Enhanced tolerance-based intuitionistic fuzzy rough set theory feature selection and ResNet-18 feature extraction model for arrhythmia classification

Abstract

Arrhythmia classification on Electrocardiogram (ECG) signals is an important process for the diagnosis of cardiac disease and arrhythmia disease. The existing researches in arrhythmia classification have limitations of imbalance data problem and overfitting in classification. This research applies Fuzzy C-Means (FCM) – Enhanced Tolerance-based Intuitionistic Fuzzy Rough Set Theory (ETIFRST) for feature selection in arrhythmia classification. The selected features from FCM-ETIFRST were applied to the Multi-class Support Vector Machine (MSVM) for arrhythmia classification. The ResNet18 – Convolution Neural Network (CNN) was applied for feature extraction in input signal to overcome imbalance data problem. Conventional feature extraction along with CNN features are applied for FCM-ETIFRST feature selection process. The FCM-ETIFRST method in arrhythmia classification is evaluated on MIT-BIH and CPCS 2018 dataset. The FCM-ETIFRST has 98.95% accuracy and Focal loss-CNN has 98.66% accuracy on MIT-BIH dataset. The FCM-ETIFRST method has 98.45% accuracy and Explainable Deep learning Model (XDM) method have 93.6% accuracy on CPCS 2018 dataset.

Keywords

Arrhythmia classification convolution neural network enhanced tolerance-based intuitionistic fuzzy rough set theory fuzzy c-means multi-class support vector machine

1. Introduction

Arrhythmia classification using Electrocardiogram (ECG) is an interesting research topic for researchers and this plays a vital role in the diagnosis and early prevention of cardiovascular diseases. Feature extraction and selection are critical processes in ECG signal classification [1]. ECG is a low cost and commonly used diagnostic tool in healthcare institutes for heart electrical signals screening. Arrhythmia can be defined as abnormal heart signals and Cardiac arrhythmia, which can be dangerous or in most cases, it can cause death. Arrhythmia consists of different types and this can be detected using an ECG test. Various researchers develops the model of automatic screening of arrhythmia classification using ECG signals. Automatic classification tools of arrhythmia using ECG signal benefits patients and also for a doctor to assist in the decision of treatment [2]. Early and accurate classification of cardiac arrhythmia in ECG signal prevent many premature deaths. Cardiac arrhythmia causes due to electrical impulses of improper conduction throughout the heart [3]. Multi-channel ECG signal continuous recording and analysis are necessary for accurate diagnosis of arrhythmia. Large amount of data is required to be processed and analyzed for arrhythmia classification. Several medications are prescribed based on the arrhythmia type of the patient. Rapid treatment is not required for some mild arrhythmia and others can be treated with medication. Treatments such as surgery, cardiac defibrillation, and pacemakers are required if a case is serious [4, 5].

Daily cardiac health monitoring is carried out based on a single-lead wearable ECG device including Atrial Fibrillation (AF) for automatic abnormal heart rhythms detection. Recently, end-to-end deep learning techniques such as Recurrent Neural Networks (RNNs), Convolutional Neural Networks (CNNs) are widely applied to meet the needs of automated feature selection and ECG signals classification [6]. Automatic cardiac disease classification is carried out based on denoised ECG signals. Feature extraction methods such as Hermit function coefficients and temporal features, deep learning networks, Wavelet-based kernel Principle Component Analysis, Wavelet Packet Decomposition, Principle Component Analysis, temporal and morphological features, and Discrete Wavelet Transform were used in existing methods [7]. Various methods of ECG signal classification were carried out based on extracted features. Some of the classifiers are Optimized block-based Neural Network, Naïve Bayes, Support Vector Machine-Radial Basis Function, Support Vector Machine (SVM), Probabilistic Neural Network, Random Forest (RF), and Back Propagation Neural Network (BPNN) were applied for arrhythmia classification [8, 9, 10]. Existing methods in arrhythmia classification have limitations of overfitting problem and imbalance data problem that degrades the efficiency of the model. The objectives and contribution of this research are discussed as follows:

1)
The FCM-ETIFRST method is proposed for the feature selection process in arrhythmia classification to avoid overfitting and imbalance data problems. The FCM-ETIFRST method selects unique features related to the class that helps to reduce the correlation of features between class and solves imbalance data problem.
2)
The Non-membership function and hesitance degree are added in fuzzy technique to control the feature selection for classification. The Non-membership function provides the probability of the features that are not selected and hesitance degree provides the similarity of features between classes. This process helps to select unique feature sets from the signal for effective classification.
3)
Tolerance Intuitionistic in the proposed method measures the similarity in Fuzzy Rough Set and helps to select the relevant features. Tolerance Intuitionistic helps to adaptively select the features from input signal and solves imbalance data problem.
4)
The ability of the FCM-ETIFRST method helps to reduce the number of features to solve the overfitting problem in the network. The ResNet18-CNN model helps to select more relevant features and the proposed FCM-ETIFRST model helps to select unique features for classification.
5)
The FCM-ETIFRST method provides higher efficiency than existing methods in arrhythmia classification. The FCM-ETIFRST method is compared with existing methods in two datasets of MIT-BIH and CPCS 2018 dataset. The FCM-ETIFRST-MSVM has 98.95% accuracy, 99.49% sensitivity, and Focal Loss-CNN model has 98.66% accuracy and 76.71% sensitivity.

The organization of the paper is given as follows: Recent research in Arrhythmia classification was reviewed in Section 2 and ResNet18 and ETIFRST models are explained in Section 3. The implementation details are given in Section 4 and the Result is discussed in Section 5. The conclusion of this research work is given in Section 6.

