implementation of the SRM is the Support Vector Machine (SVM) methodology [51,64,65]. The SVM allows for finding the hyperplane in the input feature space which divides the considered classes with the widest margin of separation. The input data that are used to define the margin are called the support vectors. The original SVM algorithm was formulated as a linearly constrained quadratic optimization problem. Consequently, the learning procedure of high computational complexity was obtained [66–68]. As the low computational cost of the detection method is of our special interest, in the proposed solution the Lagrangian Support Vector Machine (LSVM) [50] was applied. Its learning replaces the quadratic programming with the linearly convergent iterative algorithm which results in significant reduction of the computational complexity and higher efficiency when compared to the original SVM [50]. Let us consider a training set ℒ, which contains NTRN vectors (1),(2),⋯,()∈ℝ of t parameters quantitatively describing the HR signal, and the corresponding output value (1),(2),⋯,()∈󰇝−1,1󰇞 defining the absence (non-AF) ()=−1 or the presence ()=1 of the AF episode. The linear SVM classification problem of ℒ can be formulated as the constrained minimization: min ℝ × ℝ   (,)= 2+, (14) subject to the condition: (−)+≥, (15) Figure 3. Distribution of successive RR i intervals in the polar coordinate system, illustrating the definitions of the de Haan’s index describing the short-term HR variability. 2.2. LSVM Classifier The proposed method for automated recognition of AF episodes is based on a machine learning approach. To achieve high accuracy of AF detection, we applied the classification routine that originates from the Statistical Learning Theory (SLT) [ 63 ]. The SLT is the base for the machine learning methods which are characterized by a high generalization ability, meaning the high efficiency when evaluating previously unknown data i.e., data that have not been used when designing the classifier (also called as classifier training or learning). One of the major achievements of SLT is the Structural Risk Minimization (SRM) principle, which states that the quality of machine learning depends both on the empirical data and the complexity of the model. The most-known practical implementation of the SRM is the Support Vector Machine (SVM) methodology [ 51 , 64 , 65 ]. The SVM allows for finding the hyperplane in the input feature space which divides the considered classes with the widest margin of separation. The input data that are used to define the margin are called the support vectors. The original SVM algorithm was formulated as a linearly constrained quadratic optimization problem. Consequently, the learning procedure of high computational complexity was obtained [ 66 – 68 ]. As the low computational cost of the detection method is of our special interest, in the proposed solution the Lagrangian Support Vector Machine (LSVM) [ 50 ] was applied. Its learning replaces the quadratic programming with the linearly convergent iterative algorithm which results in significant reduction of the computational complexity and higher efficiency when compared to the original SVM [50]. Sensors 2020,20, 765 8 of 24 Let us consider a training set L , which contains N TRN vectors x0(1) , x0(2) , · · · , x0(NTRN)∈ Rt of tparameters quantitatively describing the HR signal, and the corresponding output value y0(1) , y0(2) , · · · , y0(NTRN)∈{−1, 1} defining the absence (non-AF) y0(n)=− 1 or the presence y0(n)= 1 of the AF episode. The linear SVM classification problem of L can be formulated as the constrained minimization: min RN×RNfSVM(w,ξ)=wTw 2+γ1Tξ, (14) subject to the condition: D(X0w−1w0)+ξ≥1, (15) and: ξ≥0, (16) where w∈Rtand w0∈Rare the parameters of two bounding planes: (xTw−w0= +1, xTw−w0=−1. (17) separating the training data with the margin 2 kwk , γ≥ 0 is a constant that controls the trade-offbetween model simplicity and model matching to the training data, 1∈RN denotes the vector with all entries equal to one, ξ∈RN is the vector of the slack (error) variables, that allow the classes to be bounded with the maximum “soft” margin i.e., with the minimum sum of deviations of training errors and maximum margin for the correctly classified vectors, D=diag(y0(1),y0(2),· · · ,y0(N)) ∈RN×N is a diagonal matrix with class labels along its diagonal, X0="xT 0(1). . .xT 0(2). . .