Computer aided diagnosis of ECG data on (1)
Digital Signal Processing 18 (2008) 25–32
www.elsevier.com/locate/dsp
Computer aided diagnosis of ECG data on the least square support
vector machine
Kemal Polat ∗ , Bayram Akdemir, Salih Güne¸s
Department of Electrical and Electronics Engineering, Selcuk University, 42075 Konya, Turkey
Available online 26 May 2007
Abstract
In this paper we describe a technique that has successfully classified arrhythmia from an ECG dataset using a least square support
vector machine (LSSVM). LSSVM was applied to the ECG dataset to distinguish between healthy persons and diseased persons
(arrhythmia). The LSSVM classifier trained with four train-test parts including a training-to-test split of 50–50%, a training-to-test
split of 70–30%, and a training-to-test split of 80–20%. We have used the classification accuracy, sensitivity and specificity analysis,
and ROC curves to test the performance of LSSVM classifier on the detection of ECG arrhythmia. The classification accuracies
obtained are 100% for all the training-to-test splits. These results show that the proposed method is more promising than previously
reported classification techniques. The results suggest that the proposed method can be used to enhance the performance of a new
intelligent assistance diagnosis system.
2007 Elsevier Inc. All rights reserved.
Keywords: ECG dataset; Least square support vector machine; ROC curves
1. Introduction
The electrocardiogram (ECG) is a noninvasive test that is used to reflect underlying heart conditions by measuring the electrical activity of the heart. By positioning leads (electrical sensing devices) on the body in standardized
locations, information about many heart conditions can be determined by looking for characteristic patterns on the
ECG [1].
The traditional parameters that can be extracted by processing ECG signals include the following: (a) The underlying rate and rhythm mechanism of the heart; (b) The orientation of the heart (how it is placed) in the chest cavity;
(c) Evidence of increased thickness (hypertrophy) of the heart muscle; (d) Evidence of damage to the various parts
of the heart muscle; (e) Evidence of acutely impaired blood flow to the heart muscle; and (f) Patterns of abnormal
electrical activity that may predispose the patient to abnormal cardiac rhythm disturbances [1].
Having so many factors to analyze for determination of arrhythmia disease, a patient makes the physician’s job
difficult. A physician usually makes decisions by evaluating the current test results from a patient and by referring to
the previous decisions she/he made on other patients with similar ECG characteristics. The former method depends
strongly on the physician’s knowledge while the latter depends on the physician’s experience in comparing the current
* Corresponding author. Fax: +90 332 241 0635.
E-mail address: kpolat@selcuk.edu.tr (K. Polat).
1051-2004/$ – see front matter 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.dsp.2007.05.006
26
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
patient with earlier patients. This task is not easy considering the number of factors to be evaluated. In this crucial
step, she/he may derive benefit from an accurate tool that lists previous decisions on patients with similar factors.
Since LSSVM is a robust and reliable classifier system and has the ability to perform fast classification, we have
chosen to apply this classifier method to this task. The computation time of LSSVM classifier is lower than the other
classifier algorithms such as artificial neural network, decision tree, and an artificial immune system. The LSSVM
classifier has been applied to various physiological signals such as carotid arterial Doppler signals, PERG signals,
EEG signals. Among these, Polat et al. applied the LSSVM classifier for diagnosing the atherosclerosis disease by
processing carotid artery Doppler signals. They obtained 100% classification accuracy for atherosclerosis disease
using LSSVM [2]. Polat et al. used the LSSVM classifier to classify the macular disease from PERG signals. They
obtained 90.91% classification accuracy for macular disease using LSSVM [3]. Übeyli et al. applied to multi-class
SVM for classifying the EEG signals. They achieved 99.28% classification success via multi-class SVM [4].
In this study, we present the results of an LSSVM diagnostic system that proved to be more effective for detecting
the presence of arrhythmia disease from ECG data. Our primary research motivation was to advance the research
of arrhythmia diseases. We have applied the least square support vector machine (LSSVM) to distinguish between
healthy and diseased persons.
The performance of the system was analyzed with regard to the classification accuracy and we generated Receiver
Operating Characteristic (ROC) curves to present our results. Our proposed system obtained 100% classification
accuracy in test phase for detecting the presence of arrhythmia disease. This performance exceeds that of other studies
applied to the ECG dataset classification problem so far.
The rest of the paper is organized as follows. We present the related work in the Section 2. We present the LSSVM
method in Section 3. In Section 4, we give the experimental data to show the effectiveness of our method. Finally, we
conclude this paper in Section 5 with future directions.
2. Related work
Classification systems have been used for diagnosis of arrhythmia disease as for other clinical diagnosis problems.