ACO Ant Colony Optimization

AF Atrial Fibrillation

AUC Area Under the Curve

BPNN Back Propagation Neural Network

CL Convolutional Layer

CNN Convolution Neural Network

DNN Deep Neural Network

DT Decision Tree

ECG Electrocardiogram

ETIFRST Enhanced Tolerance-based Intuitionistic Fuzzy Rough Set Theory

FCL Fully Connected Layer

FCM Fuzzy C MeansC-Means

GWO Grey Wolf Optimization

I-AVB First-degree Atrioventricular Block

KNN K-Nearest Neighbours

LBBB Left Bundle Branch Block

MCC Matthews Correlation Coefficient

MCL Mean Curve Length

MSVM Multi-class Support Vector Machine

MTE Mean Teager Energy

NLAF Non-Linear Activation Function

OAO One Against One

PAC Premature Atrial Contraction

PL Pooling Layer

PNN Probabilistic Neural Network

PSO Particle Swarm Optimization

PVC Premature Ventricular Contraction

RBBB Right Bundle Branch Block

RF Random Forest

RNN Recurrent Neural Networks

ROC Receiver Operating Characteristic

STD ST-segment Depression

STE ST-segment Elevated

VF Ventricular Fibrillation

WOA Whale Optimization Algorithm

XDM Explainable Deep learning Model

ZCR Zero-Crossing Rate

2. Literature review

Arrhythmia is a cardiovascular disease that is a serious threat to human health and ECG signal were used to classify arrhythmia disease. Arrhythmia classification performed in recent research was reviewed in this section.

The MIT-BIH and CPSC 2018 datasets were common datasets used by existing research for the evaluation of the models. One part of the literature review is related to the MIT-BIH dataset of existing methods and the other part is CPSC 2018 dataset.

Gnecchi et al. [11] applied quadratic wavelets of wavelet transform and Probabilistic Neural Network (PNN) for arrhythmia classification. The 17 ECG recordings from MIT-BIH were used for the classification process and test the performance. The resulting patterns were extracted from peaks and wavelets, then applied to PNN for arrhythmia classification. Mathunjwa et al. [12] applied VGG-16, VGG-19, and AlexNet models with ReLU activation function for arrhythmia classification. The model performs a selection of the optimal number of parameters in the deep learning models. The models were evaluated with training and validation data in classification. Yang and Wei [13] extracted the morphological features of ECG signals such as duration, interval, and amplitude for arrhythmia classification. The clustering based feature extraction is applied based on the QRS complex morphology. The KNN, SVM and Neural Network were used as a classifier for automatic diagnosis of arrhythmia classification.

Lu et al. [14] proposed the Focal Loss with CNN model to solve the imbalance data problem in arrhythmia classification. Focal loss can train on a small dataset and performs on imbalanced dataset. Focal loss reduces the number of parameters in the CNN for arrhythmia classification. Weight value was assigned to the minority class in the CNN model for solving the imbalance data problem. Meng et al. [15] applied the CNN model with convolutional, pooling and fully connected layers for the classification of arrhythmia. The MIT-BIH dataset was used to evaluate the model performance in arrhythmia. Ullah et al. [16] applied a 1D-CNN model with a fully connected layer, two down sampling layers, two convolutional layers for arrhythmia classification. The 1D-CNN model was applied for feature extraction and the 2D-CNN model was applied for the classification process. The wavelet threshold method was applied to eliminate the noise from the signal. A gradient descent-based optimizer algorithm with a learning rate was applied for the classification process.

Essa et al. [17] applied the CNN-LSTM model to capture the temporal dynamics and local features in ECG data for arrhythmia classification. The higher-order statistics and RR intervals integrate the classical features to highlight abnormal heartbeats classes. Different sub-sampling datasets of highly imbalance distribution were used to create a bagging model for arrhythmia classification. Weighted loss function of each model was used to provide high weight for the model. The bagging model predictions of a feedforward fully connected network were used as meta-classifier. Yan and Zhang [18] applied a hybrid model to learn the deep-seated essential features and temporal correlation for arrhythmia classification. The bandstop filter and median filter were used to pre-process the ECG signal. Feature extraction and classification were integrated into one to avoid bias in the feature extraction process.

The recent research on arrhythmia classification uses the CPCS 2018 dataset for evaluation was reviewed below.

Tutuko et al. [19] applied CNN based end-to-end implementation for arrhythmia classification. A single learning system was used in the model that didn’t consider frequency sampling and signals lengths. Cloud-based deep learning model was used to perform classification of Atrial Fibrillation detection. The 1-D CNN model was used to perform the classification of arrhythmia in the input signal. Jo et al. [20] applied six deep learning models for feature extraction and an ensemble model for the classification of arrhythmia. The explainable Deep learning Model (XDM) was an ensemble tree Neural Network based model applied for the classification process. The developed model shows considerable performance in the classification of arrhythmia. Yoo et al. [21] applied CNN end-to-end model and the attention map was fine tuned to resemble Ground Truth label attention map. A regularization loss function was measured between the averaged map and attention map to fine tune based on objective function. Multi-loss optimization method was applied to explainability and multi-label subset accuracy to find unique features of the model. Li et al. [22] applied multi-label feature selection method and kernelized fuzzy rough sets to optimize ECG feature space and optimal feature subset. The model explores the correlation between the feature map and arrhythmia disease based on sparity constraints.

From the review of existing techniques, common limitations in existing arrhythmia classification techniques are imbalance data problem and overfitting problem. The imbalance data problem is some classes consists of less data instances and model requires more training data for effective classification. The overfitting problem is caused mostly in CNN based models due to generation of more features in the feature extraction process.

3. Proposed method

The MIT-BIH and CPCS 2018 dataset signals were used for the evaluation of the FCM-ETIFRST method in arrhythmia classification. Sliding window technique is used to segment the signal into 5 s window. The conventional feature extraction method and ResNet18-CNN feature extraction were applied. The FCM-ETIFRST model is used to select the features from extracted features from the model. The selected features are applied to MSVM to perform arrhythmia classification. The flow of FCM-ETIFRST-MSVM model in arrhythmia classification is shown in Fig. 1.

Figure 1.

Fuzzy C-Means (FCM) – Enhanced Tolerance-based Intuitionistic Fuzzy Rough Set Theory (ETIFRST) technique in arrhythmia classification.

