NEURAL NETWORKS AND SVM FOR HEARTBEAT CLASSIFICATION

Malika-Djahida Kedir-Talha and Saliha Ould-Slimane

USTHB, Faculty of electronics and informatics, Laboratory of instrumentation, Bp32, Bab-Ezzouar, 16111, Algiers, Algeria

ABSTRACT

The diagnosis of cardiac dysfunctions requires the analysis of long-term ECG signal recordings, often containing hundreds to thousands of heartbeats. The purpose of this work is to propose a diagnostic system for modelling and classification of heartbeat, by use of time features and Support vector machines (SVM) classification algorithm. Neural Networks learning allow us to select a features of each heart beat on the basis of Generalized Orthogonal Forward Regression (GOFR) algorithm and a library of 132 Gaussians with different standard deviations and different means, each beat is represented by five Gaussians with different amplitudes. The parameters of this system are determined and its performance is evaluated for the MIT-BIH arrhythmia database. For a database of 364 normal heartbeats and 1148 abnormal heartbeats, we apply the SVM algorithm with Radial Basis Function kernel. Our results demonstrate that the testing performance of the neural network and SVM diagnostic system is found to be very satisfactory with a recognition rate of 99.67%.

1. INTRODUCTION

The medical monitoring is especially dedicated to patients whose disease may progress rapidly and present substantial risks. In cardiology, with monitoring of electrocardiogram ECG signal, it is possible to prevent a heart attack. This constant monitoring, can help physicians and to overcome the defect of human supervision (lack of staff, distraction by other clinical activities) and reassures patients. As it meets the needs of medical surveillance of persons at risk for heart attacks without requiring a heavy and costly hospital management.

In recent years, many algorithms have been developed for the detection and classification of ECG signals. Artificial Neural Network (ANN) is a conventional classifier used for ECG arrhythmias classification. The objective of these researches on ECG arrhythmias classification is the improvement of performance of Artificial Neural Network by application of various feature extraction techniques [1].

Discrete wavelet transform is used to improve the performance and accuracy of MLP with training algorithm and also compared with other feature extraction and data reduction methods [2].

Also an ECG beat classification system based on DWT and probabilistic neural network (PNN) is proposed to discriminate six ECG beat types [ 3].

SVMs are also applied for ECG signal analysis and arrhythmia classification, where the QRS detection is accomplished by using some other technique [4-5].

In this study, we propose a set of methods to design a system that performs real-time from biomedical ECG signal extraction on-line information that will help establish a medical diagnostic aid.

This paper describes an automatic classification by an extraction of features of electrocardiographic recordings (ECGs), through the combined use of a machine-learning algorithm termed Generalized Orthogonal Forward Regression (GOFR) and a supervised classification with SVM algorithm.

2. BANK LEARNING

The ECGs signals on which we will make our survey counts about ten records with two derivations, excerpts from Physio Bank data bases, developed largely by the Institute of Technology of the Massachusetts (MIT) and the Hospital Beth Israël of Boston (BIH). It is constituted by a set of ECGs records including one or several signals digitized and a set of annotations of beating.

Records have been digitized on 360 samples/second for each channel with the resolution of 11 bits on a range of 10 mVs. Two cardiologists or more annotated every disk independently.

For each recording of 10s, our first task will be to eliminate the base line and make cutting of ECG signals in heartbeats. We begin by applying the Tompkins algorithm [6]. In basis of a series of filters, this algorithm will detect the QRS complex. After extraction of the RR interval during the earlier phase, we detect the T wave, In order to achieve the cutting into heartbeat.

Our bank of learning consists of 364 normal heartbeats and 1148 abnormal heartbeats (Arrhythmia, Supra-ventricular Arrhythmia and Malignant-ventricular Ectopy). We have four types of beats.

The 11th International Conference on Information Sciences, Signal Processing and their Applications: Main Tracks

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For developing SVM learning, 1208 heartbeats were randomly taken from 1512 beats for training and 300 beats for testing our proposed classifier.

3. METHODS

For a given ECG signal, heartbeats of the ECG signal are detected and then each heartbeat will be modeled by Generalized Orthogonal Forward Regression (GOFR). The parameters obtained for each Gaussian function are used as features.

