
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)13142-8
10.1016/j.heliyon.2024.e37111
e37111
Research Article
ECG arrhythmia classification based on the fast ant colony clustering algorithm with improved spatiotemporal feature perception ability
Qin Shuguang sunnyqin3@gmail.com
a
Liu Linyue liulinyue@st.xatu.edu.cn
b∗
Wang Xinhong wangxinhongshx@163.com
a
Dong Ning 544715298@qq.com
c
Li Ning lining83@xaut.edu.cn
d∗∗
Zheng Qiangsun zhengqiangsun@126.com
a∗∗∗
a Department of Cardiology, The Second Affiliated Hospital of Xi'an Jiaotong University, Xi'an, 710004, China
b School of Computer Science and Engineering, Xi'an Technological University, Xi'an, 710021, China
c Department of General Surgery, The Second Affiliated Hospital of Xi'an Jiaotong University, Xi'an, 710004, China
d School of Electrical Engineering, Xi'an University of Technology, Xi'an, 710048, China
∗ Corresponding author. liulinyue@st.xatu.edu.cn
∗∗ Corresponding author. lining83@xaut.edu.cn
∗∗∗ Corresponding author. zhengqiangsun@126.com
28 8 2024
15 9 2024
28 8 2024
10 17 e371118 2 2024
23 8 2024
27 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Electrocardiograph (ECG) is one of the most critical physiological signals used for arrhythmia diagnosis. In recent years, ECG arrhythmia classification devices consisting of multi-module sensors, clustering algorithms and neural networks play an important role in monitoring and diagnosing cardiovascular diseases. However, the commonly used ECG arrhythmia classification methods are still facing some problems such as the complex model structure and long running time. To address the above problems, this paper proposes an ECG arrhythmia classification method based on the fast ant colony clustering algorithm with improved spatiotemporal feature perception ability (SFP-FACC), which uses LSTM to fit the cluster centers and avoids the time consumption of updating the cluster centers during the classification process. The spatiotemporal feature perception ability of this model with the dynamic time warping (DTW) algorithm is improved. The classification is achieved by applying the combination of Euclidean distance and DTW. The convergence speed of the model is improved by using dynamic pheromone volatility coefficient; and finally the optimal solution of the model is determined by using radix sort. Based on the MIT-BIH arrhythmia dataset, the overall accuracy of the proposed classification method in this paper achieves 99.04 %, and even the accuracy of certain types of classification achieves 100 %, and the running time is about 3.5 times faster than that of the basic models. The experiments show that the method proposed in this paper has certain advantages.

Highlights

• The LSTM is used to fit the cluster centers to reduce the time consumed by the model in updating the cluster centers during the classification process.

• The DTW algorithm is introduced to enhance the ability of the model to perceive spatiotemporal features and achieve classification by combining the Euclidean distance method.

• A mathematical model for dynamically updating the pheromone volatility coefficient is proposed to improve the model convergence speed.

Keywords

ECG arrhythmia classification
The ant colony clustering algorithm
Dynamic time warping
LSTM
Dynamic pheromone volatility coefficient
Radix sort
==== Body
pmc1 Introduction

Heart diseases, particularly those affecting the cardiovascular diseases (CVDs), are a prevalent source of mortality in the contemporary world. Arrhythmias, as a subset of CVDs, pose a serious health risk [[1], [2], [3]], with chronic conditions potentially being fatal. These irregular heartbeats are categorized into several forms, including Left Bundle Branch Block (LBBB), Atrial Premature Beats (APB), and Premature Ventricular Contractions (PVC), each reflecting varying levels of clinical severity. Atrial fibrillation (AF), for instance, stems from chaotic atrial activity and substantially raises the likelihood of experiencing a stroke or developing coronary artery disease [4,5]. Prolonged PVC may progress to more severe conditions such as ventricular tachycardia (VT) or ventricular fibrillation (VF), both of which can culminate in cardiac failure.

Different types of arrhythmias correspond to different types of ECGs, so obtaining a real-time ECG of a patient helps to quickly determine the criticality of the patient. Clinically, doctors observe the presence of arrhythmias based on the main ECG features, such as P waves, QRS complex, and T waves, etc., and then determine the type of arrhythmias. ECG-based arrhythmia classification can effectively improve the doctors’ efficiency and assist them in diagnosis. Therefore, the classification algorithms based on ECG arrhythmias have important research significance [[6], [7], [8]].

With the development of the machine learning, ECG arrhythmia classification algorithm based on the machine learning has become a hot topic in current research [9,10]. The algorithms based on the machine learning achieved ECG arrhythmia classification by extracting and analyzing medical features, statistical features and data morphology of ECGs. Machine learning algorithms for ECG arrhythmia classification can be divided into three categories: clustering algorithms and their optimization methods [11,12], convolutional neural network and its optimization methods [13,14] and recursive neural network and its optimization methods [15,16].

Traditional clustering algorithms are known for their rapid execution, which translates to efficient timing for ECG arrhythmia classification. Márquez et al. [6] proposed a clustering algorithm (PN-EAC) suitable for ECG data from multi-sensors based on the ensemble clustering paradigm and negative evidence. The concept of negative evidence is introduced, which permits exploiting information about those elements that should not be grouped together. With a classification accuracy of 98.56 % under the MIT-BIH arrhythmia dataset, this concept improved clustering accuracy by using information that should not be combined and usually discarded by traditional integrated clustering methods. Roopa et al. [17] extracted features by principal component analysis (PCA), linear discriminant analysis (LDA), and regularized locality preserving indexing (RLPI), and applied the robust spatial kernel FCM (RSKFCM) to the UCI arrhythmia dataset to validate the efficacy of the method. Swetha et al. [18] introduced the K-means clustering optimization fuzzy logic control algorithm (KC-FLC) for the detection of various arrhythmias within ECG signals. By selecting features such as heart rate (HR), mean average value (MAV) heart rate variability (HRV), and peak-to-peak amplitude to achieve 91.5 % based on the MIT-BIH arrhythmia dataset. Haldar et al. [19] used Mahalanobis distance (MD) to improve the fuzzy C-means clustering method (MD-based improved Fuzzy C-Means, FCM-M). The experimental results showed that FCM-M is effective in arrhythmia classification and the performance is better than that of traditional FCM.