CNN model applied with extra layers instead of feature selectin stage involves in creating overfitting problem due to the generation of more features in the feature extraction. Dropout technique can be applied to reduce overfitting problem and dropout technique randomly discard the features that doesn’t guarantee higher efficiency in classification. Feature Selection technique adaptively learns the features and select the relevant features for the classification that helps to improve the efficiency of the classification. This is better to apply the feature selection instead of applying extract layers in CNN for feature extraction due to adaptive learning of features.

Two common deep learning techniques for feature extraction are CNN based models and LSTM based models. CNN based models apply convolution filters in the signal to exploit spatial correlation and this is much suitable for audio and images than LSTM models. LSTM based models are effective in analysis the sequence of data and lower efficiency in exploit the spatial correlation compared to CNN.

3.1 Feature extraction

CNN based and conventional feature extraction methods were applied to extract the features from input signals.

3.1.1 Conventional feature extraction method

Hjorth Activity: Signal power is represented using an activity parameter that is time function variance, as given in Eq. (1). This activity denotes the power spectrum surface in the frequency domain.

$\displaystyle\textit{Activity}=\text{var}({y(t)})$ (1)

where the signal is denoted using $y(t)$ .

Hjorth Mobility: Mean frequency or power spectrum of standard deviation proportion are represented as mobility parameter. A first derivative variance of the square root of signal $y(t)$ divided by signal variance $y(t)$ , which is explained in Eq. (2).

$\displaystyle\textit{Mobility}=\sqrt{\frac{\text{var}\left({\frac{dy(t)}{dt}}% \right)}{\text{var}({y(t)})}}$ (2)

Hjorth Complexity: Frequency change is denoted using the complexity parameter. Signal’s similarity and a pure sine wave are compared using the parameter, where the value converges to 1 if signal is similar, as given in Eq. (3).

$\displaystyle\textit{Complexity}=\frac{\textit{Mobility}\left({\frac{dy(t)}{dt% }}\right)}{\textit{Mobility}({y(t)})}$ (3)

Mean Curve Length (MCL): Katz fractal dimension are measured using MCL and this measures EEG signals activity, as given in Eq. (4).

$\displaystyle CL[n]=\frac{1}{N}\mathop{\sum}\limits_{m=k-N+1}^{k}|{x[m]-x[{m-1% }]}|$ (4)

where epoch last sample is denoted as $k$ , the window length is denoted as $N$ , and EEG time series is denoted as $x[m]$ .

Mean Teager Energy (MTE): EEG research were widely carried out using MTE feature, as given in Eq. (5).

$\displaystyle\textit{MTE}[k]=\frac{1}{N}\mathop{\sum}\limits_{m=k-N+3}^{k}({x[% {m-1}]^{2}-x[m]x[{m-2}]})$ (5)

where epoch last sample is denoted as $k$ , the window length is denoted as $N$ , and EEG time series is denoted as $x[m]$ .

Zero Crossing Rate: The rate of signal changes from negative to zero to positive or positive to zero to negative is denoted as Zero-Crossing Rate (ZCR), as in Eq. (6).

$\displaystyle\textit{ZCR}=\frac{1}{T-1}\mathop{\sum}\limits_{t=1}^{T-1}1_{R<0}% ({S_{t}S_{t-1}})$ (6)

where indicator function is denoted as $1_{R<0}$ and length of the signal is denoted as $S$ .

3.1.2 ResNet18 – convolutional neural network

Two-dimensional signals are handled using Convolutional Neural Network (CNN) which is based on deep learning techniques and a recent neural network. Fully Connected Layers (FCLs), Pooling Layers (PLs), and Convolutional Layers (CLs) are present in the CNN model. CNN model shows significant performance improvement than traditional AI methods such as naive Bayesian classifier, Decision Tree (DT), and Support Vector Machine (SVM). CNNs have the advantage of learning features from data during training and significantly reduces the time required for feature design engineering i.e., to distinguish features/biomarkers [23, 24, 25].

CNN most important procedure is convolution and CL is the most important layer that consists of 2D convolution process of input and forward pass the kernels. The weights of each CL kernels are randomly initialized and updated at each iteration using network training of loss function. The kernel final learnt detect some types of patterns in input signals.

Three steps of CNN models are convolution, stack and Non-Linear Activation Function (NLAF). Consider $X$ input matrix and CL output $O$ , there exists kernels set $F_{j}$ , $\forall j\in[{1,\cdots,J}]$ , $C(j)$ convolution output after step 1 is given in Eq. (7).

$\displaystyle C(j)=X\otimes F_{j},\forall j\in[{1,\ldots,J}]$ (7)

where convolution operation is denoted as $\otimes$ , which inputs and filter dot product. Activation maps $C(j)$ are piled to create 3D activation map, as given in Eq. (8).

$\displaystyle D=S({C(1),\ldots,C(J)})$ (8)

where total number of filters are denoted as $J$ , and the channel direction of pile operation is denoted as ${\cal S}$ . The 3D activation map $D$ is applied to NLAF and the final activation map provides output. Three important matrixes (filters, input and output) are considered in Eq. (9).

$\displaystyle S(x)=\left\{{{\begin{array}[]{ll}{V_{1}\times Q_{1}\times H_{1}}% &{x=X}\\ {V_{K}\times Q_{K}\times H_{K}}&{x=F_{j},\forall j\in[{1,\ldots,J}]}\\ {V_{0}\times Q_{O}\times H_{O}}&{x=O}\\ \end{array}}}\right.$ (9)

where activation map channels, width, and height size are denoted as three variables of ( $V, Q, H$ ), respectively. The input, filter and output are denoted in subscripts as $I$ , $K$ , and $O$ , respectively. Two equalities are present: (i) $H_{I}=H_{K}$ , input channel $H_{I}$ equals to filter channel $H_{K}$ , and (ii) $H_{O}=J$ , denotes output channel $H_{O}$ equals to filters $J$ .

