A hybrid method for heartbeat classification via convolutional neural networks, multilayer perceptrons and focal loss

ECG denoising

The ECG signal is usually disturbed by various noises such as electromyography noise, power line interference and baseline wandering (Chen et al., 2017), which makes useful features to be difficultly extracted. In this step, most previous works typically perform a baseline wandering removal and then high-frequency noise filtering (Mondéjar-Guerra et al., 2019). However, excessive filtering will lead to the loss of some helpful information in the ECG signal. Since CNN has better noise immunity (Huang et al., 2018), we only perform baseline wandering removal and preserve as much information as possible from the raw ECG signal.

Two median filters are combined to remove the baseline wandering of the ECG signal in the article. First, the QRS complexes and P-waves are removed using a 200-ms width median filter, and then a 600-ms width median filter is further adopted to remove T-waves. The output is the baseline wandering of the ECG signal, and the baseline-corrected ECG signal can be achieved by subtracting it from the original signal. An effect of baseline wandering removal is shown in Fig. 2.

After obtaining the baseline-corrected ECG signal, the ECG is further segmented into a series of heartbeats based on the labeled R-peaks. In specific, for each heartbeat, we obtain 200 sampling points of the ECG signal segment, 90 sampling points before and 110 sampling points after the labeled R peak. The R-peak detection is not the focus of the article and we directly use labeled R-peaks in the dataset, as there are many high-precision (>99%) R-peak detection methods in the literature (Gacek & Pedrycz, 2012; Pan & Tompkins, 1985).

RR interval features extraction

The time interval between two consecutive R-peaks is normally called the RR interval (Ruangsuwana, Velikic & Bocko, 2010), which contains the dynamic information of the heartbeat. To capture this information for heartbeat classification, four features are extracted from the RR interval, namely previous RR interval, post RR interval, ratio RR and local RR interval. The previous RR interval refers to the distance between the current R-peak position and the previous R-peak, the post RR interval is the distance between the current R-peak position and the following one. The ratio RR represents the ratio of the previous RR interval and the post RR interval. These three features reflect the instantaneous rhythm of a heartbeat. The average value of the 10 RR intervals before the current heartbeat is taken as the local RR interval, which represents the overall rhythm in the past. Due to the inter-patient variations in the ECG signal, the RR interval of different patients cannot be directly compared, in this article we use the entire patient’s ECG signal to calculate the average RR interval, and subtract it from all RR characteristics (expect the ratio RR) to eliminate this effect.

Morphological features extraction via CNN architecture

Convolutional neural networks is a powerful deep neural network inspired by visual neuroscience (Chu, Shen & Huang, 2019b). It has been successfully used in speech recognition, natural language processing, image classification, and biomedical signal (Palaz & Collobert, 2015; Pourbabaee, Roshtkhari & Khorasani, 2018; Yin et al., 2017). Given an image, CNN can effectively learn high-level abstractions, which can then be input into the classifier (e.g., fully connected neural network and SVM) for classification (Zhang, Zhou & Zeng, 2017). A CNN usually consists of convolutional layers, activation functions, and pooling layers, and sometimes including batch normalization layers.

Convolutional Layer: It is the most important component in CNN and performs convolution operation on the input data (Liu & Chen, 2017). Let f_k and s be the filter and the 1D ECG signal, respectively. The output of the convolution is calculated as follows: $$C\left[i\right]=s\left(i\right)\ast f_k\left(i\right)=\sum _{m}s\left(m\right)f_k\left(i-m\right)$$where $m$ is the size of the filter and the filter f_k is realized by sharing the weights of adjacent neurons.

Activation Function: The activation function is used to determine whether the neuron should be activated. The purpose is to enable neurons to achieve nonlinear classification. Rectifier Linear Unit (ReLU) is one of the most widely used activation function, which can be expressed as $$f\left(x\right)=\mathrm{m}\mathrm{a}\mathrm{x}\left(0,x\right)$$where x is the output value of the neuron.