· · · . . .xT 0(N)#T ∈RN×t is the matrix of training input data. In contrast to SVM, the Lagrange support vector machine maximizes the margin between the separating planes with respect to both orientation ( w ) and location of the planes ( w0 ). Moreover, in the LSVM criterion function the sum of the slack variables 1Tξ (14) is replaced with the sum of squares ξTξ making the constraint (16) redundant. Consequently, the linear LSVM is defined as minimization problem of the functional: min Rt×R×RNfpLSVM(w,b,ξ)=1 2wTw+w2 0+γ 2ξTξ, (18) subject to the constraint (17). Moreover, the dual problem of (20): min RN + fdLSVM(λ)=1 2λTQλ−1Tλ, (19) where: Q=I γ+HHT∈RN×N , H=D"X0 . . .−1#∈RN×(t+1) and I∈RN×N is the identity matrix, has the non-negativity constrain only λ∈RN +. The solution can be determined based on the Karush-Kuhn-Tucker necessary and sufficient optimality conditions [ 50 ]. This leads to a linearly convergent iterative scheme which constitutes the LSVM method: λ(k+1)=Q−11+Qλ(k)−1−αλ(k)+, (20) where: kis the iteration index and Qλ(k)−1−αλ(k)+∈RN is the vector with all of its negative components set to zero. Sensors 2020,20, 765 9 of 24 The above algorithm is convergent for any starting point if: 0<α< 2 γ. (21) The parameters of the bounding planes that separate the classes can be recovered from the solution of the dual problem by using the following formulas:            w=X0TDλ, w0=−1TDλ, ξ=λ γ. (22) The LSVM approach reduces significantly the time necessary to perform calculations for the optimal (w,w0)while preserving high classification efficiency of the original SVM learning. The basic LSVM is a linear classifier, thus to handle the non-linearly separable data the so-called “kernel trick” is required. It is based on the premise that the complex non-linear classification problem will be linearly separable in some feature space of higher dimensionality and involves the non-linear transformation of input data in the high-dimensional space. The linear separating plane xTw−w0= 0 is then replaced by the non-linear surface: KxT e,XT 0eDλ=0, (23) where: xe="xT. . .−1#T ,X0e="X0 . . .−1#, and Kis the kernel function. Redefinition of the dual problem (19) by using: Q=I γ+DKX0e,XT 0eD, (24) which makes the LSVM iterative schema (20) valid for any positive semidefinite kernel K [ 50 ]. In the proposed approach we used the radial (Gaussian) kernel: K(x,y)=exp−χkx−yk2, where χ > 0. (25) 2.3. Performance Evaluation The performance (generalization ability) of the AF classification was evaluated by the classification accuracy (CA), defined as the percentage of correctly classified cases in the testing set (data which was not used during classifier training). As the AF detection process is a kind of diagnostic test giving negative or positive results, we also measured the classification quality using sensitivity (Se), specificity (Sp), positive (PPV) and negative (NPV) predictive value, calculated for the testing data set using a confusion matrix. Since evaluation of the classification efficiency is difficult when analyzing all the prognostic measures simultaneously, we calculated also the F-Score (FS), defined as a harmonic mean of Se and PPV: FS [%]=2·Se·PPV Se +PPV. (26) 2.4. Heartbeat Aggregation The aggregation of the classified heartbeats should lead to removal of accidental changes of heartbeat status, and thus to obtain more reliable information on AF episodes. This process is controlled by two parameters: the window width and percentage threshold. Each heartbeat status is validated in symmetrical window by checking if the number of the heartbeats with the same status exceeds the percentage threshold. We defined the percentage threshold for the AF status, as the number of heartbeats classified as AF to the number of all beats in the analyzed window. If the threshold is exceeded the AF status remains unchanged, otherwise is set to non-AF. The optimal values of the Sensors 2020,20, 765 16 of 24 to compare our results with those reported earlier. On this research material the LSVM classifier, fed with sixteen features describing the heart rate variability, ensured the sensitivity 98.10%, specificity 97.50%, positive predictive value 96.67%, classification accuracy 97.75 and F-Score 97.38%. After aggregation stage those performance measures increased to 98.94%, 98.80%, 98.39%, 98.86% and 98.66 respectively. Especially, significant increase of the PPV value was noted a lower number of false AF detections. Obtained performance is higher than that provided by previously developed classification method based on linear classifier, where Se =95.42% and PPV =94.97% [ 53 ]. Thus, the proposed more advanced method has better ability to detect the true occurrences of AF and provides lower number of false arrhythmias. It should be emphasized that both in case of simple linear classifier and advanced LSVM approach the aggregation stage significantly improves the efficiency of AF episodes detection. During this study the HR features have been determined in 21 beats wide