There have been several studies reported focusing on diagnosis of arrhythmia disease. These studies applied different
methods to the given problem and achieved high classification accuracies using the dataset taken from UCI machine
learning repository. Among these studies, diagnosis of arrhythmia disease was conducted by Güvenir et al. In their
study, they obtained 56.29% classification accuracy on the diagnosis of arrhythmia disease by CFI (classification
on features intervals) classification algorithm and 5-fold cross validation [5]. Soman and Bobbie [6] obtained 59.47,
58.09, and 56.04% classification accuracies using OneR, J48, and Naive Bayes algorithms on the 50–50% training-test
dataset for diagnosis of arrhythmia disease [6] while Polat et al. reached 76.2% classification accuracy using fuzzy
weighted pre-processing and artificial immune recognition system (AIRS) and 10-fold cross validation [7].
3. The least square support vector machine classifier
In this section we firstly mention about SVM classifier followed by LSSVM related to SVM.
3.1. Support vector machines (SVMs)
SVM is a reliable classification technique, which is based on the statistical learning theory. This technique was
firstly proposed for classification and regression tasks by [8].
As shown in Fig. 1, a linear SVM was developed to classify the data set which contains two separable classes such
as {+1, −1}. Let the training data consist of n datum (x1 , y1 ), . . . , (xn , yn ), x ∈ R n and y ∈ {+1, −1}. To separate
these classes, SVMs have to find the optimal (with maximum margin) separating hyperplane so that SVM has good
generalization ability. All of the separating hyperplanes are formed with
D(x) = (w ∗ x) + w0
and provide following inequality for both y = +1 and y = −1.
yi (w ∗ xi ) + w0 1, i = 1, . . . , n.
(1)
(2)
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
27
Fig. 1. The structure of a simple SVM.
The data points which provide above formula in case of equality are called the support vectors. The classification
task in SVMs is implemented by using these support vectors.
Margins of hyperplanes obey following inequality:
yk × D(xk)
Γ, k = 1, . . . , n.
(3)
w
To maximize this margin (Γ ), norm of w is minimized. To reduce the number of solutions for norm of w, following
equation is determined:
Γ × w = 1.
(4)
Then formula (5) is minimized subject to constraint (2),
1
(5)
w2 .
2
When we study on the non-separable data, slack variables ξi , are added into formula (2) and (5). Instead of formulas
(2) and (5), new formulas (6) and (7) are used:
(6)
yi (w.xi ) + w0 1 − ξi ,
C
n
i=1
1
ξi + w2 .
2
(7)
Since originally SVMs classify the data in linear case, in the nonlinear case SVMs do not achieve the classification
tasks. To overcome this limitation on SVMs, kernel approaches are developed. Nonlinear input data set is converted
into high dimensional linear feature space via kernels. In SVMs, following kernels are most commonly used.
• Dot product kernels: K(x, x ′ ) = x.x ′ ;
• Polynomial kernels: K(x, x ′ ) = (x.x ′ + 1)d , where d is the degree of kernel and positive integer number;
• RBF kernels: K(x, x ′ ) = exp(−x − x ′ 2 /σ 2 ), where σ is a positive real number.
In our experiments σ is selected 1000.
3.2. LSSVM (least squares support vector machines)
LSSVMs are firstly proposed by [9]. The most important difference between SVMs and LSSVMs is that LSSVMs
use a set of linear equations for training while SVMs use a quadratic optimization problem [10]. While formula (7)
28
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
is minimized subject to formula (6) in Vapnik’s standard SVMs, in LSSVMs formula (9) is minimized subject to
formula (8).
yi (w.xi ) + w0 = 1 − ξi ,
i = 1, . . . , n,
n
1
C 2
w2 +
ξi .
2
2
(8)
(9)
i=1
According to these formulas, their dual problems are built as following:
n
n
C 2
1
αi yi (w.xi ) + w0 − 1 + ξi .
Q(w, b, α, ξ ) = w2 +
ξi −
2
2
i=1
(10)
i=1
Another difference between SVMs and LSSVMs is that αi (Lagrange multipliers) are positive or negative in
LSSVMs but they must be positive in SVMs. Detailed information can be found in [9] and [10].
4. The experimental results
In this section, we first explain the ECG dataset we used in our experiments. We then present the performance
evaluation methods used to evaluate the proposed method. Finally, we give the experimental results and discuss our
observations from the obtained results.
4.1. ECG dataset
The dataset used in this study was obtained from the archives of machine learning datasets at the University
of California, Irvine [11]. The datasets are grouped into two broad classes to facilitate their use in experimentally
determining the presence or absence of arrhythmia, and for identifying the type of arrhythmia. In the set, Class 0
refers to ‘dead’ ECG. Classes 1 refers ‘a live’ ECG. The arrhythmia dataset has 13 attributes. Also, this dataset
contains 88 dead people and 44 a live people belong to ECG dataset. Attributes of symptoms that are obtained from
patient are listed as follows [11]:
1. Survival—the number of months patient survived (has survived, if patient is still alive). Because all the patients
had their heart attacks at different times, it is possible that some patients have survived less than one year but
they are still alive. Check the second variable to confirm this. Such patients cannot be used for the prediction task
mentioned above.