In recent years, the introduction of convolutional neural network (CNN) has offered a novel research direction for ECG arrhythmia classification. CNN are greatly valued for their ability to automatically recognize and learn from intricate patterns within ECG signals. Huang et al. [20] introduced a two-dimensional deep convolutional neural network (2D-CNN) tailored for the classification of ECG arrhythmias. This model was designed to analyze the MIT-BIH arrhythmia dataset, aiming to accurately classify 5 heartbeat types. The 2D-CNN demonstrated a remarkable achievement, reaching a 99 % accuracy in the classification process when operating with a batch size of 2500. Mathunjwa et al. [21] proposed a method for arrhythmia classification using 2D recursive map images of ECG signals and two-stage deep learning, and verified the effectiveness of the method with three datasets by CNN. Xy et al. [22] developed a method for ECG arrhythmia classification. The method combines cascaded convolutional neural network (CCNN) and expert features. Firstly, 1D-CNN is used to extract features from ECG signals, and then these features are fed into ResNet through cascading, and then combined with expert features. A random forest algorithm is used to provide reliable probability estimates for various arrhythmia types. The recognition accuracy of this method reaches 86.5 %. Che et al. [23] integrated Transformer network in CNN to improve the ability of the model to enhance the model's capability of capturing the intricate patterns present in ECG signals. And the authors introduced feature-related link constraint in the loss function to achieve a final classification accuracy of about 85 %. Atal et al. [24] optimized deep CNN by multi-objective bat algorithm (MOBA) and rider optimization algorithm (ROA), and its classifier identified ECG signals as arrhythmias and non-arrhythmias.

Recurrent Neural Network (RNN) are recognized for their proficiency in discerning temporal patterns, a capability that surpasses their ability to identify spatial relationships. This attribute renders RNN particularly adept at analyzing ECG signals, which are intrinsically rich in temporal features. Singh et al. [25] implemented the separation of regular and irregular beats of ECG signals and validated the effectiveness of LSTM with the MIT-BIH arrhythmia dataset. Essa et al. [26] presented two different deep learning bagging models. The first model, termed CNN-LSTM, was designed to capture both the local features and the temporal dynamics within ECG data. The second model, known as RRHOS-LSTM, focused on incorporating classical features such as RR intervals and higher-order statistics (HOS) into the analysis. By amalgamating the predictions of these two models through a meta-classifier, the researchers achieved a remarkable overall accuracy of 95.81 % when evaluated on the MIT-BIH arrhythmia dataset. Hou et al. [27] developed a hybrid approach for the classification of ECG arrhythmias, which integrated an autoencoder (AE) network based on LSTM with a support vector machine (SVM) classifier. This method was employed to classify five distinct heartbeat types, including normal and LBBB, etc. The efficacy of this approach was tested through MIT-BIH arrhythmia dataset. Zisou et al. [28] introduced an integrated classifier designed to discern various types of cardiac abnormalities. This classifier is a composite model, integrating a constant current neural network and a LightGBM algorithm with a fixed weight. The empirical outcomes of this integrated classifier demonstrated superior performance when compared to the two separate models.

In summary, although these research methods have achieved good research results, there still exist some problems. In practice, the diagnostic accuracy of ECG arrhythmias is required to be extremely high, while the classification accuracy of early clustering algorithms is low. CNN are adept at capturing spatial features within ECG signals, while RNN excel at extracting temporal aspects. Leveraging the strengths of these two methods, they contribute significantly to enhancing the classification accuracy. However, the basic model structure of both methods and the combined model structure of both methods are complex, which affects the speed of classification and lacks advantages in terms of timeliness. Furthermore, neural network-driven models demand substantial datasets for training. To achieve high precision, these models necessitate extensive data and undergo numerous iterative training processes. Consequently, clustering algorithms that are founded on streamlined structures, limited data sizes, and a small number of iterations can retain significant benefits when their capacity for perceiving spatiotemporal features is augmented through refinement techniques.

Considering the above problems and analysis, this paper proposes an ECG arrhythmia classification based on the fast ant colony clustering algorithm with improved spatiotemporal feature perception ability. This method extracts a total of 37 spatial and temporal features from preprocessed ECG signals, and then uses LSTM to fit the cluster centers. The ECG arrhythmia classification is realized by combining Euclidean distance and Dynamic Time Warping (DTW) algorithm, and the dynamic pheromone volatilization coefficient is used to improve the convergence speed of the model. Finally, the radix sort is used to give the optimal solution.

The main contributions of this paper are summarized as follows: (1) The LSTM is employed to determine the cluster centers, which minimizes the duration the model spends on center updates during the classification process; (2) The DTW algorithm is implemented to bolster the model's capacity for detecting spatiotemporal features, facilitating classification. This is achieved by integrating it with the Euclidean distance method. Additionally, the model's classification accuracy is enhanced through the incorporation of radix sort; (3) A mathematical model for dynamically updating the pheromone volatility coefficient is proposed for the characteristics of the pheromone concentration to improve the model convergence speed.

The rest of the paper is organized as follows: Section 2 describes the dataset, the core elements of data preprocessing, feature extraction and the improved ant colony clustering algorithm. Section 3 illustrates the experimental results. Section 4 illustrates the experimental analysis and then compares the proposed method with other methods. Section 5 presents the limitations. Section 6 presents the conclusion and provides forward-looking perspectives.