window [ 54 ]. Nevertheless, the results obtained so far by the authors are better than those provided by other automated AF detection methods reported earlier, evaluated using the MIT-BIH AF database (Table 6). The most obvious feature to measure the RR irregularity seems to be the difference between successive intervals RR. In [ 33 ] the standard density histogram of RR differences was prepared as a template—using the annotated AF episodes, and then the similarities between the density histograms of the test data and the standard density histogram were estimated using the standard coefficient of variation (CV test) and Kolmogorov-Smirnov (K-S) statistical test. For the optimal threshold of the test output found by ROC, the K-S test showed Se =94.4%, Sp =97.2%, and PPV =96.1%, for the window length of 100 intervals. Detection of AF episodes based on density histogram of RR differences was also developed by Huang et al. [ 74 ]. The proposed more advanced analysis included two steps: AF event detection using the delta RR interval distribution difference curve and AF event classification. Using the ROC curves for determining the threshold of the K-S test, the authors have achieved the higher Se and Sp (96.1% and 98.1%, respectively) for the MIT-BIH AF database. The algorithm described in [ 34 ] has been based on the extraction of simple geometric features determined from the histogram of RR prematurity, computed as the percentage variation from the current heart rate and the differences between two successive RR intervals. The feature set included: number of nonempty bins, main distribution width, difference between mean and median and geometric test of bimodality. The score system was introduced to finally classify ten-second segment as non-AF or AF period. Using the MIT-BIH AF database, the RR prematurity algorithm provided the sensitivity of 91% and PPV of 92%, while for the RR differences Se =92%, and PPV=78%. The map that plots RR intervals versus RR differences was proposed in [ 35 ]. For reference, a window was labeled as true AF episode if 1/2 of intervals in the window were annotated as AF. Threshold value of discriminative parameter—nonempty cell—was determined by ROC, and led to sensitivity 95.8% and specificity 96.4% for the optimal window length of 128 intervals. Another linear transformation of RR intervals to differentiate between AF episodes and normal sinus rhythm was described in [ 44 ]. The proposed algorithm starts with preprocessing (estimating the RR trend and filtering the ectopic beats), then two functions to measure the RR irregularity are calculated, and finally fusion of these signals is used for detection of AF episodes relying on the fixed threshold. Based on the distribution of the fusion signal output for AF and non-AF beats, the optimal detection threshold with identical values of sensitivity and specificity was set. Using the MIT-BIH AF the authors reported very high values of sensitivity (97.1%) and specificity (98.3%). For that approach a very short window of 8 beats was found as optimal. The authors underline that the proposed method can be matched to detect very short episodes, but it is at the expense of lower specificity. The next approach applying only RR interval was based on the variance of normalized RR intervals over ten-second sliding window [ 29 ]. According to the authors, the normalization improves the detection performance. The authors used the morphology independent QRS detector to compute RR intervals and variance, and then they smoothed the resulting classifications, using simple majority voting scheme over 600 beat windows, for further robustness. However, the tests carried out on the MIT-BIH AF database showed that the proposed algorithm has sensitivity of 96% but specificity only of 89%, which is sufficient Sensors 2020,20, 765 17 of 24 for AF screening only. The more advanced normalization of RR intervals by an affine transformation was proposed in [ 30 ]. Interval irregularity was represented by the sparseness of normalized interval probability distribution which was measured by the normalized entropy calculated in the window. The authors used three lengths of the window (30, 50 and 70 beats) to show their influence on the normalization. The ROC analysis enabled them to find the threshold value for the entropy classifier output, that ensured the following values of Se, Sp, PPV and CA: 96.39%, 96.38%, 95.19%, 96.38%. Table 6. An overview of published results of existing AF detection methods using the MIT-BIH Atrial Fibrillation Database. Method Features Window Key Techniques Results Se Sp PPV CA Tateno et al. 2001 [33]RR difference 100 beats Histogram, Kolmogorov-Smirnov test, ROC. 94.4 97.2 96.1 – Huang et al. 2011 [74]RR difference 23 beats Histogram, SD analysis, Kolmogorov-Smirnov test. 96.1 98.1 – – Petrucci et al. 2005 [34] RR difference, RR prematurity 60 s Geometric measures of histogram, Score system. 