2. Still-alive—a binary variable. 0 means dead at the end of survival period, 1 means still alive.
3. Age-at-heart-attack—age in years when heart attack occurred.
4. Pericardial-effusion—binary. Pericardial effusion is fluid around the heart. 0 = no fluid, 1 = fluid.
5. Fractional-shortening—a measure of contractility around the heart. Lower numbers are increasingly abnormal.
6. epss—E-point septal separation, another measure of contractility. Larger numbers are increasingly abnormal.
7. lvdd—left ventricular end-diastolic dimension. This is a measure of the size of the heart at end-diastole. Large
hearts tend to be sick hearts.
8. Wall-motion-score—a measure of how the segments of the left ventricle are moving.
9. Wall-motion-index—equals wall-motion-score divided by number of segments seen. Usually 12–13 segments are
seen in an echocardiogram. Use this variable INSTEAD of the wall motion score.
10. Mult—a derivate var which can be ignored.
11. Name—the name of the patient.
12. Group—meaningless, ignore it.
13. Alive-at-1—Boolean-valued. Derived from the first two attributes. 0 means patient was either dead after 1 year or
had been followed for less than 1 year. 1 means patient was alive at 1 year.
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
29
4.2. Performance evaluation methods
We have used three methods for performance evaluation of determination of arrhythmia disease. These methods are
classification accuracy, sensitivity and specifity analysis and ROC curves. We explain these methods in the following
subsections.
4.2.1. Classification accuracy
In this study, the classification accuracies for the datasets are measured using the equation:
|T |
assess(ti )
, ti ∈ T ,
accuracy(T ) = i=1
|T |
1, if classify(t) = t.c,
assess(t) =
0, otherwise,
(11)
where T is the set of data items to be classified (the test set), t ∈ T , t.c is the class of item t, and classify(t) returns
the classification of t by LSSVM.
4.2.2. Sensitivity, specificity, TP rate, FP rate, accuracy and F-measure
TP
(%),
TP + FN
TN
(%),
specificity =
FP + TN
FP
,
FPrate =
FP + TN
TP
,
TPrate =
TP + FN
TP + TN
,
accuracy =
TP + FN + FP + TN
2
F -measure =
,
1/specificity + 1/sensitivity
sensitivity =
(12)
(13)
(14)
(15)
(16)
(17)
where TP, TN, FP, and FN denotes true positives, true negatives, false positives, and false negatives, respectively.
4.2.3. Receiver operating characteristic (ROC) curves
A receiver operating characteristic (ROC) graph is a technique for visualizing, organizing and selecting classifiers
based on their performance. ROC graphs are commonly used in medical decision making and in recent years they have
been used increasingly in machine learning and data mining research. Although ROC graphs are apparently simple,
there are some common misconceptions and pitfalls when using them in research [12].
ROC graphs are two-dimensional graphs in which tp (true positive) rate is plotted on the Y axis and FP (false
positive) rate is plotted on the X axis. An ROC depicts relative tradeoffs between benefits (true positives) and costs
(false positives) [12].
4.3. The results and discussion
To evaluate the effectiveness of our method, we made experiments on the ECG dataset mentioned above. We
compare our results with previous results reported by earlier methods. Table 1 gives the classification accuracies of
our method and previous methods.
The LSSVM classification of ECG dataset was trained and tested in the dataset splits of 50–50, 70–30, and 80–
20%, respectively, due to training and test of all the ECG dataset. The obtained test classification accuracies were
100, 100, and 100%, respectively. In our experimental study, ECG dataset that have healthy and diseased heart are
classified by LSSVM classifier.
30
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
Table 1
Classification accuracies for ECG dataset classification problem with classification accuracies obtained by other methods in literature
Author (year)
Method
Performance
measure
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Güvenir et al. (2001)
Polat et al. (2005)
OneR
J48
Naïve Bayesian
OneR
J48
Naïve Bayesian
OneR
J48
Naïve Bayesian
CFI
Fuzzy weighted preprocessing-AIRS
50–50% training-test dataset
50–50% training-test dataset
50–50% training-test dataset
70–30% training-test dataset
70–30% training-test dataset
70–30% training-test dataset
80–20% training-test dataset
80–20% training-test dataset
80–20% training-test dataset
5-fold cross validation
10-fold cross validation
Our study (2006)
Our study (2006)
Our study (2006)
LSSVM
LSSVM
LSSVM
50–50% training-test dataset
70–30% training-test dataset
80–20% training-test dataset
Classification
accuracy (%)
59.67
69.91
70.80
58.09
74.26
75.00
56.04
67.03
74.73
56.29
76.20
100
100
100
Table 2
The obtained classification accuracy, sensitivity, specificity, TP rate, FP rate, accuracy and F -measure values by LSSVM classifier for diagnosis of
arrhythmia disease with 50–50% training-test split, 70–30% training-test split, and 80–20% training-test split
Statistical
measures
50–50%
training-test split
70–30%
training-test split
80–20%
training-test split
Sensitivity (%)
Specificity (%)
TP rate (%)
FP rate (%)
Accuracy (%)
F -measure (%)
100
100
100
0
100
100
100
100
100
0
100
100
100
100
100
0
100
100
Fig. 2. ROC curve for LSSVM on 50–50% of training-test split.