2 Methodology

The ECG arrhythmia classification method proposed in this paper first preprocesses the raw data by denoising and segmentating, and selects n data as the dataset. The randomly selects n1 data as the fitting dataset for fitting the cluster centers. The randomly selects n2 data as the training dataset to determine the model parameters. The randomly selects n3 as the test dataset for testing the model performance. And n1+n2+n3≤n,n1∩n2∩n3=∅. A total of 37 features are extracted from the preprocessed ECG signals, and ECG arrhythmia classification is achieved by combining Euclidean distance and DTW algorithms in the classification process, and the pheromone is updated using dynamic pheromone volatility coefficients, and the optimal solution is finally obtained based on the radix sort. The flow chart of the proposed classification method is shown in Fig. 1. The implementation process of the classification method proposed in this paper is shown below.ECG arrhythmia classification based on the fast ant colony clustering algorithm with improved spatiotemporal feature perception ability	
1.	Data preprocessing:	
2.	 The high-frequency noise and baseline drift from raw data were removed by 6-layer wavelet transform	
3.	 Determination of fiducial features of QRS complex, P-wave and T-wave (medical features)	
4.	 Dividing raw data into single cycle ECG signals	
5.	 Selecting a total of 400 data in N, 300 data in L, 200 data in R, 200 data in A, and 300 data in V as dataset. Randomly selecting 10 data from 5 types as fitting dataset. Randomly selecting 50 data from 5 types as training dataset for determining the model parameters. Randomly selecting a total of 110 data in N, 110 data in L, 110 data in R, 80 data in A, 56 data in V as testing dataset	
6.	Fitting cluster centers based on LSTM model:	
7.	 Fitting 5 cluster centers through the LSTM model	
8.	Feature extraction：	
9.	 Extracting 36 spatial features from cluster centers and test data, including 16 medical features and 20 mathematical features. And extracting temporal features, DTW values	
10.	Improved Ant Colony Clustering Algorithm:	
11.	 Arrhythmia classification based on Euclidean distance and DTW	
12.	 Dynamically update pheromone volatilization coefficient, update pheromone	
13.	 Determining the optimal solution based on radix sort	
14.	Giving results such as accuracy and comparing with other models	

Fig. 1 The flow chart of the proposed classification method in this paper.

Fig. 1

2.1 Dataset

The MIT-BIH arrhythmia dataset [29] contains 48 half-hourly two-channel dynamic ECG records, which are digitized at a rate of 360 samples per second per channel (sampling rate) in the 10 mV range at 11-bit resolution. In the majority of ECG recordings, one channel typically employs a modified limb lead II (MLII), which is acquired by positioning electrodes on the chest. The other channel often corresponds to lead V1, although it may alternatively be leads V2, V4, or V5, depending on subject considerations. During digitization, analog records are played on a Del Mar Avionics Model 660 device. An initial set of beat annotations is established utilizing a simple slope-sensitive QRS detector, thereby ascribing a 'normal' designation to each identified cardiac event. Subsequent to this preliminary labeling, omissions and inaccuracies within the annotations are addressed by two credentialed cardiologists, who review and augment the dataset with additional labels. They also added tempo labels, signal quality labels and annotations. In this paper, 1 min duration ECG signal recordings from each subject were procured for experimental analysis, and subsequent to processing, the data were identified. The description of the 5 categories of heart rhythms are shown in Table 1, and their morphology is shown in Fig. 2.Table 1 Type description.

Table 1Symbol	Type	Description	
N	Normal Beat		
L	Left Bundle Branch Block Beat	Left Bundle Branch Block (LBBB) is diagnosed by the distinct QRS morphology at leads I, aVL, V1, V2, V5, and V6	
R	Right Bundle Branch Block Beat	Right Bundle Branch Block (RBBB) is diagnosed by the rsR′ pattern at V1 and V2	
A	Atrial Premature Beat	Abnormal heartbeat suddenly after normal heartbeat during Atrial Premature beat, pre-emerging P waves and QRS waves	
V	Premature Ventricular Contraction	The Premature Ventricular Contraction (PVC) indicate the electrical impulse from an abnormal site; specifically, the P wave or QRS morphology of PVC differs from that in normal heart beats	

Fig. 2 The morphology of 5 types of cardiac rhythms.

Fig. 2

2.2 Data preprocessing

In the paper, a 6-layer wavelet transform [[30], [31], [32]] was implemented as a preprocessing step for ECG signal analysis. This method effectively removes high-frequency noise and baseline drift. The wavelet transform process involves decomposing the ECG signals into a series of low-frequency and high-frequency components through successive filtering and downsampling steps. The reconstruction process essentially reverses the decomposition, combining the retained frequency components to recreate a signal that is as close as possible to the original ECG recording, but with the added benefit of reduced noise and improved signal quality for further analysis. The ECG signals were downsampled through a low-frequency filter to obtain the approximate coefficients. The purpose of the high-frequency filter is to ensure that the signal is anti-aliasing. After the high-frequency filtering, the ECG signal is then downsampled. The detailed coefficients obtained from this process represent the high-frequency variations in the original signal. The wavelet transform equations are as follows:(1) cAj+1(n)=∑mcAj(m)h(m−2n)

(2) cDj+1(n)=∑mcAj(m)g(m−2n)

The reconstruction equation is as follows:(3) cAj(n)=∑mcAj+1(m)h(n−2m)+cDj+1(m)g(n−2m)

In this paper, the analysis of ECG signals involved the classification of key waveforms, which are critical for the diagnosis of cardiac conditions. The methodology included the following steps [[33], [34], [35], [36]]: (1) The positive and negative peak values within the ECG signal were computed. These peak values correspond to the highest and lowest points in the signal waveform, which typically represent the voltage changes across the heart during a cardiac cycle; (2) By analyzing the calculated maximum values, the peaks and valleys of the ECG waveform were identified. Peaks usually correspond to the R-waves in the QRS complex, which are the most prominent features of the ECG signal and indicate ventricular depolarization. Valleys might represent the S-waves or the T-waves, which follow the R-waves and are part of the repolarization process; (3) Specific threshold values were set to detect the QRS complex, P-wave, and T-wave; (4) In cases where additional R-waves were detected in error, conversely, if an R-wave was missed, it was manually removed or inserted for to maintain the integrity of the ECG signal.

The test data were segmented into single cycles based on R waves. totally with 400 N, 300 L, 200 R, 200 A, and 300 V. 10 data of each type were selected, a total of 50 ECG signals as the fitting dataset. 50 data of each type were selected, a total of 250 ECG signals as the training dataset. A total of 110 N, 110 L, 110 R, 80 A, 56 V, and 466 ECG signals were selected as the testing dataset. The fitting dataset, training dataset and testing dataset do not overlap each other to avoid the problem of false high classification accuracy.