Pooling layer: The pooling layer, also known as the down-sampling layer, is an operation that decreases the computational intensity by reducing the output neuron dimension of the convolutional layer, and can handle some variations due to signal shift and distortion (Zhang, Zhou & Zeng, 2017). The most widely used pooling method is the max-pooling, which is to apply the maximum function over input $s$. Let m be the filter size, and the output is: $$M\left(x\right)=\mathrm{m}\mathrm{a}\mathrm{x}\left\{s\left(x+k\right)|\left|k\right|\le {\displaystyle \frac{m-1}{2}}\right\}$$Batch Normalization Layer: The batch normalization layer is a technology for standardizing network input, applied to either the activations of a prior layer or inputs directly, which can accelerate the training process, and provides some regularization, reducing generalization error. Let $B=\left\{x_i,i=1,\cdots ,m\right\}$ be a mini-batch of the entire training set, the output of batch normalization is as follows: $$\widehat{x_i}={\displaystyle \frac{x_i-{\mu }_B}{\sqrt{{\sigma }_B^2+ϵ}}}$$where ${\sigma }_{\mathrm{B}}$ and μ_B are the variance and the mean of training set $B$, respectively. $ϵ$ is an arbitrarily small constant to ensure the denominator is not zero.

A CNN is developed and utilized for heartbeat morphological feature extraction in this article. The CNN architecture is displayed in Fig. 1. It contains three convolutional blocks and three pooling layers. Each convolutional block includes a convolution layer, a ReLU activation function and a batch normalization layer. The kernel of the convolution is reduced as the network structure becomes deeper. For instance, the first convolution kernel is 11, while the second is reduced to 5. A batch normalization and ReLU activation are applied after each convolution operation, and a max-pooling is used to reduce the spatial dimension. Note that the parameters of the convolutional network are usually set based on the author’s experience. The detailed parameters of CNN architecture are listed in Table 1. The output of the last pooling layer is the morphological features extracted by CNN from the heartbeat. An illustration of the morphological features extracted from the heartbeat is shown in Fig. 1C.

MLP classifier

The CNN-based morphological features and RR interval features are combined as the input of the classifier in the article. In general, any classifier (i.e., SVM and random forest (RF)) can be used for heartbeat classification. Here, we adopt a multilayer perceptron (MLP, also known as fully connected neural networks in deep learning) as the classifier. The reason behind this is that CNN and MLP can be combined for parameter training (we call it one-step training). Compared with other methods, this usually achieves better performance. Specifically, our MLP classifier contains an input layer, a hidden layer and an output layer. The input layer consists of two parts of information: CNN-based morphological features and RR interval features. The hidden layer has 64 neurons, and each neuron is connected to the input features. The output layer neurons are 4 in the article, each representing a kind of arrhythmia or normal heartbeat. The details of our method are shown in Fig. 1 and Table 1.

Loss function

Before training a deep neural network, a loss function is first needed. The cross-entropy loss is the most widely used in deep neural network classification (Chu, Wang & Lu, 2019a). However, this loss function does not address the class imbalance problem. A focal loss function is introduced in the article to deal with this problem.

Cross-entropy loss

The cross-entropy is a measure in information theory (Robinson, Cattaneo & El-Said, 2001). It is based on entropy and calculates the difference between two probability distributions. Closely related to KL divergence that computers the relative entropy between two probability distributions, but the cross-entropy calculates the total entropy between the distributions. The cross-entropy is usually taken as the loss function in deep neural network classification (Chu, Wang & Lu, 2019a).

Let $t_i$ and $p_i$ be the ground truth and the estimated probability of each category, the cross-entropy loss is computed by: $$CE=-\sum _i^C{t}_i\cdot \mathrm{l}\mathrm{o}\mathrm{g}\left(p_i\right)$$where $C$ refers to the category set of the heartbeat. In the cross-entropy loss, each category is treated equally, which causes the majority category to overwhelm the loss and the model tends to classify to the majority category in an imbalanced environment.