The obtained classification accuracy, sensitivity, specificity, TP rate, FP rate, accuracy and F -measure values by
LSSVM classifier for diagnosis of arrhythmia diseases with a training-to-test split of 50–50%, a training-to-test split
of 70–30%, and a training-to-test split of 80–20%, were shown in Table 2.
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
31
Fig. 3. ROC curve for LSSVM on 70–30% of training-test split.
Fig. 4. ROC curve for LSSVM on 80–20% of training-test split.
To compare the classification performances of LSSVM with a training-to-test split of 50–50%, a training-to-test
split of 70–30%, and a training-to-test split of 80–20% ROC (Receiver Operator Characteristic) curves method is
preferred. According to this method, ROC curves are computed for all datasets. While ROC curve of LSSVM with
50–50% training-test dataset was shown in Fig. 2, ROC curve of LSSVM with 70–30% training-test dataset was
shown in Fig. 3. ROC curve of LSSVM with 80–20% training-test dataset was shown in Fig. 4.
Medical decision support system designed by LSSVM that we have built gave very promising results in classifying
the healthy and patient subjects. We are proposing a complimentary system that can be coupled to software of the
medical decision making devices. The benefit of the system is to assist the physician to make the final decision
without hesitation.
5. Conclusion and future work
The LSSVM structure that we have built has given very promising results in classifying the healthy and arrhythmia
diseased heart. We are not claiming to replace the currently used devices for ECG data; on the other hand we are
32
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
proposing a complementary system that can be coupled to software of the ECG devices. The end benefit would be to
assist the physician to make the final decision without hesitation.
Classification systems that are used in medical decision-making provide medical data to be examined in shorter
time and more detailed. In this study, for the diagnosis of arrhythmia disease, a medical decision making system based
on LSSVM is proposed.
Our system is of the better clinical application over others, especially to diagnose of population in the shorter
period. Since it is noninvasive, very easy to use and it has the potential of profiting not only by the experts in LSSVM
research, but also especially biomedical engineers developing real-world medical applications. The stated results show
that the proposed method could point out the ability of design of a new intelligent assistance diagnosis system.
Acknowledgment
This study is supported by the Scientific Research Projects of Selcuk University (Project No. 05401069).
References
[1] http://www.medicinenet.com/electrocardiogram_ecg_or_ekg/article.htm (last accessed: April 19, 2007).
[2] K. Polat, F. Latifo˘glu, S. Kara, S. Güne¸s, Pattern detection of atherosclerosis from carotid artery Doppler signals using fuzzy weighted preprocessing and least square support vector machine (LSSVM), Ann. Biomed. Eng. 35 (5) (2007) 724–732.
[3] K. Polat, S. Kara, A. Güven, S. Güne¸s, A hybrid automated detection system based on least square support vector machine classifier and k-N N
based weighted pre-processing for diagnosing of macular disease, in: Lecture Notes in Computer Science, vol. 4432, 2007, pp. 338–345.
[4] I. Guler, E.D. Übeyli, Multiclass support vector machines for EEG-signals classification, IEEE Trans. Inf. Technol. Biomed. 11 (2) (2007)
117–126.
[5] H.A. Güvenir, B. Acar, Feature selection using a genetic algorithm for the detection of abnormal ECG recordings, in: Proceedings of the
World Conference on Systemics, Cybernetics and Informatics (ISAS/SCI 2001), Orlando, FL, 2001, pp. 437–442.
[6] T. Soman, P.O. Bobbie, Classification of arrhythmia using machine learning techniques, in: Proc. of 4th International Conference on System
Science and Engineering (ICOSSE), Copacabana, Rio de Janeiro, Brazil, 2005.
[7] K. Polat, S. Sahan,
¸
S. Güne¸s, A new method to medical diagnosis: Artificial immune recognition system (AIRS) with fuzzy weighted preprocessing and application to ECG arrhythmia (2005), Expert Syst. Appl. 31 (2) (2006) 264–269.
[8] V. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995.
[9] J.A.K. Suykens, J. Vandewalle, Least squares support vector machine classifiers, Neural Process. Lett. 9 (3) (1999) 293–300.
[10] D. Tsujinishi, S. Abe, Fuzzy least squares support vector machines for multi-class problems, Neural Networks Field 16 (2003) 785–792.
[11] ftp://ftp.ics.uci.edu/pub/machine-learning-databases (last accessed: April 19, 2007).