2.3 Selection of spatiotemporal features of ECG signals

In this paper, the analysis of ECG signals involves the extraction and examination of both spatial and temporal features, which are crucial for the accurate diagnosis of ECG arrhythmias. The spatial features include medical features and statistical features. Among the medical features, the amplitude of the R wave can provide insights into the condition of the ventricles; an abnormal QRS duration may indicate conditions such as bundle branch block or ventricular hypertrophy; abnormalities in the P wave can suggest atrial disorders like atrial fibrillation or flutter; a prolonged or shortened PR interval can indicate conduction abnormalities. Statistical features are derived from statistical analysis of the ECG signal. Temporal features refer to the time-related characteristics of the ECG signal, such as the regularity of the rhythm, the intervals between successive heartbeats, and the timing of the various waveform components relative to each other.

When the details of the ECG signals are neglected and R waves are focused on, the skewness in statistical features can reflect the skew direction of different types of ECG signals. Features such as upper quartile, lower quartile, upper truncation point, lower truncation point, and flatness can effectively reflect the data patterns of different types of ECG signals. In this paper, the DTW algorithm [37,38] is introduced to calculate the DTW values between testing data and cluster centers to achieve the extraction of temporal features of ECG signals, and achieve classification by DTW combined with Euclidean distance. 37 ECG signal features are shown in Table 2. In this paper, 36 features of the 5 cluster centers are normalized and the feature relationships of the 5 cluster centers are shown by heatmap in Fig. 3.Table 2 Selection of ECG signal features.

Table 2ECG Signal Features	Feature Names	
Spatial Features	Medical Features	1. R-wave area, 2. R-wave amplitude, 3. R-wave width value, 4. QS area, 5. QRS duration, 6. T-wave amplitude, 7. P-wave amplitude, 8. P duration, 9. PR interval, 10. R-wave left slope, 11. R-wave right slope, 12. R-wave left width, 13. R-wave right width, 14. R-wave left angle, 15. R-wave right angle, 16. R-wave angle	
Statistical Features	17. skewness, 18. positive area, 19. negative area, 20. zero-crossing signal, 21. average value, 22. variance, 23. standard deviation, 24. coefficient of variation, 25. maximum, 26. minimum, 27. maximum absolute value, 28. full distance (extremely poor), 29. quartile, 30. upper quartile, 31. lower quartile, 32. interquartile range, 33. three means, 34. upper truncation point, 35. lower truncation point, 36. flatness	
Temporal Feature	37. DTW	

Fig. 3 Feature relationship heatmap figure.

Fig. 3

2.4 Ant colony clustering algorithm

The ant colony clustering algorithm [39], is a nature-inspired optimization technique that has been applied to the task of ECG arrhythmia classification. In the context of ECG arrhythmia classification, this algorithm is utilized to group similar ECG waveform patterns together, effectively classifying them into clusters that correspond to different types of arrhythmias. The validity and effectiveness of the ant colony clustering algorithm for ECG arrhythmia classification have been confirmed through its application to the MIT-BIH arrhythmia dataset [11]. The ECG arrhythmia classification process utilizing the ant colony clustering algorithm begins with the determination of the number of arrhythmia types or clusters that will be used to categorize the ECG data. The algorithm employs the Euclidean distance as a measure of dissimilarity between different ECG waveforms or objects. The Euclidean distance, which in this case, represents the feature space of the ECG signals. During the clustering process, the dissimilarity between each testing data point (ECG waveform) and the center of each cluster is calculated. The transfer probability equation is as follows:(4) Pija(t)={[τij(t)]α[ηij(t)]β∑S∈Ja(i)[τis(t)]α[ηis(t)]β,ifj∈Ja(i)0,else

where τij(t) is the pheromone on the t-th iteration (i, j); α is the relative importance of the pheromone; β is the relative importance of the heuristic factor; and Ja(i) is the set of sample points allowed to be selected by ant a in the next step. The equation for calculating the heuristic factor is as follows:(5) ηij=1dij

where dij is the length of the path between (i, j). The pheromone calculation equations are as follows:(6) τij(t+1)=(1−ρ)τij(t)+Δτij,0<ρ<1

(7) Δτij=∑a=1mΔτija

(8) Δτija={1La,through(i,j)0,else

where ρ is the pheromone volatility coefficient; Δτij is the pheromone increment; La is the traversal total path length by ant a during this iteration process; m is the number of ants. The Euclidean distance calculation equation is as follows:(9) E(xk,yl)=∑i=1n(xik−yil)2

where E is the Euclidean distance between the testing data and the cluster center; n is the number of features, with a total of 36; xik and yil represent the i-th feature of the k-th testing data and the i-th feature of the l-th cluster center, respectively.

There exist some defects in the ECG arrhythmia classification based on the basic ant colony clustering algorithm. Although the number of clusters is known, the cluster centers need to be updated continuously during the classification process, which affects the model running time. The traditional ant colony algorithm [40] relies mostly on experiences and experiments to determine ρ. When ρ takes a fixed value, it cannot adjust itself according to the increase in the number of iterations. Moreover, in the application of ECG arrhythmia classification, the accuracy of the classification is valued more than the traversal total path length.

The basic ant colony clustering algorithm, while effective for ECG arrhythmia classification, does have certain limitations that can impact its performance and efficiency. One of the primary issues is the continuous updating of cluster centers during the classification process. This requirement for constant adjustment can lead to increased computational overhead and extended model running times, which may not be ideal for real-time or high-throughput applications.

Additionally, the traditional ant colony algorithm [40] often relies on empirical knowledge and experimental tuning to set its parameters. When a parameter, such as ρ, is set to a fixed value, it does not adapt dynamically to the changing conditions as the number of iterations increases. This lack of self-adjustment can lead to suboptimal performance, as the algorithm may not converge efficiently or accurately to the best possible clustering solution.

In the context of ECG arrhythmia classification, the focus is often on achieving high accuracy in the classification of cardiac rhythms rather than optimizing the traversal total path length by the ants.