Padding is denoted as $B$ , the stride is denoted as $A$ , ( ${V_{O},Q_{O},H_{O}}$ ) values are given in Eqs (10) and (11).

$\displaystyle V_{O}=1+f_{fl}[{({2\times B+V_{1}-V_{K}})/A}]$ (10) $\displaystyle Q_{O}=1+f_{fl}[{({2\times B+Q_{1}-Q_{K}})/A}]$ (11)

where floor function is denoted as $f_{fl}$ . The Rectified Linear Unit (ReLU) is selected as NLAF $\sigma$ , as given in Eq. (12).

$\displaystyle\sigma_{\textit{ReLU}}({d_{ij}})=\textit{ReLU}({d_{ij}})=\max({0,% d_{ij}})$ (12)

where activation map $D$ element is denoted as $d_{ij}\in D$ . ReLU is more commonly applied NLAF than sigmoid and hyperbolic tangent, as given in Eqs (13) and (14).

$\displaystyle\sigma_{HT}({d_{ij}})=\tanh({d_{ij}})=({e^{d_{ij}}-e^{-d_{ij}}})/% ({e^{d_{ij}}+e^{-d_{ij}}})$ (13) $\displaystyle\sigma_{SM}({d_{ij}})=({1+e^{-d_{ij}}})^{-1}$ (14)

The ReLU main advantage is its improved gradient propagation, i.e., compared to $\sigma_{SM}$ . Fewer vanishing gradient problems is present in ReLU and ReLU is one-sided compared to $\sigma_{HT}$ . The architecture of CNN is shown in Fig. 2.

Figure 2.

Convolutional neural network architecture.

3.2 Fuzzy C-Means (FCM) – Enhanced Tolerance-based Intuitionistic Fuzzy Rough Set Theory (ETIFRST) feature selection

The FCM-ETIFRST feature selection method is applied to extracted features to select relevant features for arrhythmia classification.

3.2.1 Fuzzy C-Means

Feature selection is based on Fuzzy C-Means clustering technique [26, 27, 28]. The FCM method has the advantage of producing better results for overlapped datasets than the k-means method. The data point is assigned membership to every cluster to form the appropriate cluster. The data point is applied with membership based on the distance of the data point and cluster centre $c$ . If more data is near to $c$ and the cluster has more data point membership.

The estimated membership is increased for every iteration. An enhanced fuzzy C-means algorithm is implemented in the proposed method. The algorithm is given as follows:

Step 1: Clusters number $c$ varies from 2 to $c_{\max}$ . A certain value $c$ is considered and initial class prototypes is selected and use $\epsilon>0$ .

Step 2: Signal $\varsigma$ of new linearly weighted sum in terms of $\varsigma_{k}$ using Eq. (15).

$\displaystyle\varsigma_{k}=\frac{1}{1+\alpha}\left({x_{k}+\left({\frac{\alpha}% {N_{R}}}\right)\mathop{\sum}\limits_{j\in N_{k}}x_{j}}\right)$ (15)

where $k^{\text{th}}$ pixel gray value of $\varsigma$ are $\varsigma_{k}$ and $x_{k}$ (8-bit resolution is usually encoded for gray value) and $k^{\text{th}}$ pixel gray value, respectively. The neighbour $x_{j}$ , the set of neighbour has $N_{k}$ present in window nearby $x_{k}$ . The mean-filtered pixel value is $\mathop{\sum}\limits_{j\in N_{k}}x_{j}$ where neighbour terms effect controls $\alpha$ with a value approximately near to 1.

Step 3: Signal matrix $\varsigma$ is updated using Eq. (16).

$\displaystyle f_{il}=\frac{({\varsigma_{l}-v_{i}})^{\frac{-2}{s-1}}}{\mathop{% \sum}\nolimits_{j=1}^{c}({\varsigma_{l}-v_{j}})^{\frac{-2}{s-1}}}$ (16)

The $i^{\text{th}}$ cluster prototype is $v_{i}$ and $f_{il}$ is gray value $l$ of fuzzy membership that is respect to cluster $i$ . The $l$ value varies from 1 to the number of gray levels denoted as $d$ (gray level has a maximum value of 256 levels) of the signal and each fuzzy membership of $s$ weighted component parameter that estimates the final classification of fuzziness.

Step 4: Prototype $v_{i}$ is calculated using Eq. (17).

$\displaystyle v_{i}=\frac{\mathop{\sum}\nolimits_{i=1}^{d}x_{l}f_{il}^{s}% \varsigma_{l}}{\mathop{\sum}\nolimits_{i=1}^{d}x_{l}f_{il}^{s}}$ (17)

Convergence criteria are measured as $|{v_{\textit{new}}-v_{\textit{old}}}|<\epsilon$ by repeating step 3 and 4, cluster prototypes holds vectors $v$ that is represented as $v=[{v_{1},v_{2}\ldots v_{c}}]$ .

3.2.2 Enhanced fuzzy rough set feature selection

Enhanced fuzzy rough set feature selection involves in applying non-membership function and hesitance degree to select unique set of features from the signal. The non-membership function helps to select the features to distinguish between the classes and hesitance degree helps to differentiate between more similar classes. This technique helps to solve imbalance data problem and overfitting problem by selecting unique features for classification.

The FCM has a wide range of applications and is significantly applied in numerous fuzzy clustering methods. Every sample point of membership degree to the class centre is used as objective function optimization.

Euclidean distance is applied for the objective function of sample point and clustering centre. Solving non-similarity index value function is the minimum value of every clustering centre. The generalization is given in Eq. (18).