[12] F. Fawcett, An introduction to ROC analysis, Pattern Recogn. Lett. 27 (8) (2006) 861–874.
www.elsevier.com/locate/dsp
Computer aided diagnosis of ECG data on the least square support
vector machine
Kemal Polat ∗ , Bayram Akdemir, Salih Güne¸s
Department of Electrical and Electronics Engineering, Selcuk University, 42075 Konya, Turkey
Available online 26 May 2007
Abstract
In this paper we describe a technique that has successfully classified arrhythmia from an ECG dataset using a least square support
vector machine (LSSVM). LSSVM was applied to the ECG dataset to distinguish between healthy persons and diseased persons
(arrhythmia). The LSSVM classifier trained with four train-test parts including a training-to-test split of 50–50%, a training-to-test
split of 70–30%, and a training-to-test split of 80–20%. We have used the classification accuracy, sensitivity and specificity analysis,
and ROC curves to test the performance of LSSVM classifier on the detection of ECG arrhythmia. The classification accuracies
obtained are 100% for all the training-to-test splits. These results show that the proposed method is more promising than previously
reported classification techniques. The results suggest that the proposed method can be used to enhance the performance of a new
intelligent assistance diagnosis system.
2007 Elsevier Inc. All rights reserved.
Keywords: ECG dataset; Least square support vector machine; ROC curves
1. Introduction
The electrocardiogram (ECG) is a noninvasive test that is used to reflect underlying heart conditions by measuring the electrical activity of the heart. By positioning leads (electrical sensing devices) on the body in standardized
locations, information about many heart conditions can be determined by looking for characteristic patterns on the
ECG [1].
The traditional parameters that can be extracted by processing ECG signals include the following: (a) The underlying rate and rhythm mechanism of the heart; (b) The orientation of the heart (how it is placed) in the chest cavity;
(c) Evidence of increased thickness (hypertrophy) of the heart muscle; (d) Evidence of damage to the various parts
of the heart muscle; (e) Evidence of acutely impaired blood flow to the heart muscle; and (f) Patterns of abnormal
electrical activity that may predispose the patient to abnormal cardiac rhythm disturbances [1].
Having so many factors to analyze for determination of arrhythmia disease, a patient makes the physician’s job
difficult. A physician usually makes decisions by evaluating the current test results from a patient and by referring to
the previous decisions she/he made on other patients with similar ECG characteristics. The former method depends
strongly on the physician’s knowledge while the latter depends on the physician’s experience in comparing the current
* Corresponding author. Fax: +90 332 241 0635.
E-mail address: kpolat@selcuk.edu.tr (K. Polat).
1051-2004/$ – see front matter 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.dsp.2007.05.006
26
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
patient with earlier patients. This task is not easy considering the number of factors to be evaluated. In this crucial
step, she/he may derive benefit from an accurate tool that lists previous decisions on patients with similar factors.
Since LSSVM is a robust and reliable classifier system and has the ability to perform fast classification, we have
chosen to apply this classifier method to this task. The computation time of LSSVM classifier is lower than the other
classifier algorithms such as artificial neural network, decision tree, and an artificial immune system. The LSSVM
classifier has been applied to various physiological signals such as carotid arterial Doppler signals, PERG signals,
EEG signals. Among these, Polat et al. applied the LSSVM classifier for diagnosing the atherosclerosis disease by
processing carotid artery Doppler signals. They obtained 100% classification accuracy for atherosclerosis disease
using LSSVM [2]. Polat et al. used the LSSVM classifier to classify the macular disease from PERG signals. They
obtained 90.91% classification accuracy for macular disease using LSSVM [3]. Übeyli et al. applied to multi-class
SVM for classifying the EEG signals. They achieved 99.28% classification success via multi-class SVM [4].
In this study, we present the results of an LSSVM diagnostic system that proved to be more effective for detecting
the presence of arrhythmia disease from ECG data. Our primary research motivation was to advance the research
of arrhythmia diseases. We have applied the least square support vector machine (LSSVM) to distinguish between
healthy and diseased persons.
The performance of the system was analyzed with regard to the classification accuracy and we generated Receiver
Operating Characteristic (ROC) curves to present our results. Our proposed system obtained 100% classification
accuracy in test phase for detecting the presence of arrhythmia disease. This performance exceeds that of other studies
applied to the ECG dataset classification problem so far.
The rest of the paper is organized as follows. We present the related work in the Section 2. We present the LSSVM
method in Section 3. In Section 4, we give the experimental data to show the effectiveness of our method. Finally, we
conclude this paper in Section 5 with future directions.
2. Related work
Classification systems have been used for diagnosis of arrhythmia disease as for other clinical diagnosis problems.