2.5 Fast ant colony clustering algorithm with improved spatiotemporal feature perception ability

In addressing the shortcomings of ECG arrhythmia classification using the basic ant colony clustering algorithm, this paper introduces a series of innovative improvements. The method refines the determination of cluster centers. The proposed classification method incorporates both Euclidean distance and DTW to measure the dissimilarity between ECG waveforms. Furthermore, this paper advocates for the use of dynamic pheromone volatility coefficients in updating the pheromones. To ensure the highest classification accuracy, this paper also employs radix sort that can efficiently organize and prioritize the pheromone trail information. The pseudo-code of the improved ant colony clustering algorithm is shown below.ECG Arrhythmia classification Based on Improved Ant Colony Clustering Algorithm	
1.	Step 1: Improved Ant Colony Clustering Algorithm	
2.	Fitting 5 cluster centers through the LSTM model	
3.	 whilei≤numberofiterations	
4.	 whilea≤numberofants	
5.	 Randomly determine the starting point of the ant	
6.	 whiles≤numberofsamplepoints	
7.	 Recording the path traveled by each ant	
8.	 classification based on Euclidean distance and DTW	
9.	 Updating pheromone based on dynamic pheromone volatility coefficient (Equation (22))	
10.	 Calculating the transition point according to Equation (4)	
11.	 Path calculation	
12.	 end while	
13.	 end while	
14.	 Determining the optimal solution of the current model based on radix sort	
15.	 end while	
16.	Step 2: Determining the optimal solution based on radix sort	

2.5.1 Fitting cluster centers based on LSTM model

In this paper, LSTM [41] is introduced to fit cluster centers to improve the quality of cluster centers. Avoid the time consuming problem of constantly updating the cluster centers during the process of classification of the model, so as to improve the running speed of the model. The forget gate of LSTM is as follows:(10) Ct=ft×Ct−1+it×Ct˜

(11) ft=σ(Wf·[ht−1,xt]+bf)

where ft is the forget gate, indicating which features of Ct−1 are used to calculate Ct; Sigmoid is usually selected as the σ activation function. The update gate layer is as follows:(12) it=σ(Wi·[ht−1,xt]+bi)

(13) Ct˜=tanh(WC·[ht−1,xt]+bC)

(14) Ct=ft*Ct−1+it*Ct˜

where it is the input gate for which features controlled by Ct˜ are used to update Ct, and Sigmoid is usually selected as the σ activation function; Ct˜ represents the update value of the unit state, and the activation function usually uses tanh. The output gate layer is as follows:(15) ot=σ(Wo[ht−1,xt]+bo)

(16) ht=ot*tanh(Ct)

where ht is obtained from the output gate ot and the unit state Ct; the mean value of bo is initialized to 1.

In the ant colony clustering algorithm, the initial cluster centers are generally determined by randomly selecting c points, and the random determination method is less effective. And the cluster centers need to be continuously updated during the clustering process, which will affect the running speed. Therefore, in this paper, the cluster centers are fitted by LSTM to avoid continuously updating the cluster centers. The fitting results of type R are shown in Fig. 4.Fig. 4 Fitting results of type R.

Fig. 4

2.5.2 Classification based on Euclidean distance and DTW

After ECG signal features are extracted, the data representing each testing data are no longer a sequence, but characterize its individual features, so Euclidean distance [42] is suitable as a method for classification. The incorporation of the DTW in the model serves to significantly enhance its ability to recognize and account for the temporal features present in ECG signals. By employing DTW, the model can more effectively capture the critical temporal changes that occur in ECG signals, such as the shifting positions of the R-peaks, P-waves, and T-waves, as well as the overall morphology of the cardiac cycles. And the use of DTW ensures that the model is not only sensitive to the immediate amplitude values of the ECG signal but also to the sequence and duration of the cardiac events. As shown in Fig. 2, the 5 types of heart rhythms differ significantly, and the DTW can effectively distinguish different types of heart rhythms, providing a strong basis for the introduction of DTW. The pseudo-code based on Euclidean distance with DTW to achieve classification is shown below.classification Based on Euclidean Distance and DTW	
1.	Step 1: Calculating the DTW distance matrix between each test data and 5 cluster centers	
2.	Step 2: classification based on Euclidean distance and DTW	
3.	 whilek≤416	
4.	 whilel≤5	
5.	 Calculating the distance matrix	
6.	 ifj==1	
7.	 Dkl(i,1)=E(Aik,B1l)+Dkl[i−1,1]	
8.	 elseifi==1	
9.	 Dkl(1,j)=E(A1k,Bjl)+Dkl[1,j−1]	
10.	 esle	
11.	 Dkl(i,j)=E(Aik,Bjl)+min{Dklmin(i,j−1),Dklmin(i−1,j),Dklmin(i−1,j−1)}	
12.	 end if	
13.	 Start from the upper right corner and work your way to the lower left to find the registration path. Finding the smaller of the three lower left points as the next node	
14.	 end while	
15.	 Outputting the DTW value of the kth test data and 5 cluster centers	
16.	 Calculating the similarity between the 36 features of each test data and the cluster center by Euclidean distance (Equation (9))	
17.	 Normalizing the calculated 5 Euclidean distance values	
18.	 E*(xk,yl)i=E(xk,yl)i−E(xk,yl)minE(xk,yl)max−E(xk,yl)min,1≤l≤5,1≤i≤5	
19.	 Calculating the mean of 5 Euclidean distances after normalization	
20.	 ifindex(min(E*(xk,yl)))!=DTWlk	
21.	 The value of ∼ min(E*(xk,yl)) add the mean of 5 Euclidean distances after normalization	
22.	 end if	
23.	 Currently, index(min(E*(xk,yl))) is the cluster type to which it belongs	
24.	 k=k+1	
25.	end while	

The mathematical description of the DTW algorithm is shown in Equations (17), (18), (19). This paper comprehensively learns ECG signals from multiple features and overall morphology, thereby improving the classification accuracy of this method.(17) Dkl(i,1)=E(Aik,B1l)+Dkl[i−1,1]

(18) Dkl(1,j)=E(A1k,Bjl)+Dkl[1,j−1]

(19) Dkl(i,j)=E(Aik,Bjl)+min{Dklmin(i,j−1),Dklmin(i−1,j),Dklmin(i−1,j−1)}

where Dkl is the cumulative distance matrix between the k-th testing data and the center of the l-th class cluster; E(Aik,Bjl) is the Euclidean distance between the i-th point of the k-th testing data and the j-th point of the center of the l-th class cluster. The maximum-minimum normalization equation is as follows:(20) x*=x−min(x)max(x)−min(x)