3.1. Generalized Orthogonal Forward Regression

For each beat, it is necessary to extract the features. Our study was performed on a time features [7] . With a learning neural network, we model the heartbeat by a set of Gaussians with different, amplitudes, averages and standards deviation. We will note the heartbeat s(t) and y(t) its model

( )∑

=

−−=

N

i i

ii

tAty

12

2

)2

exp()(σμ

Ai the weighting of the ith Gaussian. µi the average of the ith Gaussian σi the standard deviation of the ith Gaussian. N number of Gaussian

We applied the algorithm, Generalized Orthogonal Forward Regression (GOFR) whose steps are as follows:

• Construction of the library • Selection of the most relevant Gaussian Bi • Optimization of Gaussian parameters • Orthogonalization of the heartbeat • Orthogonalization of the library

3.1.1 Construction of the library For a heartbeat of Np samples, B is the following set:

( )

[ ][ ]

⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪

⎬

⎫

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎨

⎧

∈∈

=

=

= +

max

1

...12,0

2

2

,

kki

N

Ni

B

B

k

kp

i

kp

i

iii

σ

μ

σμ

Bi(µi,σi) , Is the Gaussian function of standard

deviation (σi) and average (μi). Nb is the number of Gaussian of the library B. Kmax =6 we chose it in order to have a rich library with Nb=132 Gaussians [8].

The Gaussians which constitute the library B with the different centred widths on different temporal sites are represented in the figure 1. Each graph represents the family of Gaussians which have the same width and sweeps the 342 points .

Figure 1. Gaussians of the library

The library will be constituted by the family of Gaussians found. We notice that {Ai}, the amplitudes of the preset Gaussian in the library B, are not calculated yet and will be deducted during the successive iterations of GOFR algorithm.

This method consists in initializing the parameters (standard deviations, averages and amplitudes of each Gaussian) with values close to the optimal values. This algorithm is used to find the five most relevant Gaussians which are selected from the library and adjusted with the beat model [9].

3.1.2 Selection of the Gaussian At each step, the algorithm selects the most relevant

Gaussian of the library. As previously, the index mi of the selected Gaussian

is that of Bik for which the absolute value of the cosin

with the heartbeat ECG signal Si is maximal

[ ] ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⋅=

∈ ik

i

ik

i

Nki BS

BSMAXh

b...1 (3)

S1 is the heartbeat signal S at the first step.

3.1.3 Optimization After selecting the first most relevant Gaussian Bm1 , the next step is to optimize the Gaussian parameters. The optimization of Bm1 is the minimization of the mean square error J between the initial heartbeat S1 and the first function Bm1 with respect to the standard deviation σm1 , the temporal position µm1 and the amplitude Am1

E1(k)= S(k) at the first iteration

Optimization was performed by Projected Gradient algorithm [7].This is an algorithm of minimization of first order applied to the cases of optimization under constraints [10].This optimization has the advantage of being fast because it takes into account only three parameters: Am1, σm1 , µm1 of the Gaussian selected.

Once this optimization performed, the parameters σ*

m1, µ*m1 and A*

m1 of the optimal Gaussian B*m1 are

now adjusted, and represent the solutions to the optimization problem. At this stage, one characteristic wave of the heartbeat (P,Q, R, S or T ) is modeled by Gaussian B*

m1 . The model at this first iteration is thus:

(4)

(2)

(1)

831

)

2)(

exp()( 2*

2**

i

ii

kAky

σμ−

−=

3.1.4 Orthogonalization We performed two orthogonalizations: one, for the original heartbeat signal S and the second for all the Gaussian library B (figure 2).

Figure 2. Orthogonalization step

The orthogonalization is performed in relation with

the adjusted B*m1 and not from the selected Bm1

)6.....(........................................*

** *1

1*11

*11

*11

112

mmm

m BBB

BSSS −=

)7.(..........1],1[......*

** *1

1*11

*11

*11

112 mNkB

BBBB

BB bmmm

mkkk −∈∀−=

S2 and the {B2

k}k=[1,N]-m1 are respectively the remainder of the heartbeat signal and the projection of their regressors in the orthogonal space with respect to B*

m1 . After the first orthogonalization, we have Nb -1

regressors (Gaussians) to modelize the heatbeat S2, which is used for the next iteration (selection, optimization and orthogonalization).

Subsequent iterations are based on the same pattern in three steps: • The selection of the best regressor Bmi of the library • Adjusting the whole parameters of the selected regressor for the new B*m . • The orthogonalization of the regressors and the remaining signal from B*mi (optimization).

We note that we have chosen five iterations to facilitate and minimize the classification error.

Each cardiac characteristic wave P,Q, R, S and T is fitted by exactly one Gaussian function.

At each iteration, the algorithm models only one wave of heartbeat.

3.2. Support Vector Machines Classifier

This paper describes heartbeat classification using GOFR and SVM where GOFR is used for features selection and SVM is trained for classification part.

Support vector machines (SVM) build on developments in computational learning theory. Because of their accuracy and ability to deal with a large number of predictors, they have more attention in biomedical applications. The majority of the previous classifiers separate classes using hyperplanes that split the classes, using a flat plane, within the predictor space. SVMs broaden the concept of hyperplane separation to data that cannot be separated linearly, by mapping the predictors onto a new, higher-dimensional space in which they can be separated linearly [11].