92 – 92 – Lian et al. 2011 [35] RR interval, RR difference 128 beats Mapping RR intervals versus RR differences, thresholds. 95.8 96.4 – – Petrenas et al. 2015 [44]RR interval 8 beats Thresholds 97.1 98.3 – – Logan et al. 2005 [29]RR interval 600 beats Variance of normalized RR interval, simple majority voting. 96 89 – – Islam et al. 2016 [30]RR interval 70 beats Normalization of RR intervals by an affine transformation. 96.39 96.38 95.19 96.38 Babaeizadeh. et al. 2009 [16] RR interval P-wave measurements -Stationary first-order Markov process, decision tree. 94 99 98 – Zhou et al. 2014 [36]RR interval 127 beats Mapping the RR sequence into symbolic one, Shannon entropy, ROC. 96.89 98.25 97.62 97.67 Zhou et al. 2015 [75]RR interval 127 beats Online version of [36] 97.37 98.44 97.89 97.99 Cui et al. 2017 [37]RR interval 150 beats Mapping the RR sequence into symbolic one, dissimilarity index. 97.04 97.96 – 97.78 Dash et al. 2009 [38]RR difference 128 beats Turning points, RMSSDD, Shannon entropy, ROC. 94.4 95.1 – – Lake et al. 2011 [15]RR difference 12 beats Coefficient of sample entropy (CoSEn), ROC. 91 94 – – Kennedy et al. 2016 [32]RR difference 30 beats Random forest, k-nearest neighbor. 97.6 98.3 92.1 – Andersen et al. 2017 [39] RR interval ECG features 300 beats 30 s Sample entropy, Shannon entropy, CoSEn, SVM. 96.81 94.27 96.20 98.84 –96.45 96.68 Kumar et al. 2018 [76]ECG features 1000 samples Wavelet transform, Random forest. 95.8 97.8 – 96.8 Nuryani et al. 2015 [40]RR difference SVM with radial basis function. 95.81 98.44 – 97.50 Colloca et al. 2013 [41] RR difference Median HR 30 Entropy, SVM with radial basis function 99.20 - 59.33 86.60 Faust et al. 2018 [46]- 100 Deep Recurrent Neural Network (RNN) with Long Short-Term Memory (LSTM). 98.51 98.32 – 98.67 Andersen et al. 2019 [45]- 31 Deep learning combining with the convolutionaland Recurrent-Neural Networks. 98.98 96.95 95.76 97.80 Wrobel et al. 2018 [53] HR irregularity features 21 Linear classifier 95.42 96.12 94.97 95.62 Proposed method 2019 HR irregularity features 21 LSVM 98.94 98.39 98.86 98.66 Sensors 2020,20, 765 18 of 24 The sequence of RR interval is assumed to be controlled by a stationary first-order Markov process characterized by a transition probability matrix as it was proposed for the first time by Moody and Mark [ 4 ] for automated detection of the AF episodes. As Markov score reflects the relative likelihood of RR intervals sequence in AF episode versus no-AF one, it can be compared to the fixed threshold applied to classify the sequences [ 16 ]. In that work the duration statistics with combining all records into one provided the values of Se, Sp, and PPV: 94%, 98% and 97%. Furthermore, a possibility of improvement of the AF episode detection by additional information on ECG morphology was investigated. When the RR interval Markov score was completed with the two P-wave measurements: the location (P-R interval variation) and the morphology (similarity between two consecutive P-waves) the Sp and PPV increased to 99%, while the Se remained unchanged. As the author concluded reduction of the false positive cases is a result of detecting valid P-waves on the ECG recording with irregular rhythm other than AF. Nevertheless, the sensitivity which defines the ability to detect true AF occurrences was significantly lower than the value achieved by our method. In [ 37 ] the changes in RR duration during the sequence have been represented as the binary words, where value of 1 corresponds to increase of interval duration, and 0 means no change or a decrease. Then, the testing segment is classified by comparing its information-based dissimilarity index with those obtained for the templates of AF episode and normal sinus rhythm. Parameters of the classification model: the number of bits, window length and the shift for the dissimilarity comparison boundary were optimized to provide the best performance expressed by sensitivity of 97.04%, specificity of 97.96% and classification accuracy of 97.78%. Another approach based on mapping the RR sequence into symbolic one was proposed in [ 36 ]. The detection proceeds in three stages: the initial, where a RR interval sequence is pre-processed with nonlinear and integer filters, the second, where the information of the RR interval changes is converted into symbolic sequence, and final, where the Shannon entropy is calculated to discriminate whether or not the sequence relates to AF episode. Optimal discrimination threshold