There have been several studies reported focusing on diagnosis of arrhythmia disease. These studies applied different
methods to the given problem and achieved high classification accuracies using the dataset taken from UCI machine
learning repository. Among these studies, diagnosis of arrhythmia disease was conducted by Güvenir et al. In their
study, they obtained 56.29% classification accuracy on the diagnosis of arrhythmia disease by CFI (classification
on features intervals) classification algorithm and 5-fold cross validation [5]. Soman and Bobbie [6] obtained 59.47,
58.09, and 56.04% classification accuracies using OneR, J48, and Naive Bayes algorithms on the 50–50% training-test
dataset for diagnosis of arrhythmia disease [6] while Polat et al. reached 76.2% classification accuracy using fuzzy
weighted pre-processing and artificial immune recognition system (AIRS) and 10-fold cross validation [7].
3. The least square support vector machine classifier
In this section we firstly mention about SVM classifier followed by LSSVM related to SVM.
3.1. Support vector machines (SVMs)
SVM is a reliable classification technique, which is based on the statistical learning theory. This technique was
firstly proposed for classification and regression tasks by [8].
As shown in Fig. 1, a linear SVM was developed to classify the data set which contains two separable classes such
as {+1, −1}. Let the training data consist of n datum (x1 , y1 ), . . . , (xn , yn ), x ∈ R n and y ∈ {+1, −1}. To separate
these classes, SVMs have to find the optimal (with maximum margin) separating hyperplane so that SVM has good
generalization ability. All of the separating hyperplanes are formed with
D(x) = (w ∗ x) + w0
and provide following inequality for both y = +1 and y = −1.
yi (w ∗ xi ) + w0 1, i = 1, . . . , n.
(1)
(2)
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
27
Fig. 1. The structure of a simple SVM.
The data points which provide above formula in case of equality are called the support vectors. The classification
task in SVMs is implemented by using these support vectors.
Margins of hyperplanes obey following inequality:
yk × D(xk)
Γ, k = 1, . . . , n.
(3)
w
To maximize this margin (Γ ), norm of w is minimized. To reduce the number of solutions for norm of w, following
equation is determined:
Γ × w = 1.
(4)
Then formula (5) is minimized subject to constraint (2),
1
(5)
w2 .
2
When we study on the non-separable data, slack variables ξi , are added into formula (2) and (5). Instead of formulas
(2) and (5), new formulas (6) and (7) are used:
(6)
yi (w.xi ) + w0 1 − ξi ,
C
n
i=1
1
ξi + w2 .
2
(7)
Since originally SVMs classify the data in linear case, in the nonlinear case SVMs do not achieve the classification
tasks. To overcome this limitation on SVMs, kernel approaches are developed. Nonlinear input data set is converted
into high dimensional linear feature space via kernels. In SVMs, following kernels are most commonly used.
• Dot product kernels: K(x, x ′ ) = x.x ′ ;
• Polynomial kernels: K(x, x ′ ) = (x.x ′ + 1)d , where d is the degree of kernel and positive integer number;
• RBF kernels: K(x, x ′ ) = exp(−x − x ′ 2 /σ 2 ), where σ is a positive real number.
In our experiments σ is selected 1000.
3.2. LSSVM (least squares support vector machines)
LSSVMs are firstly proposed by [9]. The most important difference between SVMs and LSSVMs is that LSSVMs
use a set of linear equations for training while SVMs use a quadratic optimization problem [10]. While formula (7)
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K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
is minimized subject to formula (6) in Vapnik’s standard SVMs, in LSSVMs formula (9) is minimized subject to
formula (8).
yi (w.xi ) + w0 = 1 − ξi ,
i = 1, . . . , n,
n
1
C 2
w2 +
ξi .
2
2
(8)
(9)
i=1
According to these formulas, their dual problems are built as following:
n
n
C 2
1
αi yi (w.xi ) + w0 − 1 + ξi .
Q(w, b, α, ξ ) = w2 +
ξi −
2
2
i=1
(10)
i=1
Another difference between SVMs and LSSVMs is that αi (Lagrange multipliers) are positive or negative in
LSSVMs but they must be positive in SVMs. Detailed information can be found in [9] and [10].
4. The experimental results
In this section, we first explain the ECG dataset we used in our experiments. We then present the performance
evaluation methods used to evaluate the proposed method. Finally, we give the experimental results and discuss our
observations from the obtained results.
4.1. ECG dataset
The dataset used in this study was obtained from the archives of machine learning datasets at the University
of California, Irvine [11]. The datasets are grouped into two broad classes to facilitate their use in experimentally
determining the presence or absence of arrhythmia, and for identifying the type of arrhythmia. In the set, Class 0
refers to ‘dead’ ECG. Classes 1 refers ‘a live’ ECG. The arrhythmia dataset has 13 attributes. Also, this dataset
contains 88 dead people and 44 a live people belong to ECG dataset. Attributes of symptoms that are obtained from
patient are listed as follows [11]:
1. Survival—the number of months patient survived (has survived, if patient is still alive). Because all the patients
had their heart attacks at different times, it is possible that some patients have survived less than one year but
they are still alive. Check the second variable to confirm this. Such patients cannot be used for the prediction task
mentioned above.