2.5.3 Updating pheromone based on dynamic pheromone volatility coefficient ρ

When the pheromone volatility coefficient ρ is set to a high value, the pheromone on the optimal paths diminishes more rapidly. This can lead to a situation where the algorithm does not converge on the best solution. Conversely, when ρ is small, the pheromone on the non-optimal paths decreases more slowly, allowing these paths to retain a higher pheromone concentration even after many iterations. This can result in the ants continuing to select these non-optimal paths. Therefore, it is essential to tune ρ to strike a balance between exploration (searching for new paths) and exploitation (reinforcing the best-known paths) to ensure the algorithm's efficiency and accuracy in finding the optimal solution. The pheromone concentration decreased gradually during the regulation process, and this paper improves ρ by the smoothing cost of selecting a function that is consistent with this characteristic to speed up the model convergence. The smoothing cost formula is shown in equation (21). The smaller the smoothing cost indicates that the function is smoother, making the model smoother in the process of convergence without large oscillations. lnxx+lnx is monotonically decreasing at x≥3, and x>lnx ensures that 0<ρ<1. The pheromone volatility coefficient formula and the inverse substitution into Equation (6) are as shown in equations (22), (23).(21) cost(x,y)=∑i=0n−2(xi+xi+2−2xi+1)2+(yi+yi+2−2yi+1)2

where cost is the smoothing cost function; x is the independent variable and y is the function value to be selected.(22) ρ=ln(N+2)(N+2)+ln(N+2)+b

(23) τij(t+n)=N+2(N+2)+ln(N+2)×τij(t)+Δτij

where N is the number of iterations; b is a constant, set to 0.17 by ρ∈[0.2,0.5] [43,44].

2.5.4 Determining the optimal solution of the model based on radix sort

In this paper, radix sort [[45], [46], [47]] is employed to prioritize the accuracy of ECG arrhythmia classification while also taking into account the traversal total path length. The classification result accuracy is first sorted from large to small, then the traversal total path length is sorted from small to large. After a traversal of m ants, the classification result accuracy of all ants is sorted from large to small, and then the traversal total path length of all ants is sorted from small to large to get the local solution set, and then the first group of classification result accuracy and the traversal total path length in the local solution set are added to the global solution set. After n iterations to form the final global solution set, then the last group of ECG arrhythmia classification result accuracy and traversal total path length in the global solution set is the comprehensive optimal solution. The method's ability to focus on accurate classification while maintaining an efficient traversal total path contributes to its practical applicability in real-world cardiac diagnostics. The radix sort is shown in Fig. 5. The first column (0-col) is the number of classification errors and the second column (1-col) is the traversal total path length. Fig. 5 shows that when the traversal total path length is the shortest but the accuracy rate is not the highest, it is not the optimal solution.Fig. 5 Based radix sort in the context of cardiac diagnostics.

Fig. 5

2.6 Experiment and statistical metrics

In this paper, ECG arrhythmia classification was performed based on the MIT-BIH arrhythmia dataset. An enumeration method was employed to systematically determine the key parameters of the proposed ECG arrhythmia classification method. Table 3 in this paper provides a detailed overview of these key parameters, which are crucial for the proper functioning and high accuracy of the proposed classification method.Table 3 The key parameters of the classification method proposed in this paper.

Table 3LSTM	Ant Colony Clustering Algorithm	
Parameter Name	Parameter Value	Parameter Name	Parameter Value	
Input Window Size	40	Number of Iterations	150	
Dropout	0.1	Number of Ants	30	
Lose Function	mse	Number of Cluster Centers	5	
Learning Rate	0.001	Number of Test data	416	
Epochs	200	α	1	
Batch Size	4	β	1	

This paper is based on MATLAB2021a to implement preprocessing, segmenting ECG signals, extracting ECG signal features and ECG arrhythmia classification. The LSTM fitting cluster center was implemented under Python 3.8. The operating system was the 64-bit Windows operating system with 8.00 GB of RAM and an Intel(R) Core(TM) i7-5500U CPU @ 2.40 GHz processor.

The sensitivity (Se), the specifity (Sp), the positive predictivity (Pp) and F1 score are the four statistical metrics chosen to evaluate the proposed method, as shown in the following equation.(24) Se=TPTP+FN×100%

(25) Sp=TNTN+FP×100%

(26) Pp=TPTP+FP×100%

(27) F1=2×Se×PpSe+Pp

The experimental comparison model, as showed in Table 4, provides a structured overview of the various methods and parameters used in this study for ECG arrhythmia classification.Table 4 Experimental comparison model description.

Table 4Model	Description	
M1	Ant colony clustering algorithm， ρ=0.2,α=1,β=1	
M2	Ant colony clustering algorithm， ρ=0.3,α=1,β=1	
M3	Ant colony clustering algorithm， ρ=0.5,α=1,β=1	
M4	Introduction of LSTM to fit the cluster centers， ρ=0.2,α=1,β=1	
M5	Introduction of LSTM to fit the cluster centers， ρ=0.3,α=1,β=1	
M6	Introduction of LSTM to fit the cluster centers， ρ=0.5,α=1,β=1	
M7	Introduction of DTW to enhance temporal feature perception ability, ρ=0.2,α=1,β=1	
M8	Introduction of LSTM to fit the cluster centers and DTW to enhance temporal feature perception ability， ρ=0.2,α=1,β=1	
SFP-FACC	Introduction of LSTM to fit clustering centers, DTW to enhance temporal feature perception ability and dynamically update pheromone volatility coefficients ρ， α=1,β=1	

3 Results

First, the classification results of the basic ant colony clustering algorithm under ρ=0.2, ρ=0.3 and ρ=0.5 are tested, as shown in Table 5, and the traversal total path length convergence are shown in Fig. 6. Fig. 6 provides the performance of three different models (M1, M2, and M3) in terms of their traversal total path length and convergence speed. It is evident that the traversal total path lengths of M2 and M3 converge more rapidly compared to M1. In Table 5, the overall classification accuracy of M1 is 87.50 %, which is 2.65 % higher than that of M2 and 4.33 % higher than that of M3, so M1 is chosen as the main comparison model, with ρ=0.2 as the main test model.Table 5 Experimental results.