The simplest version of a SVM is the so-called Maximal Margin Classifier. It works only for data which are linearly separable. It is a good start for understanding the basic ideas behind more sophisticated SVMs. Consider a linearly separable dataset (xi, yi); where xi is the input pattern for the ith example and di is the corresponding desired output (-1,1). The assumption, the dataset is linearly separable, means there exist a hyperplane working as the decision surface. We can write: wT * x + b > 0 then; yi =+1 wT * x + b. <0 then; yi = -1

where wT * x + b. is the output function. The distance from the hyperplane to the closest point is called the geometric margin.

The margin is defined as the width of largest tube not containing samples that can drawn around the decision boundary like it shown in figure 3.

Figure 3. Principle of linear separation of two classes

SVM uses kernel technique to deal with nonlinear problem as many prediction machines. The kernel : K (xi, yj) can be any function satisfying Mercer’s condition; in particular it is possible to use RBF or polynomial kernels. Some conventional kernels are :

• RBF : )exp(),( 2iiii yxyxK −−= γ

• Polynomial Fonction : K (xi, yj) = (xi T yj)d. • Linear kernel : K (xi, yj) = xi T yj.

4. RESULTS AND DISCUSSION

This paper describes heartbeat classification using GOFR and SVM where GOFR is used for features selection and SVM is trained for classification part.

(5)

(8)

832

The ECG signals taken from MIT-BIH arrhythmia database are used in training to classify three different pathologies, (Arrhythmia, Supraventricular Arrhythmia and Malignant-ventricular Ectopy) plus normal ECGs.

For a given ECG signal, the heartbeats are detected as shown in figure 4, then each heartbeat is modeled by Generalized Orthogonal Forward Regression (GOFR).

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

1.5

2

2.5

Time(s)

ECG(m

v)

detection of T wave

ECG

wave T

Figure 4. Detection of heartbeat

The objective of the modeling phase in this application is to extract the features. The parameters A*

i, σ*i , µ*

i obtained for each Gaussian function are used as features.

At this stage, our algorithm runs for five iterations, i.e. every four steps are iterated five times:

• Selection of the most relevant Gaussian Bi (figure 5)

• Optimization of the parameters Ai, σi , µi (figure 6) To optimize the parameters {Ai},{ µi }and { σi } this means to adapt the parameters of the selected Gaussian to the heartbeat ; therefore, minimizing the cost J which is nonlinear for these parameters. The model Y (equation 1) obtained is the decomposition of the signal to a sum of five Gaussian functions.

• Orthogonalization of the heartbeat • Orthogonalization of the library B

After five iterations of that four step algorithm, the heartbeat has been modeled into Gaussian as shown in figure 7.

Figure 5. Selected Gaussian

Figure 6. Optimized Gaussian (OG)

Finally, this model is a linear combination of five Gaussian functions which represent each characteristic wave of the heartbeat [6].

Figure 7. Model of heartbeat

For developing SVM Learning, we put together all heartbeats extracted from all signals and considered them as a dataset . Randomly 1212 beats were taken from 1512 beats used for training . Among the 1512 beats , 300 are used for testing. The class distribution of the samples in training and test data sets are summarized in table 1.

Class Training set Test set Total Nomal 214 150 364 Abnormal 998 150 1148

Table 1. Class distribution of the samples in training and test data sets Furthermore, it is obvious that kernel parameter

selection is crucial to get good performance. Besides, the use of appropriate kernel parameter will overcome the problems of under-fitting and over-fitting so the best classification process is yielded. Support vector machines (SVMs) are based on preprocessing the data to represent patterns in a high dimension—typically much higher than the original feature space. With an appropriate nonlinear mapping to a sufficiently high dimension, data from two categories can always be separated by a hyperplane. As a result, while the original features bring sufficient information for good classification, mapping to a higher-dimensional feature space make available better discriminatory evidence that are absent in the original feature space. The problem of training an SVM is to select the nonlinear functions that map the input to a higher-dimensional space. Often this choice will be informed by the designer’s knowledge of the problem domain. In the absence of such information, we might choose to use polynomials, Gaussians or other basis

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functions. The dimensionality of the mapped space can be arbitrarily high (though in practice it may be limited by computational resources). For training the SVMs we chose Radial Basis Function (RBF) and tried to find an appropriate kernel parameters σ, and γ (The upper bound σ for penalty term and kernel parameter γ plays a critical role in performance of SVMs). The optimal σ, and γ values can only be ascertained after trying out different values. In addition, the choice of parameter σ the SVM is crucial in order to have a suitably trained SVM. The SVM has to be trained for different kernel parameters until we get the best result. For a database of 364 normal heartbeats and 1148 abnormal heartbeats, we obtained the following confusion matrix:

Normal heartbeat Abnormal heartbeat Normal

heartbeat 214 0

Abnormal heartbeat 0 998

Table 2. Confusion matrix of training set

Normal heartbeat Abnormal heartbeat Normal

heartbeat 148 2

Abnormal heartbeat 3 147

Table 3. Confusion matrix of test set

The results of table 2, prove the efficiency of the proposed classifier at the learning step. The test step which is summarized in Table 3, gives six misclassifications for a set of 300 beats. In order to assess the results of this training phase, the performance of the classifier is determined by the following statistical parameters [2]:

Overall classification accuracy, Tc Sensitivity: true positive ratio TPR Specificity : true negative ratio TNR

are calculated by using confusion matrix

TNR=100%.TN/(TN+FP) (9)

TPR=100%.TP/(TP+FN) (10)

Performance Training set Test set Validation set TPR 100 98,01 99,17 TNR 100 98,66 99,82 Tc 100 98,33 99,67

Table 4. Performance of proposed classifier

The results in table 4 reflect the performance of the proposed classifier . We think that the performance of the method will be better if the number of the beats for the learning is increased.

It is interesting to compare our method with other recognition systems presented in the literature.

Method Number of beat type Accuracy(%) Proposed classifier 4 99,67 PNN-DWT 6 99,65 F Hyb-HOSA 7 96,06 NNM 5 97,78 Neuro-Fussy 4 98,00 SOM-SVD 4 92,2 MLP-LVQ 2 96,8 MLP-Fourier 3 98

Table 5. Comparative results of different ECG beat classification methods

Some representative ECG beat recognition systems are chosen for this comparison: ECG recognition using fuzzy hybrid neural network (FHyb-HOSA) [12], a modified mixture of experts network structure for ECG beats classification with diverse features neural network model (NNM) [13] , ECG beat classification using neuro-fuzzy network (Neuro-Fuzzy) [1] , expert system using Kohonen and singular value decomposition SVD (SOM-SVD) [14] , ECG beat classification using LVQ (Learning Vector Quantization) and autoregression AR MLP (MLP-LVQ) [15] and Fourier and MLP (MLP-Fourier) [16]. Table 5 compares the accuracy of these systems. Since different numbers of beat types were exploited in different systems, the averaged classification accuracy was calculated for comparison. The result shows that our proposed method provides relatively higher classification accuracy than the other systems. It is difficult to compare the results since both the beat type and beat numbers are different. However, we note that the same MIT-BIH database was used to testify the performance.

Our method has the advantage of exploiting the temporal representation of the signal. Time frequency transformation is not necessary. The discrete wavelet transform DWT-PNN [3-17] can give similar performance but the optimization of the classification time has to be confirmed. In our case, our program implemented in Matlab7.10, takes 15 s for one hour of Holter recording.

5. CONCLUSION

In this paper, we have presented the approach to ECG beat classification that is based on using time features. Heartbeats of the ECG signal are detected and then they are modeled by Generalized Orthogonal Forward Regression (GOFR). The parameters (A*

i, σ*i , µ*

i ) obtained for each Gaussian function are used as features. SVM is trained for classification with radial basis function Kernel .

This study shows that the proposed method is an excellent model for t he computer-aided diagnosis of heart diseases based on ECG signals.

The advantage of this method over other current methods is that this technique selects only time features. It doesn't require time- frequency transforms. In this case,

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the computing time for any classification is reduced and the possibility of operating in real time is feasible.

The recognition rate is highly dependent on the choice of the database taken as abnormal. Some abnormalities may be a source of misclassification because the anomaly is not present on each heartbeat while the bank of learning is performed on each heart beat. In the design of our learning bank, it is important to work closely with a cardiologist, to distinguish the normal from the abnormal heartbeat.

An immediate application of this work is a diagnostic aid for automatic classification of Holter recordings, regardless of the recording time. Knowing that our program implemented in Matlab7.10, takes 15 s for one hour Holter recording, the implementation of the program in C++ can significantly reduce the classification time of recording normal or abnormal heartbeats.

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[9] R. Dubois, P. Maison-blanche, B. Quenet, and G. Dreyfus, “Automatic ECG Wave Extraction in Long-term Recordings using Gaussian mesa Function Models and Nonlinear Probability Estimators, ” Computer Methods and Programs in Biomedicine, vol. 88, no 3, pp. 217-233, 2007.

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[15] G.E. Oien , N.A. Bertelsen, T. Eftestol, and J.H. Husoy, “ECG rhythm classification using artificial neural networks,” in: I EEE Digital Signal Processing Workshop, pp. 514–517, 1996.

[16] K. Minami, H. Nakajima, and T. Toyoshima, “Real-time discrimination of ventricular tachyarrhythmia with Fourier-transform neural network,” IEEE Trans. Biomed. Eng,vol.46, pp.179–185, 1999.

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