$\displaystyle J({U,c_{1},c_{2},\ldots,c_{c}})=\mathop{\sum}\limits_{i=1}^{c}J_% {i}=\mathop{\sum}\limits_{i=1}^{c}\mathop{\sum}\limits_{j}^{n}u_{ij}^{m}d_{ij}% ^{2}$ (18)

where weighted index number is denoted as $m$ , the $j^{\text{th}}$ sample point of $i^{\text{th}}$ clustering centre of Euclidean distance is $d_{ij}=k_{ci}-x_{jk}$ , the fuzzy set of clustering centre, and $u_{ij}$ is between 0 and 1. The constraint formula of Lagrangian multiplier is constructed based on derivate of input parameters in Eqs (19) and (20) to reach the minimum.

$\displaystyle c_{i}=\frac{\mathop{\sum}\nolimits_{j=1}^{n}u_{ij}^{m}x_{j}}{% \mathop{\sum}\nolimits_{j=1}^{n}u_{ij}^{m}}$ (19) $\displaystyle\mu_{ij}=\frac{1}{\mathop{\sum}\nolimits_{k=1}^{c}\left({\frac{d_% {ij}}{d_{kj}}}\right)^{\frac{2}{m-1}}}$ (20)

The FCM output are centres $c$ and membership matrix $U$ . Every object degree contains $U$ belongs to each centre.

Fuzzy rough set of lower approximation is given in Eq. (21).

$\displaystyle\textit{sim}_{a}({x_{i},x_{j}})=1-\sqrt{\alpha({\mu_{a}({x_{i}})-% \mu_{a}({x_{j}})})^{2}+\beta({v_{a}({x_{i}})-v_{a}({x_{j}})^{2}+\gamma({\pi_{a% }({x_{i}})-\pi_{a}({x_{j}})^{2}})})}$ (21)

where object $x_{i}$ of hesitancy degree, non-membership, and membership are denoted as $\pi_{a}({x_{i}})$ , $\upsilon_{a}({x_{i}})$ and $\mu_{a}({x_{i}})$ , respectively. The weighted factors are $\alpha$ , $\beta$ and $\gamma$ .

Each pixel membership degree is normalized and initialized as in Eq. (22).

$\displaystyle\mu_{D}({x_{ij}})=\frac{x_{ij}-({x_{ij}})_{\min}}{({x_{ij}})_{% \max}-({x_{ij}})_{\min}}$ (22)

where signal value of minimum and maximum intensity is denoted as $({x_{ij}})_{\max}$ and $({x_{ij}})_{\min}$ . Complexity is reducing in normalization that calculates and ranges is present between 0 to 1.

Non-membership value is present in the new method in uncertainty presence. A high grade of certainty is measured based on observations when membership value is near to 0 or 1 and membership value is near to 0.5 for high grade of uncertainty. Non-membership value is measured in Eq. (23).

$\displaystyle v_{D}({x_{ij}})=({1-\mu_{D}({x_{ij}})})\left({\exp\left({\frac{-% \mu_{D}({x_{ij}})}{a\sigma}}\right)}\right)^{\frac{1}{a}}$ (23)

where ( $\mu_{D}({x_{ij}})$ ) membership value measures standard deviation, is in the range of 0.39–0.41. Hesitation degree is measured using $\pi_{D}({x_{ij}})=1-\mu_{D}({x_{ij}})-v_{D}({x_{ij}})$ .

Every feature of fuzzy clustering gets every object membership degree, as given in Eq. (24).

$\displaystyle\mu R_{a}(x)=U_{\textit{FCM}(a)}[x]$ (24)

Model equality is based on equivalence relations; approximate similarity or equality is measured based on fuzzy equivalence. Fuzzy equivalence relation $R$ is used, as in Eq. (25).

$\displaystyle R({x,y})=\frac{a-a|{x-y}|+b\min({x,y})}{a-({a-1})|{x-y}|+b\min({% x,y})}$ (25)

The size of the opening on one side is denoted as value $b$ . Two object similarity is used to describe the function, selects $b$ equal to 0 to make sure function is a balance of two objects if small values or great values.

3.3 Multi-class support vector machine

Support Vector Machine (SVM) is a supervised learning machine for the classification process [29, 30]. SVM is viewed as binary classifier and data of decision boundary is used to classify patterns of two alike classes. A distance between optimal separating hyperplane is denoted as margin $1/|{|w|}|$ and instances are present in either side, as this is important for SVM. Support vectors are vectors lie on this margins and solution is represented as a linear combination in a linear separable case of only support vectors ignore other data. The SVM model complexity is not affected number of selected features.

SVM method is based on input data that is linearly non-separable projection to high-dimensional feature space and select an optimal hyperplane in feature space of maximum possible margin. Training set labelled as $\{{X_{i},y_{i}}\}$ , $i=1,2,\ldots l$ , number of training samples is denoted as $l$ and finding optimal hyperplane based on weight vector $w$ and bias $b$ , as in Eq. (3.3).

$\displaystyle\min\left({\frac{1}{2}}\right)|{|w|}|^{2}+C\mathop{\sum}\limits_{% i=1}^{l}\xi_{i}$

(26) $\displaystyle\text{subject to }y_{i}({w^{T}x_{i}+b})\geqslant 1-\xi_{i}\text{ % and }\xi_{i}\geqslant 0.$

where class label $y\in\{{-1,1}\}$ is based on the input feature vector of $x$ . The margin maximize between two classes is provided in Eq. (3.3). The training errors are reduced based on a large slack variable $\xi_{i}$ of penalizing solutions with penalty cost $C$ . Margin is minimized by larger $C$ value and hard to ignore constraints. The kernel trick is given in Eq. (3.3).

