ECG Arrhythmia Classification Using Vague C-Means Clustering Based on Multiresolution Analysis

2.1 Dataset description

The data set used for experimental studies containing normal sinus rhythm and eleven arrhythmia types was collected from the MIT-BIH ECG Arrhythmia Database [9]. This database includes 48 records taken from 47 subjects (25 men and 22 women). Each record is of two channels which is sampled at 360 Hz and its duration is 30 minutes. The following rhythm types were selected into account in investigations: Normal sinus rhythm (NSR), sinus bradycardia (SB), ventricular tachycardia (VT), sinus arrhythmia (SA), atrial premature contraction (APC), paced beat (PB), right bundle branch block (RBB), left bundle branch block (LBB), atrial fibrillation (AFib) atrial flutter (AFlut), atrial couplet (ACoup) and ventricular trigeminy (VTrig). The morphologies of RR intervals of twelve rhythm types are shown in Figure 1. Some rhythm types have similar frequencies and amplitude ranges, it is difficult to differentiate one from the other. Firstly, the desired rhythm was obtained by subtracting the specified time interval (Table 1) from the nine patient’s relevant records. Patterns were created by extracting RR intervals from obtained signal fragments. Ahlstrom and Tompkins algorithm [10, 11], which is the first derivative-based algorithm, is used to determine R peaks. Each RR intervals were arranged as 200 samples by resampling.

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Figure 1. The morphologies of ECG signals used (a) NSR, (b) SB, (c) VT, (d) SA, (e) APC, (f) PB, (g) RBB, (h) LBB, (i) AFib, (j) AFlut, (k) ACoup, (l) Vtrig

2.2 Preprocessing

As it is known, the ECG signal is periodic so it can be divided into periods. The process of dividing ECG signals into periods is called QRS detection. Before QRS detection, the ECG signal should be filtered to eliminate noises on the signal. For this aim, a high pass filter which has is 0,09 Hz corner frequency and a low pass filter which has a 30 Hz corner frequency are used. Signals that have been filtered and noise eliminated are used in QRS detection. It can be divided into RR intervals with the algorithm. There are many QRS detection methods in the literature. When these algorithms are examined in general, they can be grouped under three main classes [11]. First-class QRS detection algorithms are based on statistical methods [11]. Second-class QRS detection algorithms are based on examinations in the time and frequency spectrum such as Hilbert transform, and wavelet transform [12, 13]. Third-class QRS detection algorithms consist of artificial intelligence systems such as artificial neural networks and fuzzy logic, which have been widely used in recent years [8, 14]. In this study, a statistical method based on first and second-order derivatives improved by Ahlstrom and Tompkins algorithm [11] is utilized.

Each extracted RR interval is called a pattern, so a data set that includes 318 patterns is formed in this study (Table 1) [9, 15].

Table 1. ECG signals taken from MIT-BIH arrhythmia database [9, 15]

*NP: Number of patterns

2.3 Vague c-means clustering

The most widely used clustering algorithm is fuzzy c-means (FCM) clustering. This algorithm, which was introduced by Dunn and later extended by Bezdek, is an iterative clustering technique. It divided data into “c” fuzzy partitions which provide the smallest objective function.  In the algorithm, Let’s assume that be an array $S=\left\{ {{s}_{1}},~{{s}_{2}},\ldots ,{{s}_{n}} \right\}~$with n data points. Each data point is d dimensional feature vector. This data can be separated into clusters (c, 1<c<n) and each pattern has a membership value for each cluster. The membership function is adopted as follows [1-5]:

${{u}_{ij}}=1/\underset{k=1}{\overset{c}{\mathop \sum }}\,{{\left( {{s}_{j}}-{{v}_{i}}/{{s}_{j}}-{{v}_{k}} \right)}^{2/\left( m-1 \right)}}$                (1)

In Eq. (1), $v$ is cluster centers and $m$ is the fuzzifier coefficient. Cluster centers in the FCM clustering algorithm are calculated as in Eq. (2).

${{v}_{i}}=\underset{j=1}{\overset{n}{\mathop \sum }}\,u_{ij}^{m}{{s}_{j}}/\underset{j=1}{\overset{n}{\mathop \sum }}\,u_{ij}^{m}$                 (2)

In the beginning, each cluster center is started randomly, iteration is continued to reach the local minimum for the objective function. The objective function is calculated as in Eq. (3).

${{J}_{FCM}}=\underset{i=1}{\overset{c}{\mathop \sum }}\,\underset{j=1}{\overset{n}{\mathop \sum }}\,u_{ij}^{m}{{\left( {{s}_{j}}-{{v}_{i}} \right)}^{2}}$                   (3)

In the vague c-means (VCM) clustering algorithm [16], which was introduced by Xu etc., the membership function is redefined as follows, unlike Eq. (1) above, as truth membership function (${{t}_{ij}}$) and false membership function (${{f}_{ij}}$). $\beta$ is a positive constant.