2. Still-alive—a binary variable. 0 means dead at the end of survival period, 1 means still alive.
3. Age-at-heart-attack—age in years when heart attack occurred.
4. Pericardial-effusion—binary. Pericardial effusion is fluid around the heart. 0 = no fluid, 1 = fluid.
5. Fractional-shortening—a measure of contractility around the heart. Lower numbers are increasingly abnormal.
6. epss—E-point septal separation, another measure of contractility. Larger numbers are increasingly abnormal.
7. lvdd—left ventricular end-diastolic dimension. This is a measure of the size of the heart at end-diastole. Large
hearts tend to be sick hearts.
8. Wall-motion-score—a measure of how the segments of the left ventricle are moving.
9. Wall-motion-index—equals wall-motion-score divided by number of segments seen. Usually 12–13 segments are
seen in an echocardiogram. Use this variable INSTEAD of the wall motion score.
10. Mult—a derivate var which can be ignored.
11. Name—the name of the patient.
12. Group—meaningless, ignore it.
13. Alive-at-1—Boolean-valued. Derived from the first two attributes. 0 means patient was either dead after 1 year or
had been followed for less than 1 year. 1 means patient was alive at 1 year.
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
29
4.2. Performance evaluation methods
We have used three methods for performance evaluation of determination of arrhythmia disease. These methods are
classification accuracy, sensitivity and specifity analysis and ROC curves. We explain these methods in the following
subsections.
4.2.1. Classification accuracy
In this study, the classification accuracies for the datasets are measured using the equation:
|T |
assess(ti )
, ti ∈ T ,
accuracy(T ) = i=1
|T |
1, if classify(t) = t.c,
assess(t) =
0, otherwise,
(11)
where T is the set of data items to be classified (the test set), t ∈ T , t.c is the class of item t, and classify(t) returns
the classification of t by LSSVM.
4.2.2. Sensitivity, specificity, TP rate, FP rate, accuracy and F-measure
TP
(%),
TP + FN
TN
(%),
specificity =
FP + TN
FP
,
FPrate =
FP + TN
TP
,
TPrate =
TP + FN
TP + TN
,
accuracy =
TP + FN + FP + TN
2
F -measure =
,
1/specificity + 1/sensitivity
sensitivity =
(12)
(13)
(14)
(15)
(16)
(17)
where TP, TN, FP, and FN denotes true positives, true negatives, false positives, and false negatives, respectively.
4.2.3. Receiver operating characteristic (ROC) curves
A receiver operating characteristic (ROC) graph is a technique for visualizing, organizing and selecting classifiers
based on their performance. ROC graphs are commonly used in medical decision making and in recent years they have
been used increasingly in machine learning and data mining research. Although ROC graphs are apparently simple,
there are some common misconceptions and pitfalls when using them in research [12].
ROC graphs are two-dimensional graphs in which tp (true positive) rate is plotted on the Y axis and FP (false
positive) rate is plotted on the X axis. An ROC depicts relative tradeoffs between benefits (true positives) and costs
(false positives) [12].
4.3. The results and discussion
To evaluate the effectiveness of our method, we made experiments on the ECG dataset mentioned above. We
compare our results with previous results reported by earlier methods. Table 1 gives the classification accuracies of
our method and previous methods.
The LSSVM classification of ECG dataset was trained and tested in the dataset splits of 50–50, 70–30, and 80–
20%, respectively, due to training and test of all the ECG dataset. The obtained test classification accuracies were
100, 100, and 100%, respectively. In our experimental study, ECG dataset that have healthy and diseased heart are
classified by LSSVM classifier.
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K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
Table 1
Classification accuracies for ECG dataset classification problem with classification accuracies obtained by other methods in literature
Author (year)
Method
Performance
measure
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Soman and Bobbie (2005)
Güvenir et al. (2001)
Polat et al. (2005)
OneR
J48
Naïve Bayesian
OneR
J48
Naïve Bayesian
OneR
J48
Naïve Bayesian
CFI
Fuzzy weighted preprocessing-AIRS
50–50% training-test dataset
50–50% training-test dataset
50–50% training-test dataset
70–30% training-test dataset
70–30% training-test dataset
70–30% training-test dataset
80–20% training-test dataset
80–20% training-test dataset
80–20% training-test dataset
5-fold cross validation
10-fold cross validation
Our study (2006)
Our study (2006)
Our study (2006)
LSSVM
LSSVM
LSSVM
50–50% training-test dataset
70–30% training-test dataset
80–20% training-test dataset
Classification
accuracy (%)
59.67
69.91
70.80
58.09
74.26
75.00
56.04
67.03
74.73
56.29
76.20
100
100
100
Table 2
The obtained classification accuracy, sensitivity, specificity, TP rate, FP rate, accuracy and F -measure values by LSSVM classifier for diagnosis of
arrhythmia disease with 50–50% training-test split, 70–30% training-test split, and 80–20% training-test split
Statistical
measures
50–50%
training-test split
70–30%
training-test split
80–20%
training-test split
Sensitivity (%)
Specificity (%)
TP rate (%)
FP rate (%)
Accuracy (%)
F -measure (%)
100
100
100
0
100
100
100
100
100
0
100
100
100
100
100
0
100
100
Fig. 2. ROC curve for LSSVM on 50–50% of training-test split.