$\displaystyle\max\mathop{\sum}\limits_{i}\lambda_{i}-\frac{1}{2}\mathop{\sum}% \limits_{i}\mathop{\sum}\limits_{j}\lambda_{i}\lambda_{j}y_{i}y_{j}K({X_{i},X_% {j}})$ (27) $\displaystyle\text{such that }\mathop{\sum}\limits_{i}\lambda_{i}y_{i}=0\text{% and }0\leqslant\lambda_{i}\leqslant C,i=1,\ldots,l\text{ and }\xi_{j}% \geqslant 0.$

where Lagrangian multiplier is denoted as $\lambda_{i}$ . The linear equality constraints of dual problem are solved using a simple sequential minimal optimization. The kernel function $K({x_{i},x_{j}})$ is applied for mapping process and most commonly used kernels are

(1)
Linear Kernel: $K({x_{i},x_{j}})=x_{i}^{T}x_{j}$
(2)
Polynomial: $K({x_{i},x_{j}})=({\gamma x_{i}^{T}x_{j}+r})^{d},\gamma>0$
(3)
Gaussian Radial Basis function: $K({x_{i},x_{j}=\exp({-\gamma|{x_{i}^{T}-x_{j}}|^{2}})})$
(4)
Sigmoid: $K({x_{i},x_{j}})=\mbox{tanh}({\gamma x_{i}^{T}x_{j}+r})$

SVM classifier solution for an unknown feature vector $X$ is discussed as follows.

An SVM model is successfully applied for multi-class classification based on binary SVMs group. The One against one method performs pairwise classification based on $k({k-1})/2$ binary model for $k$ -class problem. Each model is provided in Eq. (28).

$\displaystyle f(X)=\text{sign}\left({\mathop{\sum}\limits_{i}^{l}\lambda_{i}y_% {i}K({X_{i},X})+b}\right),f(X)\to\{{-1,1}\}$ (28)

A $k$ -class problem of binary models $k({k-1})/2$ is constructed for pairwise classification based on One Against One (OAO) method. The data of two unlike classes in each model is used and k-class classification problem is converted into $k({k-1})/2$ different tasks. Maximum voting is used for test data class prediction.
4. Simulation setup

Dataset used to evaluate FCM-ETIFRST-MSVM model for arrhythmia classification and parameter settings of the model were described in this section.

Datasets: FCM-ETIFRST-MSVM model is evaluated using two datasets such as MIT-BIH [31] and CPCS 2018 [32]. MIT-BIH dataset consists of normal, and Ventricular Fibrilation classes of ECG signal with a sampling frequency of 360 Hz. The classes in CPSC 2018 datasets are ST-segment Elevated (STE), ST-segment Depression (STD), Premature Ventricular Contraction (PVC), Premature Atrial Contraction (PAC), Right Bundle Branch Block (RBBB), Left Bundle Branch Block (LBBB), First-degree Atrioventricular Block (I-AVB), Atrial Fibrillation (AF), Ventricular Fibrillation (VF) and Normal. The individuals of 45 ECG of 19 females and 26 males were presented in the dataset. The sample signals from MIT-BIH dataset is shown in Figs 3–5.

Figure 3.

Sample signal from MIT-BIH dataset.

Figure 4.

Lead I sample signal.

Figure 5.

Lead II sample signal.

Parameter settings: CNN parameter settings are 20 epochs, 20 validation frequency, 0.01 learning rate, stochastic gradient descent optimizer and ResNet 18 architecture. SVM parameter settings as true standardize, auto kernel scale, and linear kernel function. The CNN extracts 512 features, and the conventional extracts 56 features, totally of 568 features are extracted. The FCM-ETIFRST model selects 506 features from 568 features.

Metrics: Accuracy, Sensitivity, Specificity, Precision and Matthews correlation coefficient (MCC), as given in Eqs (29)–(33).

$\displaystyle\textit{Accuracy}(\%)=\frac{TP+TN}{TP+TN+FP+FN}\times 100$ (29) $\displaystyle\textit{Sensitivity}(\%)=\frac{TP}{TP+FN}\times 100$ (30) $\displaystyle\textit{Specificity}(\%)=\frac{TN}{TN+FP}\times 100$ (31) $\displaystyle\textit{Precision}(\%)=\frac{TP}{TP+FP}\times 100$ (32) $\displaystyle\textit{MCC}=\frac{TP\times TN-FP\times FN}{\sqrt{({TP+FP})({TP+% FN})({TN+FP})({TN+FN})}}$ (33)

System Configuration: RAM is 16 GB, processor is Intel i7, 6 GB RAM and Windows 10 OS. MATLAB 2020b version was used to implement the model.

5. Results

The FCM-ETIFRST method is compared with various classifiers and feature selection techniques on MIT-BIH dataset. The FCM-ETIFRST also evaluated with various k-fold validation for arrhythmia classification.

Table 1
Fuzzy C-Means (FCM) – Enhanced Tolerance-based Intuitionistic Fuzzy Rough Set Theory (ETIFRST) performance on various classifiers

Methods	Accuracy (%)	Sensitivity (%)	Specificity (%)	Precision (%)	MCC (%)
KNN	88.99	87.53	89.44	88.91	86.50
RF	91.22	92.38	93.11	91.01	90.24
DE	89.65	89.68	88.28	89.33	87.21
DNN	49.26	49.63	50.81	50.74	48.76
MSVM	98.95	99.49	99.49	98.45	97.99

Figure 6.

Accuracy and sensitivity for various classifiers.

Figure 6 and Table 1 show the performance of the FCM-ETIFRST method for various classifiers such as Multi-Class Support Vector Machine (MSVM), Deep Neural Network (DNN), Decision Tree (DT), Random Forest (RF), and K-Nearest Neighbours (KNN). The DNN and RF have lower efficiency due to overfitting problem in arrhythmia classification. The DE has imbalance data problem and KNN has outlier sensitivity that degrades the performance. MSVM has the advantage of handling high-dimensional data and CNN extracted features helps to overcome imbalance data problem. The FCM-ETIFRST method selects the unique features to represents the class that solves the problem of imbalance and overfitting. Modified Non-membership function helps to provide exploitation and modified membership function performs exploration. Similarity measure helps to maintain the exploration and exploitation of the feature selection process. MSVM shows a higher sensitivity than other classifiers due to its efficiency in handling the features.