Focal loss

A characteristic of cross-entropy loss is that even easy-to-classify examples can cause significant losses, which will cause the loss of easy examples that constitute most of the dataset during the training process to negatively affect rare classes (Lin et al., 2017). The focal loss is designed to deal with this imbalanced problem by reshaping the cross-entropy loss function by reducing the attention to easy examples and focusing on difficult ones. A general formula for focal loss is expressed as: $$FL=-\sum _i^C{t}_i\cdot {\left(1-p_i\right)}^{\gamma }\mathrm{l}\mathrm{o}\mathrm{g}\left(p_i\right)$$where $\gamma$ acts as the modulating factor. As shown in Fig. 3, the higher the $\gamma$ value, the lesser the cost incurred by well-classified examples. In practice, the α-balanced variant of the focal loss is usually used when one or more categories are highly imbalanced, which is defined as: $$F{L}^{{}^{\prime }}=-\sum _i^C{t}_i\cdot {\alpha }_i{\left(1-p_i\right)}^{\gamma }\mathrm{l}\mathrm{o}\mathrm{g}\left(p_i\right)$$where ${\alpha }_i$ is the weighting factor of each category.

Data set

The ECG dataset from the MIT-BIH arrhythmia database (Moody & Mark, 2001) is used to test our proposed method. This dataset contains 48 30-min ambulatory two leads ECG signal records collected from 47 subjects. Each ECG signal is sampled at 360 Hz with an 11-bit resolution. The first lead is the modified-lead II (ML II), and the second lead depends on the record, one of V1, V2, V4 or V5. The heartbeat of these ECG signals is independently labeled by two or more doctors, and there are about 110,000 heartbeats.

According to the recommendation of AAMI, these heartbeats are further divided into five heartbeat classes. Table 2 shows the mapping of AAMI classes and MIT-BIH arrhythmia heartbeat types. Since Q is practically non-existent, we ignore it like others (Mar et al., 2011; Zhang et al., 2014). Meanwhile, four recordings with paced beats are removed in consistent with the AAMI recommended practice, namely 102, 104, 107 and 217. Since all records have ML II ECG signals and they are widely used in wireless body sensor network (WBSN) based ECG applications, this lead ECG signal is used for heartbeat classification in the article.

As we mentioned in related works, the article focuses on the heartbeat classification under the inter-patient paradigm. To facilitate comparison with existing works, we follow De Chazal, O’Dwyer & Reilly (2004) to split the dataset into two subsets. Each contains regular and complex arrhythmia records and has roughly the same number of heartbeat types. Table 3 shows the details of two subsets. The first (DS1) is used for training whereas the second (DS2) is used to test the heartbeat classification performance (De Chazal, O’Dwyer & Reilly, 2004). No patient appears in both subsets at the same time.

Model training and performance metrics

In the study, the general focal loss (non-α-balanced focal loss) is used as the loss function, and the modulating factor $\gamma$ is set to the default value ( $\gamma$ = 2). Since Adam can accelerate the model training, we use it as the optimizer. The batch size of the model is set to 512 and the maximum epoch is 50. The initial learning rate is 0.001, and reduced by 0.1 times every 10 epochs. In addition, in order to avoid overfitting, the l2 penalty is set to 1e−3 based on trial and error. The model is implemented using Keras and trained on the NVIDIA GeForce RTX 2080Ti graphical processing unit.