${{t}_{ij}}={{s}_{j}}-{{v}_{i}}^{-\beta }/\underset{k=1}{\overset{c}{\mathop \sum }}\,{{s}_{j}}-{{v}_{k}}^{-\beta }$                   (4)

${{f}_{ij}}={{s}_{j}}-{{v}_{i}}^{\beta }/\underset{k=1}{\overset{c}{\mathop \sum }}\,{{s}_{j}}-{{v}_{k}}^{\beta }$                           (5)

In VCM (Figure 2), for the calculation of cluster centers (${{v}_{i}}$), Eq. (2) is utilized like FCM. But the membership function is defined as ${{u}_{ij}}={{t}_{ij}}$. The definition of the objective function in the VCM clustering algorithm is given as in Eq. (6) [16]. $\lambda$ is a balancing factor here.

${{J}_{VCM}}=\underset{i=1}{\overset{c}{\mathop \sum }}\,\underset{j=1}{\overset{n}{\mathop \sum }}\,t_{ij}^{m}{{s}_{j}}-{{v}_{i}}^{2}+\lambda \underset{j=1}{\overset{n}{\mathop \sum }}\,\left( 1/max\left( 1-{{f}_{ij}} \right) \right)$                     (6)

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Figure 2. Flowchart of vague c-means clustering [16, 17]

Since the used data set contains multi-labeled RR intervals extracted from the ECG signal, the classification models must produce a decision sequence that separately shows which classes the test data set contains.

These decision sequences on multi-labeled classification tasks represent functional confusion matrices which include TP, FP, TN, and FN values, and analyze how a classification model can recognize patterns of different classes. So, TP, FP, TN, and FN are the most valuable indicators in evaluating the success of classification models. It can be seen from Table 2 that the best classification model in the classification of the 12-class ECG data set is DWT1-VCM. Confusion matrices found with DWT1-VCM were presented for each arrhythmia type in Figure 8. It can be seen in Figure 8 that RR intervals that belong to NSR, SB, PB, RBB, LBB, AFlut, and ACoup ECG signal types could be detected with 100% accuracy by using the DWT1-VCM model. The percentage of average true negatives for all ECG signal types was determined to be 80%. Against this, patterns of VT signal type could not be collected under a single cluster with DWT1-VCM.

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Figure 8. Class-dependent confusion matrices for the best classifier model DWT1-VCM

VT patterns were classified into clusters containing RBB, LBB, and ACoup signal types. But, as can be seen in Table 2, VCM, and DWT2-VCM models could classify 2 of these VT patterns into the same class. This arrhythmia type has quite different signal morphologies in the data set, so classification models had difficulty in collecting all VT patterns in the same class. There is the same circumstance in classifying VTrig patterns. DWT1-VCM model could be classified with 33.3% accuracy. In VCM, FCM, and DWT2-VCM, classification accuracy is about the same for VTrig patterns. Although 100% classification accuracies could not be achieved in SA and AFib, these signal types could be classified with high accuracies of 93.33% and 86.67% using the DWT1-VCM classifier. The false negative rate in the results of the DWT1-VCM model was found as 12,5%. This value can be interpreted as the classifier assigning 12.5% of data from different classes to a cluster consisting of data from the same class. These false negative and false positive rates are the limitations of vague c-means clustering in ECG classification. Furthermore, the significance test was applied to the results of DWT1-VCM. In significance testing, h=0 was obtained. The returned value of h = 0 represents that ttest2 does not reject the null hypothesis at the default 5% significance level.

In addition to these experiments, another experiment was conducted with some 30 min-long records of ECG signal. In this experiment, it is tried to define ECG signal classes on recordings #100, 103, 113, 107, and 109 using trained DWT1-VCM. The results are presented in Table 3. Recording #100 contains 2273 beats and three signal classes: 2239 NSR beats, 33 APC beats, and 1 Premature Ventricular Contraction beat. DWT1-VCM, which is the best classification model in this study, could detect 2211 NSR beats. APC beats could not be classified. For NSR beats, sensitivity can be found as 98.75%. In record number 103, which contains 2082 NSR beats, 2036 of them could be detected correctly with DWT1-VCM. Additionally, two APC beats were detected here in the recording. Sensitivity is 100% for APC and 97.8% for NSR. Recordings #113 also contains predominantly NSR signal class. 1789 of 1795 beats belong to the NSR signal class. All 6 of them are APC. When this recording was classified with DWT1-VCM, 1744 of 1789 NSR beats could be detected. However, only 1 out of 6 APC beats could be classified. The sensitivity value for NSR was found to be 97.5%. Likewise, 1820 of the 2078 PB in recording #107 were found correctly with DWT1-VCM. In this recording, where PB is concentrated, a sensitivity value of 87.6% was reached in PB detection. Recording #109 was also tested with the trained DWT1-VCM because of contained a different ECG signal class. Looking at the classification results of this record containing 2492 LB beats, it can be seen that 2412 of them were classified correctly with DWT1-VCM. In this case, it can be said that the sensitivity is 96.8% in the classification of LB beats. Additionally, the experimental results presented in Table 3, are an indication of success for the vague c-means clustering algorithm proposed for ECG classification in this study in classifying different rhythm types on a patient record in the clinic.