of Shannon Entropy was obtained by ROC analysis. The RR sequences of 127 beats were processed. The following value of Se, Sp, PPV and CA were: 96.89% 98.25% 97.62% 97.67%, while for the online version of the algorithm: 97.37%, 98.44%, 97.89% and 97.99% [75]. The entropy concept, referring to the disorder or uncertainty of a process, was used in many methods for automated detection of AF episodes, usually being included in the feature set, but also as the only measure of RR irregularity. Three statistics describing randomness, variability and complexity of the RR interval time series were proposed in [ 38 ]. The turning points ratio, root mean square of successive RR differences and Shannon entropy were employed to characterize the atrial fibrillation. Using the thresholds and data segment of 128 beats determined by ROC the sensitivity of 94.4% and specificity of 95.1% were achieved for the signals from the MIT-BIH Atrial Fibrillation Database. The optimized sample entropy measure, called coefficient of sample entropy (CoSEn), being able to detect very short AF episodes (even 12 beats) was proposed by Lake and Moorman [ 15 ]. This feature estimated the probability that short templates will match with other segments within the analyzed RR interval time series. That process was controlled by two parameters: the template length and the tolerance matching, whose optimal values were established by ROC analysis. The authors found the cutoffCoSEn value, which differentiate between AF and normal sinus rhythms, to provide a sensitivity of 91% and a specificity of 94%. In [ 32 ] the CoSEn was combined with three other features: the coefficient of variance, root mean square of the successive differences, and median absolute deviation. The detection performance of each irregularity measure was assessed individually by ROC analysis, and CoSEn performed best. The above parameters were also used as the input features set for two classifiers: random forest (RF) and k-nearest neighbor. Both classification models significantly improved the Sp and PPV values over CoSEn, but with substantial drop in Se. The best specificity of 98.3% and PPV of 92.1% were provided by RF model, while the sensitivity achieved the best value 97.6% when using CoSEn as the only discriminative feature. Those results were reported for the combined database, with MIT-BIH AF among others. When only MIT-BIH AF database was employed, Sensors 2020,20, 765 19 of 24 the authors noticed significant reduction of detection performance for CoSEn and median absolute deviation, expressed by smaller area under the ROC curve. Three entropy features: sample entropy, coefficient of sample entropy, Shannon entropy, together with two linear measures: root mean square and normalized root mean square of successive differences constituted the set of RR irregularity measures being tested in [ 39 ]. Apart from that HR approach, the authors investigated the ECG-driven approach with two features: peak-to-average power ratio and log-energy entropy, extracted from 2-level stationary wavelet transform coefficients. The support vector machine was used for classification in both approaches. Three different segment lengths were evaluated: 60, 100, 300 beats for HR and 10, 15, 30 s for ECG data. Like in [ 35 ], any segment containing at least of 50% AF beats was labeled as true AF when processing ECG. For HR approach this level was reduced to 30%. The longest windows provided the best results for both HR (Se 96.81%, Sp 96.20%, CA 96.45%) and ECG (94.27%, 98.84%, 96.98%, respectively) approaches. The performance of AF detection using the features extracted exclusively from ECG signals was assessed by Kumar [ 76 ]. As the data was taken from MIT-BIH database, the obtained results may be related to those provided by the HR-based methods described here. The proposed classification method employed two features: the log-energy entropy and permutation entropy computed from the sub-band signals obtained using flexible analytic wavelet transform. Using random forest classifier, the authors reported sensitivity of 95.8%, specificity of 97.8% and accuracy of 96.8%. Two features: the average of RR differences in a defined duration, and the standard deviation of differences in a defined duration, were examined as the inputs of the classifier based on SVM with radial basis function in [ 40 ]. The proposed method showed following performance on the MIT-BIH AF database: Se =95.81%, Sp =98.44% and CA =97.50%. The same SVM classifier was employed in [ 41 ]. The input set comprised more RR interval features: median heart rate, minimum RR interval, mean RR interval, various entropy measures, and difference irregularity measure. The MIT-BIH AF