Table 5Model	Overall Accuracy	Total Errors	N	L	R	A	V	Running Time	Path Length	
M1	87.50 %	52	100 %	86.00 %	100 %	78.26 %	60.00 %	152.457	226.529	
M2	84.85 %	63	100 %	94.00 %	50.00 %	91.30 %	95.71 %	157.19	227.824	
M3	83.17 %	70	100 %	92.00 %	99.00 %	78.26 %	27.14 %	154.926	228.503	
M4	89.90 %	42	100 %	90.00 %	84.00 %	71.74 %	95.71 %	48.455	230.4115	
M5	89.90 %	42	100 %	90.00 %	84.00 %	71.74 %	95.71 %	40.855	230.2873	
M6	89.90 %	42	100 %	90.00 %	84.00 %	71.74 %	95.71 %	47.504	230.7251	
M7	98.80 %	5	100 %	100 %	100 %	91.30 %	98.57 %	159.24	228.002	
M8	99.04 %	4	100 %	100 %	100 %	93.49 %	98.57 %	45.932	229.231	
SFP-FACC	99.04 %	4	100 %	100 %	100 %	93.49 %	98.57 %	46.072	229.051	

Fig. 6 Comparison of traversal path lengths among models.

Fig. 6

Compared with M1, the overall accuracy of M4 is improved by 2.4 %. Compared with the methods that continuously update the cluster centers during the classification process, the methods that introduce LSTM to fit the cluster centers (M4, M5, and M6) do not have the fluctuation in the number of classification errors unlike M1, M2, and M3. The reason is that the larger ρ would make the pheromone volatilize too fast and easily miss the optimal path. M4 not only improves the classification accuracy, but also speeds up the model running time, about 3.5 times faster.

Compared with M1, the overall accuracy of M7 is improved by 11.3 %, L accuracy is improved by 14 %, A accuracy, by 13.04 %, and V accuracy, by 38.57 %, with a small difference in the model running time.

Compared with M1, the overall accuracy of M8 is improved by 11.54 %, L accuracy is improved by 14 %, A accuracy, by 15.23 %, V accuracy, by 38.57 %, with about 3.5 times faster in the model running time. Compared with M4, the overall accuracy of M8 is improved by 9.14 %, L accuracy is improved by 10 %, R accuracy, by 16 %, A accuracy, by 21.75 %, and V accuracy, by 2.86 %, with a smaller difference in model running time. Compared with M7, the overall accuracy of M8 is improved by 0.24 %, A accuracy is improved by 2.19 %, and the model running time is about 3.5 times faster.

The overall accuracy of SFP-FACC achieves 99.04 %, and the accuracy of N, L and R achieves 100 %; A and V accuracy are 93.49 % and 98.57 %, respectively.

The evaluation of the classification results of the proposed method in this paper, is shown in Table 6 and Fig. 7. The matrix of classification results, as shown in Fig. 8, Fig. 1 A was mistakenly classified into L, 3 V were mistakenly classified into N, R and A. The distribution of classification results is shown in Fig. 9. Because there are many ECG signal features, through testing, this paper selected P wave amplitude and skewness to show the classification of testing data.Table 6 Classification results evaluation.

Table 6SFP-FACC	N	L	R	A	V	
Se	100 %	100 %	100 %	93.48 %	98.57 %	
Sp	99.68 %	99.68 %	99.68 %	100 %	99.71 %	
Pp	99.01 %	99.01 %	99.01 %	100 %	98.57 %	
F1	99.50 %	99.50 %	99.50 %	96.63 %	98.57 %	

Fig. 7 Classification results evaluation.

Fig. 7

Fig. 8 (a) Matrix of classification results; (b) Matrix of classification accuracy.

Fig. 8

Fig. 9 Comparison between the real distribution and the distribution of classification result: (a) Real distribution of 416 data; (b) Distribution of classification result.

Fig. 9

4 Discussion

As can be seen from Table 5 and Fig. 6, M2 and M3 are able to find optimal or near-optimal solutions in a shorter amount of time or with fewer iterations, which can be an advantage in scenarios where computational efficiency is a concern. However, it is also noted that the traversal total path lengths for M2 and M3 are longer than that of M1. Despite the differences in traversal total path length and convergence speed, the classification accuracy is highlighted as the most critical factor in practical applications. The results show that the introduction of DTW to enhance the temporal feature perception ability of the proposed model in this paper is effective. The results show that the model with the introduction of LSTM fitted clustering center and DTW enhanced temporal feature perception ability in this paper has obvious advantages and both outperform the performance of the single method introduced alone. Compared with M1, M4, M7 and M8, the traversal total path length of SFP-FACC converges faster, indicating that the dynamic pheromone volatility coefficient proposed in this paper can accelerate the convergence speed of the model without affecting the model running speed. The analysis of the traversal total path length in this paper serves a dual purpose: it reflects the model's capability to seek out superior solutions, and it indirectly provides insight into the model's classification accuracy.

As can be seen from Table 6 and Fig. 7, Fig. 8, Fig. 9, the classification method proposed in this paper had the characteristics of fast operation and high accuracy rate on the MIT-BIH arrhythmia dataset, which had certain advantages in practical applications.

The classification method introduced in this paper demonstrates a set of advantages when compared to other current methods, particularly in terms of overall accuracy and model running speed, as shown in Table 7. The proposed method in this paper has demonstrated a significant enhancement in accuracy rate when compared to the methods previously introduced by Swetha et al. [18], Essa et al. [26], and Fan et al. [48]. The improvement ranges from 3.23 % to 12.97 %, which is a notable advancement in the field of ECG arrhythmia detection. This increase in accuracy suggests that the proposed method has been successful in more effectively capturing the complex patterns and features within ECG signals that are indicative of various arrhythmias. Moreover, the model proposed in this paper is simpler and runs faster compared to the combined models. The observations per second, is a critical metric for evaluating the speed and efficiency of an ECG arrhythmia classification method. In the context of this paper presented, the proposed method exhibits a remarkable processing speed, with 40,632 obs/sec. This is a significant improvement over the method proposed by Swetha et al. [18], which is 410 obs/sec. The nearly 99 times faster speed of the proposed method compared to the KC-FLC. The method by Essa et al. [26] has a running time of 780secs. The method by Fan et al. [48], on the other hand, has a significantly reduced running time of 78secs, indicating a faster processing capability. The proposed method in this paper further improves upon these times, with a total running time of 46.072secs. This total is divided into 5secs for fitting the clustering center and 41.072secs for classifying the heart rhythm types.Table 7 Comparison with other methods.