To evaluate the performance of our proposed method, three widely used metrics are adopted, namely positive predictive value (PPV), sensitivity (SE), and accuracy (ACC), which are defined as: $$PP{V}_i={\displaystyle \frac{T{P}_i}{T{P}_i+F{P}_i}}$$ $$S{E}_i={\displaystyle \frac{T{P}_i}{T{P}_i+F{N}_i}}$$ $$AC{C}_i={\displaystyle \frac{T{P}_i+T{N}_i}{T{P}_i+T{N}_i+F{P}_i+F{N}_i}}$$where $T{P}_i$ (true positive) refers to the number of the $ith$ class is correctly classified, $F{P}_i$ (false positive) is equal to the number of heartbeats misclassified as the $ith$ class, $T{N}_i$ (true negative) is the number of heartbeats that are not in the $ith$ class and not classified into the $ith$ class, and $F{N}_i$ (false negative) is equal to the number of heartbeats of the $ith$ class classified as other classes. $PP{V}_i$ indicates the proportion of positive correct classification, and $S{E}_i$ reflects the sensitivity of the classifier in the $ith$ class. $AC{C}_i$ is the ratio of all correct classifications.

Since the heartbeat classes are imbalanced, f1-score (F1) is also selected as the performance measure, defined as: $$F{1}_i={\displaystyle \frac{2\times PP{V}_i\times S{E}_i}{PP{V}_i+S{E}_i}}$$f1-score takes both the positive predictive value $PP{V}_i$ and sensitivity $S{E}_i$ into account, and is generally useful than $AC{C}_i$ in the imbalance class distribution (Chen, 2009).

Comparison with existing works

Based on De Chazal, O’Dwyer & Reilly (2004), the dataset is divided into DS1 and DS2 datasets. DS1 is used for training and DS2 is used to test our proposed method. For fair evaluation, we compare works (Chen et al., 2017; De Chazal, O’Dwyer & Reilly, 2004; Garcia et al., 2017; Liu et al., 2019; Mar et al., 2011; Zhang et al., 2014) that adopt the same strategy. As SVEB and VEB are more important than other classes, we list the detailed information of these two classes in Table 4. The experimental results show that the proposed method has better recognition in the inter-patient paradigm, with F1s of SVEB and VEB of 74.29% and 92.40%, respectively. In particular, the PPV of SVEB is 68.34%, indicating that the proposed method has better SVEB recognition ability. The 93.72% SE of VEB is superior to most reported works. The evaluation results of all four-classes are listed in Table 5. The results related to PPV and SE are close to or surpass those obtained with existing works except for F. For category F, it is mainly composed of the fusion of ventricular beat and normal beat, which is very close to the normal heartbeat. Meanwhile, compared with other categories, F has the least number and the most serious imbalance. As a result, the performance of existing works is unstable in this category, usually a large number of N is predicted as F or F is predicted as N. In the article, although the focus loss is introduced, due to the high imbalance of F, the proposed method cannot extract the discriminate features. Mar et al. (2011) although, obtains the best PPV in F, a large number of N is incorrectly classified as F. We suggest that category F can be included in other categories in future research.

Focal loss vs. Cross-entropy loss

Since the heartbeat has an imbalanced class distribution, the cross-entropy loss is replaced by the focal loss as the loss function of the model in the article. The performance comparison of the two losses is listed in Table 6. Both losses have similar overall accuracy, but compared to cross-entropy loss, the overall PPV, SE and F1 of the focal loss are significantly improved. An overall PPV of 64.68%, SE of 68.55%, and F1 of 66.09% are achieved by the focal loss, while the cross-entropy loss obtains an overall PPV of 59.82%, SE of 66.77%, and F1 of 62.67%. The corresponding metrics increased by 4.86%, 1.78%, and 3.42%, respectively. In addition, for each specific class, the PPV, SE, and F1 of the focal loss also have achieved comparable or better performance than the cross-entropy loss, especially in the F1.

The confusion matrix of the two losses is listed in Table 7. The focal loss achieves a total of 45,952 correct predictions, while the cross-entropy obtains 45,358 correct predictions. With the focal loss, the total correct prediction has slightly increased, perhaps due to the suppression of easy-to-classify samples by focal loss.