database was used in that study, but only during the training stage, when very good results have been achieved (sensitivity =99.07%, PPV =98.27%, accuracy =98.84). When testing on a series of 200 signals from the MIT-BIH Arrhythmia database, the best accuracy was 86.60% for the window of 30 beats, sensitivity reached 99.20%, but PPV was only 59.33%. The newest approach to automated AF detection proposed in [ 46 ] and [ 45 ] has been based on deep learning algorithm, which aims to develop the classification model by using all available information from the input. In case of AF detection from the ECG signals it means no need for extraction of the feature neither from raw ECG nor from RR interval time series. In those works the RR data from MIT-BIH AF were partitioned using sliding window of 100 beats [ 46 ] or 31 beats but shifted with 10 beats [ 45 ], and then fed to Recurrent Neural Network with Long Short-Term Memory. In both works very good results were reported: Se =98.51%, Sp =98.32%, CA =98.67% in [ 46 ], and 98.98%, 96.95%, 97.80% with PPV of 95.76% in [ 45 ], when median filtering was used as post processing to improve the detection performance. It should be noted, however that development of the deep learning algorithm has been enabled by recent advances in parallel computing on Graphics Processing Units. The computational complexity of deep learning model is much higher than traditional feature-based classifier. This limits its application in wearable devices for long term monitoring with online AF detection, like wristband monitor in a form of wrist bracelet. 5. Conclusions Despite serious medical consequences, atrial fibrillation is still an underestimated clinical and diagnostic problem. Recognition of this form of arrhythmia requires a long-term monitoring of the heart rhythm, since very often patients are asymptomatic. Moreover, the AF episodes can occur accidentally and may last from minutes to hours. The objectivity and efficiency of the visual analysis of long-term recordings can be improved by automated AF detection. The paper proposed a LSVM-based approach with an original training stage which outperforms other automated AF detection methods based on the information on beat-to-beat irregularity proposed Sensors 2020,20, 765 20 of 24 in the literature. Our method ensures a very high efficiency in detection of true AF episodes expressed by sensitivity of 98.94%, and at the same time low number of false episodes, as the positive predictive value reached 98.36%. These results were achieved with post-processing aggregation stage, showing a need for final verification of the classified beats. It also turned out that extending the input feature vector to include parameters describing the heart irregularity and being typically used in the fetal heart rate analysis, had positive effect on classification efficiency. Designing the LSVM-based classifier to deal with such large amount of data like from MIT-BIH AF Database led us to valuable conclusion. Not the size of the training set is of crucial importance, but the occurrence of the input vectors containing the quantitative parameters of HR variability description which allow separating the AF and non-AF heartbeats with the widest separation margin (support vectors), thus guaranteeing the best classification quality. Author Contributions: Conceptualization, R.C, K.H. and J.W.; Data curation, A.M., R.M and R.K.; Methodology, R.M., T.K., R.K. and J.J.; Software, R.C., J.W. and A.M.; Supervision, K.H. and R.C.; Validation, J.W., T.K., M.J. and J.M.L.; Writing-original draft, K.H. and R.C.; Writing-review & editing, K.H., M.J., J.J. and J.M.L. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: This scientific research work was supported by the National Science Centre and the National Centre for Research and Development in Poland under the grants 2017/27/B/ST6/01989 and STRATEGMED2/269343/18/NCBR/2016, as well as from the Ministry of Science and Higher Education funding for statutory activities (BK-2019, BK-2020). Conflicts of Interest: The authors declare no conflict of interest. References 1. Lau, J.K.; Lowres, N.; Neubeck, L.; Brieger, D.B.; Sy, R.W.; Galloway, C.D.; Albert, D.E.; Freedman, S.B. iPhone ECG application for community screening to detect silent atrial fibrillation: A novel technology to prevent stroke. Int. J. Cardiol. 2013,165, 193–194. [CrossRef] 2. Grond, M.; Jauss, M.; Hamann, G.; Stark, E.; Veltkamp, R.; Nabavi, D.; Horn, M.; Weimar, C.; Köhrmann, M.; Wachter, R.; et al. Improved Detection of Silent Atrial Fibrillation Using 72-Hour Holter ECG in Patients With Ischemic Stroke: A Prospective Multicenter Cohort Study. 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