Table 2

Feature selection method comparison

Methods	Accuracy (%)	Sensitivity (%)	Specificity (%)	Precision (%)	MCC (%)
PSO	85.89	84.69	86.14	80.59	86.38
GWO	83.33	84.23	84.06	83.24	86.00
ACO	96.17	92.03	94.83	97.08	97.54
WOA	95.31	90.67	96.00	94.04	96.30
Proposed FCM-ETIFRST	98.95	99.49	99.49	98.45	97.99

Figure 7.

Accuracy and sensitivity of various feature selection methods.

Figure 7 and Table 2 show various feature selection models such as Whale Optimization Algorithm (WOA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Grey Wolf Optimization (GWO) were applied for arrhythmia classification. Modified Non-membership function increases the exploration and Modified membership function increases the exploitation in feature selection. Similarity measure in FCM-ETIFRST method balance the exploration-exploitation and overcome trap into local optima. The existing feature selection methods have either struck into local or global features in the feature selection process. The existing feature selection methods have lower sensitivity due to their poor convergence in feature selection. The FCM-ETIFRST method has a sensitivity of 99.49% and ACO method has a 92.03% sensitivity. The FCM-ETIFRST shows significant improvement in the sensitivity measure.

Table 3

K-fold validation performance analysis

K-fold values	Accuracy (%)	Sensitivity (%)	Specificity (%)	Precision (%)	MCC (%)
4-fold	97.99	97.08	97.55	97.19	96.65
5-fold	98.95	99.49	99.49	98.45	97.99
7-fold	97.83	96.09	97.19	97.95	96.74
9-fold	97.47	96.28	96.15	96.37	95.45
10-fold	98.67	95.47	96.33	95.93	90.61

Figure 8.

K-fold validation comparison.

The FCM-ETIFRST-MSVM model is evaluated for various k-fold validation in arrhythmia classification, as given in Fig. 8 and Table 3. The FCM-ETIFRST method shows higher performance in 4-fold to 10-fold cross validation. The performance reduction in 7-fold to 10-fold validation is due to reduces in the number of training data. The FCM-ETIFRST-MSVM model has 98.97% accuracy in 5-fold cross validation and 98.67% accuracy in 10-fold cross validation.

Table 4

Feature selection and classifier performance on MIT-BIH dataset

Classifiers	Feature selection	Accuracy (%)	Sensitivity (%)	Specificity (%)	Precision (%)	MCC (%)
KNN	PSO	77.76	76.46	78.09	75.14	77.18
	GWO	75.90	75.75	76.17	73.66	74.64
	ACO	80.62	79.01	77.94	81.04	82.86
	WAO	83.72	84.19	82.85	83.15	85.85
	Proposed	88.99	87.53	89.44	88.91	86.50
RF	PSO	83.18	82.74	81.38	79.77	83.23
	GWO	85.58	84.94	88.97	89.42	85.26
	ACO	89.70	86.63	81.11	86.23	89.19
	WAO	88.05	87.96	87.18	86.85	88.54
	Proposed	91.22	92.38	93.11	91.01	90.24
DT	PSO	75.78	74.88	72.07	73.64	76.28
	GWO	79.59	78.93	76.64	73.97	80.54
	ACO	87.75	86.37	84.14	83.55	88.41
	WAO	85.65	84.89	87.69	89.54	82.07
	Proposed	89.65	89.68	88.28	89.33	87.21
DNN	PSO	50.00	49.00	46.00	52.00	51.00
	GWO	45.00	44.00	47.00	49.00	42.00
	ACO	52.00	54.00	51.00	55.00	56.00
	WAO	48.00	49.00	51.00	47.00	46.00
	Proposed	49.26	49.63	50.81	50.74	48.76
MSVM	PSO	85.89	84.69	86.14	80.59	86.38
	GWO	83.33	84.23	84.06	83.24	86.00
	ACO	96.17	92.03	94.83	97.08	97.54
	WAO	95.31	90.67	96.00	94.04	96.30
	Proposed	98.95	99.49	99.49	98.45	97.99

The classifier with various feature selection performance is evaluated and compared with other techniques, as shown in Table 4. This shows that FCM-ETIFRST-MSVM feature selection and MSVM classifier shows higher performance in the arrhythmia classification than existing methods. The FCM-ETIFRST-MSVM model has advantage of selects unique set of features due to non-membership function and hesitance degree. The DNN model has overfitting problem and RF has instable performance in the arrhythmia classification.

Table 5

Feature Extraction performance on MIT-BIH dataset for arrhythmia classification

Feature extraction	Accuracy (%)	Sensitivity (%)	Specificity (%)	Precision (%)	MCC (%)
Alexnet	83.49	79.99	81.22	82.17	80.02
Googlenet	85.78	81.08	79.77	86.89	84.42
VGG16	95.27	96.33	95.37	94.95	93.12
VGG19	93.97	92.27	94.15	95.52	93.95
Proposed (Resnet18)	98.95	99.49	99.49	98.45	97.99

Table 6

Comparative analysis on MIT-BIH dataset

Methods	Accuracy (%)	Sensitivity (%)
Wavelet-PNN [11]	92.75	–
AlexNet [12]	94.7	90.88
Morphological features [13]	97.7	–
Focal Loss – CNN [14]	98.66	76.71
CNN [15]	98.84	98.83
CNN [16]	97.38	–
CNN-LSTM [17]	95.81	–
Proposed method	98.95	99.49

Figure 9.

Area Under the Curve of proposed model on MIT-BIH dataset.

Figure 10.

Comparative analysis of MIT-BIH dataset.

Various deep learning techniques are applied as feature extraction and compared with proposed ResNet18 model, as shown in Table 5. The FCM-ETIFRST-MSVM and ResNet18 model has higher performance compared with existing methods. The ResNet18 model architecture extracts the relevant features from the input signal. Existing deep learning models have overfitting problem that degrades the performance of the classification.