Table 7Reference	Method	Database	Accuracy	Observations Per second	Running Time	
Swetha [18]	KC-FLC	MIT-BIH	91.50 %	410 obs/sec	–	
Essa [26]	Bagging Models	MIT-BIH	95.81 %	–	780 s	
Fan [48]	FRM-CNN	MIT-BIH	86.07 %	–	78 s	
Chen [49]	MACN + UDA	MIT-BIH	94.35 %	–	–	
Che [50]	CNN_Transformer_LC	CPSC 2018	78.56 %	–	–	
Wang [51]	DAEDA-uda	MIT-BIH	97.59 %	–	–	
Ramkumar [52]	AE-biLSTM	MIT-BIH	97.15 %	-	-	
Li [53]	–	MIT-BIH	88.99 %	-	-	
Houssein [54]	MRFO-SVM	MIT-BIH	98.26 %	–	–	
Li [55]		MIT-BIH	99.00 %	6681 obs/sec	449 s	
This paper	SFP-FACC	MIT-BIH	99.04 %	40,632 obs/sec	46.072 s	

Chen et al. [49] introduced an unsupervised Multi-path Atrous Convolutional Network for the classification of ECG heartbeats. A key contribution is the introduction of two novel loss functions for ECG heartbeat classification: Cluster-aligning loss and Cluster-separating loss. Despite the method's effectiveness, the overall classification accuracy achieved by Chen et al.'s method was 94.35 %, which is 4.69 % lower than the accuracy achieved by the method proposed in the this paper. Che et al. [50] integrated a transformer network into CNN with the aim of capturing the temporal dynamics of ECG signals. Additionally, the researchers introduced a novel link constraint into the loss function to improve the classification ability of the embedded vector. And this method achieved an overall classification accuracy of 78.56 % in the CPSC 2018 competition data. Wang et al. [51] introduced an innovative approach to ECG arrhythmia classification with the development of a Domain-Adaptative ECG Arrhythmia Classification (DAEAC) model. This model is grounded in convolutional network and incorporates unsupervised domain adaptation (UDA), which showed good performance under the MIT-BIH database. Ramkumar et al. [52] explored the integration of an Auto-Encoder with Bidirectional Long Short-Term Memory to enhance the performance of ECG arrhythmia classification, and this approach achieved 97.15 %. Li et al. [53] used overlapping the segments to mitigate the effect of inter-cluster imbalance, but this approach made the segmented data contain some of the same features.

Houssein et al. [54] implemented a feature filtering technique using Mantra ray individual encoding to preprocess the ECG signals. Their approach led to an overall classification accuracy of 98.26 %. However, the process relied significantly on empirical knowledge and fixed values. In contrast, the dynamic approach used in this paper is designed to be more flexible and adaptive.

Compared to Li et al. [55], SFP-FACC fits the clustering center by LSTM to improve the running time of the model. When evaluated under the MIT-BIH dataset, CM achieved an overall detection accuracy of 99.00 %, a detection speed of 6681 obs/sec, and a running time of 449 s. Our current article with an overall detection accuracy of 99.04 %, a significantly higher detection speed of 40632 obs/sec, and a markedly reduced running time of 46.072 s.

5 Limitations

In this paper, though the classification accuracy is improved to a certain extent by randomly selecting data and fitting cluster centers with LSTM, this method has certain contingency, and the sliding window of LSTM model will lead to spatial-temporal deviation of feature sequences. Parameters α and β are still determined manually.

6 Conclusion

As one of the most critical physiological signals for arrhythmia diagnosis, ECG has become an effective way to achieve arrhythmia classification by ECG signals. This paper proposes the fast ant colony clustering algorithm with improved spatiotemporal feature perception ability (SFP-FACC) for ECG arrhythmia classification. This method introduced LSTM to fit cluster centers, effectively solved the time consumption problem of updating cluster centers during the classification process. This method used dynamic pheromone volatility coefficients to improve the model convergence speed. The integration of DTW into the model serves as a significant enhancement, particularly in the context of perceiving temporal features within ECG signals, the model's ability to capture the temporal dynamics of ECG signals is significantly improved. The classification accuracy and the traversal total path length were improved by using the radix sort algorithm. Based on the MIT-BIH arrhythmia dataset, the overall classification accuracy of the proposed method achieved 99.04 %, with observations per second of 40,632obs/sec, and the running time of 46.072secs. Compared with the basic ant colony clustering algorithm, the proposed classification method achieved a significant improvement in overall classification accuracy and is about 3.5 times faster than the basic ant colony clustering algorithm in terms of the running time. Compared with other ablation experiments, the classification method proposed in this paper has different degrees of improvement in overall classification accuracy, model convergence speed and the traversal total path length. Compared with some of the current researches, the proposed classification method improved the classification accuracy by about 7.01 %, with obvious advantages in the model running speed and model processing capability. In summary, the proposed classification method can meet the practical needs and is suitable to be combined with sensors to realize a real-time monitoring or classification system of ECG rhythm as an auxiliary tool to assist physicians in diagnosis and improve work efficiency.

In the future research, we will do further research on the cluster center determination method and solve the deviation problem caused by the sliding window mechanism of LSTM. Establishing a mathematical model for dynamic updating α and β. In future experiments, we will design our own self-testing devices with multi-module sensors to collect relevant data to further improve the reliability of this method.

Ethical and informed consent for data used

We have used the data available in the public domain and have not conducted any experiments involving human beings in this study.

Data availability and access

‘The MIT-BIH dataset’ at https://archive. physionet.org/physiobank/database/html/mitdbdir/intro.htm (2022-08-10).

CRediT authorship contribution statement

Shuguang Qin: Methodology. Linyue Liu: Writing – review & editing, Writing – original draft, Methodology. Xinhong Wang: Writing – review & editing. Ning Dong: Data curation. Ning Li: Writing – review & editing, Funding acquisition. Qiangsun Zheng: Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research was funded by 10.13039/501100001809 National Natural Science Foundation of China (82270335 ).
==== Refs
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