The obtained classification accuracy, sensitivity, specificity, TP rate, FP rate, accuracy and F -measure values by
LSSVM classifier for diagnosis of arrhythmia diseases with a training-to-test split of 50–50%, a training-to-test split
of 70–30%, and a training-to-test split of 80–20%, were shown in Table 2.
K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
31
Fig. 3. ROC curve for LSSVM on 70–30% of training-test split.
Fig. 4. ROC curve for LSSVM on 80–20% of training-test split.
To compare the classification performances of LSSVM with a training-to-test split of 50–50%, a training-to-test
split of 70–30%, and a training-to-test split of 80–20% ROC (Receiver Operator Characteristic) curves method is
preferred. According to this method, ROC curves are computed for all datasets. While ROC curve of LSSVM with
50–50% training-test dataset was shown in Fig. 2, ROC curve of LSSVM with 70–30% training-test dataset was
shown in Fig. 3. ROC curve of LSSVM with 80–20% training-test dataset was shown in Fig. 4.
Medical decision support system designed by LSSVM that we have built gave very promising results in classifying
the healthy and patient subjects. We are proposing a complimentary system that can be coupled to software of the
medical decision making devices. The benefit of the system is to assist the physician to make the final decision
without hesitation.
5. Conclusion and future work
The LSSVM structure that we have built has given very promising results in classifying the healthy and arrhythmia
diseased heart. We are not claiming to replace the currently used devices for ECG data; on the other hand we are
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K. Polat et al. / Digital Signal Processing 18 (2008) 25–32
proposing a complementary system that can be coupled to software of the ECG devices. The end benefit would be to
assist the physician to make the final decision without hesitation.
Classification systems that are used in medical decision-making provide medical data to be examined in shorter
time and more detailed. In this study, for the diagnosis of arrhythmia disease, a medical decision making system based
on LSSVM is proposed.
Our system is of the better clinical application over others, especially to diagnose of population in the shorter
period. Since it is noninvasive, very easy to use and it has the potential of profiting not only by the experts in LSSVM
research, but also especially biomedical engineers developing real-world medical applications. The stated results show
that the proposed method could point out the ability of design of a new intelligent assistance diagnosis system.
Acknowledgment
This study is supported by the Scientific Research Projects of Selcuk University (Project No. 05401069).
References
[1] http://www.medicinenet.com/electrocardiogram_ecg_or_ekg/article.htm (last accessed: April 19, 2007).
[2] K. Polat, F. Latifo˘glu, S. Kara, S. Güne¸s, Pattern detection of atherosclerosis from carotid artery Doppler signals using fuzzy weighted preprocessing and least square support vector machine (LSSVM), Ann. Biomed. Eng. 35 (5) (2007) 724–732.
[3] K. Polat, S. Kara, A. Güven, S. Güne¸s, A hybrid automated detection system based on least square support vector machine classifier and k-N N
based weighted pre-processing for diagnosing of macular disease, in: Lecture Notes in Computer Science, vol. 4432, 2007, pp. 338–345.
[4] I. Guler, E.D. Übeyli, Multiclass support vector machines for EEG-signals classification, IEEE Trans. Inf. Technol. Biomed. 11 (2) (2007)
117–126.
[5] H.A. Güvenir, B. Acar, Feature selection using a genetic algorithm for the detection of abnormal ECG recordings, in: Proceedings of the
World Conference on Systemics, Cybernetics and Informatics (ISAS/SCI 2001), Orlando, FL, 2001, pp. 437–442.
[6] T. Soman, P.O. Bobbie, Classification of arrhythmia using machine learning techniques, in: Proc. of 4th International Conference on System
Science and Engineering (ICOSSE), Copacabana, Rio de Janeiro, Brazil, 2005.
[7] K. Polat, S. Sahan,
¸
S. Güne¸s, A new method to medical diagnosis: Artificial immune recognition system (AIRS) with fuzzy weighted preprocessing and application to ECG arrhythmia (2005), Expert Syst. Appl. 31 (2) (2006) 264–269.
[8] V. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995.
[9] J.A.K. Suykens, J. Vandewalle, Least squares support vector machine classifiers, Neural Process. Lett. 9 (3) (1999) 293–300.
[10] D. Tsujinishi, S. Abe, Fuzzy least squares support vector machines for multi-class problems, Neural Networks Field 16 (2003) 785–792.
[11] ftp://ftp.ics.uci.edu/pub/machine-learning-databases (last accessed: April 19, 2007).
[12] F. Fawcett, An introduction to ROC analysis, Pattern Recogn. Lett. 27 (8) (2006) 861–874.