The Area Under the Curve (AUC) of FCM-ETIFRST-MSVM and ResNet18 for arrhythmia classification on MIT-BIH dataset is shown in Fig. 9. The point on the Receiver Operating Characteristic (ROC) curve corresponds to have an equal probability of miss-classifying a positive or negative sample. From Fig. 9, it clearlyt shows that the FCM-ETIFRST-MSVM and ResNet18 model shows 0.9895 AUC for the classification which indicates that TPR of the model significantly increases for the arrhythmia classification.

5.1 Comparative analysis

The FCM-ETIFRST-MSVM method is compared with existing research models in arrhythmia classification in MIT-BIH and CPCS 2018 dataset. The FCM-ETIFRST-MSVM method and existing methods were compared on the MIT-BIH dataset in Fig. 10 and Table 6. This shows FCM-ETIFRST-MSVM model has higher efficiency due to its modified non-membership and membership function providing efficient exploration-exploitation in feature selection. The existing models have imbalance data problems and overfitting problems in the classification performance.

Table 7
Comparative analysis on CPCS 2018 dataset

Methods	Accuracy (%)	Sensitivity (%)
CNN [19]	96.36	93.65
XDM [20]	93.6	79.3
CNN [21]	68.9	–
Proposed Method	98.45	99.36

The FCM-ETIFRST-MSVM and existing models were evaluated on CPCS 2018 dataset, as given in Fig. 11 and Table 7. The existing models have limitations of overfitting that degrades the performance of arrhythmia classification. The FCM-ETIFRST-MSVM model effectively balances the exploration-exploitation that improves the efficiency of classification. The Proposed method has achieved the accuracy of 98.45%, CNN [21] model has 68.9% accuracy, and XDM [20] model has 93.6% accuracy.

Figure 11.

Comparative analysis of CPCS 2018 dataset.

6. Conclusion

Diagnosis of arrhythmia is mainly based on ECG signals due to its capacity to analyze the abnormal activity in the heartbeat. The existing researches in arrhythmia classification have limitations of imbalance and overfitting problem. This research applies FCM-ETIFRST-MSVM model to improve arrhythmia classification efficiency and overcome the overfitting problem. The modified Non-membership function improves the exploitation efficiency and the modified membership function improves exploration efficiency in the feature selection process. The MSVM model has higher efficiency in classification than DNN due to its capacity to handle high-dimensional data. The FCM-ETIFRST model has higher efficiency in feature selection due to its advantage in balancing the exploration-exploitation in feature selection which helps to improve convergence. The FCM-ETIFRST-MSVM model has higher efficiency in arrhythmia classification on MIT-BIH and CPCS 2018 dataset. The FCM-ETIFRST-MSVM model has 99.49% sensitivity and CNN has 98.83% sensitivity on the MIT-BIH dataset. The FCM-ETIFRST-MSVM has 99.36% sensitivity and XDM has 79.3% sensitivity on arrhythmia classification on CPCS 2018 dataset. The future work of the FCM-ETIFRST-MSVM model involves in improving the model to train in small training dataset.

Funding

This research received no external funding.

Data availability

The datasets generated during and/or analysed during the current study are available in the MIT-BIH/CPSC 2018 repository, https://archive.physionet.org/cgi-bin/atm/ATM, http://2018.icbeb.org/Challenge.html.

Footnotes

Conflict of interest

The authors declare that they have no conflict of interest.

Author’s Bios

	Miss Rajeshwari M R is currently as an Assistant Professor in the department of Computer Science and Engineering at Ghousia College of Engineering, Ramanagara, Bangalore, India. She received her M. Tech in Computer Science and Engineering from the University of VTU in 2007, Belgaum, India.
	Dr Kavitha K S is currently as a Professor in the department of Computer Science and Engineering at Global Academy of Technology, Bangalore, India. She received her Ph.D in Data Mining from the University of Anna in 2015, Chennai, India.

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ACO	Ant Colony Optimization
AF	Atrial Fibrillation
AUC	Area Under the Curve
BPNN	Back Propagation Neural Network
CL	Convolutional Layer
CNN	Convolution Neural Network
DNN	Deep Neural Network
DT	Decision Tree
ECG	Electrocardiogram
ETIFRST	Enhanced Tolerance-based Intuitionistic Fuzzy Rough Set Theory
FCL	Fully Connected Layer
FCM	Fuzzy C MeansC-Means
GWO	Grey Wolf Optimization
I-AVB	First-degree Atrioventricular Block
KNN	K-Nearest Neighbours
LBBB	Left Bundle Branch Block
MCC	Matthews Correlation Coefficient
MCL	Mean Curve Length
MSVM	Multi-class Support Vector Machine
MTE	Mean Teager Energy
NLAF	Non-Linear Activation Function
OAO	One Against One
PAC	Premature Atrial Contraction
PL	Pooling Layer
PNN	Probabilistic Neural Network
PSO	Particle Swarm Optimization
PVC	Premature Ventricular Contraction
RBBB	Right Bundle Branch Block
RF	Random Forest
RNN	Recurrent Neural Networks
ROC	Receiver Operating Characteristic
STD	ST-segment Depression
STE	ST-segment Elevated
VF	Ventricular Fibrillation
WOA	Whale Optimization Algorithm
XDM	Explainable Deep learning Model
ZCR	Zero-Crossing Rate

Enhanced tolerance-based intuitionistic fuzzy rough set theory feature selection and ResNet-18 feature extraction model for arrhythmia classification

Abstract

Keywords

1. Introduction

3. Proposed method

3.1.1 Conventional feature extraction method

3.2.1 Fuzzy C-Means

Table 1 Fuzzy C-Means (FCM) – Enhanced Tolerance-based Intuitionistic Fuzzy Rough Set Theory (ETIFRST) performance on various classifiers

Table 7 Comparative analysis on CPCS 2018 dataset

Funding

Data availability

Footnotes

Conflict of interest

Author’s Bios

References

Table 1
Fuzzy C-Means (FCM) – Enhanced Tolerance-based Intuitionistic Fuzzy Rough Set Theory (ETIFRST) performance on various classifiers

Table 7
Comparative analysis on CPCS 2018 dataset