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Detection of ECG Arrhythmia using a differential expert system approach based on principal component analysis and least square support vector machine

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Detection of ECG Arrhythmia using a diﬀerential expertsystem approach based on principal component analysisand least square support vector machine
Kemal Polat
*
, Salih Gu¨nes
Selcuk University, Electrical and Electronics Engineering Department, 42035 Konya, Turkey
Abstract
Changes in the normal rhythm of a human heart may result in diﬀerent cardiac arrhythmias, which may be immediatelyfatal or cause irreparable damage to the heart sustained over long periods of time. The ability to automatically identifyarrhythmias from ECG recordings is important for clinical diagnosis and treatment. In this study, we have detected onECG Arrhythmias using principal component analysis (PCA) and least square support vector machine (LS-SVM). Theapproach system has two stages. In the ﬁrst stage, dimension of ECG Arrhythmias dataset that has 279 features is reducedto 15 features using principal component analysis. In the second stage, diagnosis of ECG Arrhythmias was conducted byusing LS-SVM classiﬁer. We took the ECG Arrhythmias dataset used in our study from the UCI (from University of Cal-ifornia, Department of Information and Computer Science) machine learning database. Classiﬁer system consists of threestages: 50–50% of training-test dataset, 70–30% of training-test dataset and 80–20% of training-test dataset, subsequently,the obtained classiﬁcation accuracies; 96.86%, 100% ve 100%. The end beneﬁt would be to assist the physician to make theﬁnal decision without hesitation. This result is for ECG Arrhythmias disease but it states that this method can be usedconﬁdently for other medical diseases diagnosis problems, too.
2006 Elsevier Inc. All rights reserved.
Keywords:
ECG Arrhythmia; Principal component analysis (PCA); Least square support vector machine (LSSVM); ROC curves
1. Introduction
With improvements in medical knowledge systems in medical institutes and hospitals, determining usefulknowledge is becoming more diﬃcult. Especially, because the conventional manual data analysis techniquesare not eﬀective in diagnosis, using computer based analyses are becoming inevitable in disease diagnosis. So,it is the time to develop modern, eﬀective and eﬃcient computer based systems for decision support. There area number of data analysis techniques: statistical, machine learning and data abstraction. Medical analysis
0096-3003/$ - see front matter
2006 Elsevier Inc. All rights reserved.doi:10.1016/j.amc.2006.08.020
*
Corresponding author.
E-mail addresses:
kpolat@selcuk.edu.tr (K. Polat), sgunes@selcuk.edu.tr (S. Gu
¨nes
).Applied Mathematics and Computation 186 (2007) 898–906
www.elsevier.com/locate/amc
using machine learning techniques has begun to be conducted for last 20 years. The advantages of usingmachine learning schemes in medical analysis have caused human support and costs to decrease and causeddiagnosis accuracy to increase [1].One of the central problems of the information age is dealing with the enormous amount of raw informa-tion that is available. More and more data is being collected and stored in databases or spreadsheets. As thevolume increases, the gap between generating and collecting the data and actually being able to understand itis widening. In order to bridge this knowledge gap, a variety of techniques known as data mining or know-ledge discovery is being developed. Knowledge discovery can be deﬁned as the extraction of implicit, previ-ously unknown, and potentially useful information from real world data, and communicating thediscovered knowledge to people in an understandable way [2–4].The motivation behind the research reported in this paper is the results obtained from extensions of anongoing research eﬀort. The research reported in [6,5] is on developing a non-invasive ECG hardware andembedded software for capturing, analysing, diagnosing, and recommending remedies for homecare patientswith heart conditions. In the eﬀort, we focused on the (hardware) acquisition and (software) analysis of ECGsignals for early diagnosis of Tachycardia heart disease. The work reported here builds on the initial work by,ﬁrst, using machine learning techniques to study and understand the accurate prediction of arrhythmic dis-eases and suggestive remedies based on the classiﬁcation schemes or models [6,5].The used data source is taken from the University of California at Irvine (UCI) machine learning repository[7]. This dataset is commonly used among researchers who use machine learning (ML) methods for ECGArrhythmia classiﬁcation and so it provides us to compare the performance of our system with other con-ducted studies related with this problem.In this study, we have proposed the system that has two stages. Firstly, dimension of ECG Arrhythmiadataset that has 279 features is reduced to 15 features using principal component analysis. Then, we usedLS-SVM diagnosis ECG Arrhythmia. The obtained classiﬁcation accuracy of our system was very promisingwith regard to the other classiﬁcation applications in literature for this problem.The rest of the paper is organized as follows. Section 2 gives the background information including ECGArrhythmia classiﬁcation problem and previous research in corresponding area. Also, we explained themethod in Section 2 with subtitles of proposed a new medical diagnosis method and measures for performanceevaluation. In each subsection of that section, the detailed information is given. The results obtained in appli-cations are given in Section 3. This section also includes the discussion of these results in speciﬁc and generalmanner. Consequently in Section 4, we conclude the paper with summarization of results by emphasizing theimportance of this study and mentioning about some future work.
2. Materials and method
2.1. ECG Arrhythmia dataset
The dataset used in this study was obtained from the archives of machine learning datasets at the Univer-sity of California, Irvine [7]. The datasets are grouped into three broad classes to facilitate their use in exper-imentally determining the presence or absence of arrhythmia, and for identifying the type of arrhythmia. Inthe set, Class 01 refers to ‘normal’ ECG. Classes 02–15 refer to diﬀerent classes of arrhythmia and Class 16refers to the rest of unclassiﬁed data. The arrhythmia dataset has 279 attributes, 206 of which are linear val-ued and the rest are nominal. There are 452 instances, and as indicated above, 16 classes. But we have used totwo classes as the presence or absence of arrhythmia in our experiments. There are missing values in the data-set. In such cases, probabilistic values were assigned according to the distribution of the known values for theattributes.
2.2. Previous research in ECG Arrhythmia dataset
There has been much work in the ﬁeld of classiﬁcation and most work has been based on neural networks,Markov chain models and support vector machines (SVMs). The datasets used to train these methods areoften small. In [5], direct-kernel methods and support vector machines are used for pattern recognition in
K. Polat, S. Gu¨ nes
/ Applied Mathematics and Computation 186 (2007) 898–906
899
magnetocardiography. In [8], self-organizing maps (SOM) are used for analysis of ECG signals. The SOMshelps discover a structure in a set of ECG patterns and visualize a topology of the data. In [9] machine learningmethods like artiﬁcial neural networks (ANNs) and logically weighted regression (LWR) methods are used forautomated morphological galaxy classiﬁcation. The focus of the investigation described in this paper is toevaluate three standard machine-learning algorithms applied to classify cardiac arrhythmias. All related pre-vious research cited in this paper use classes, features, and machine learning methods and related software,which we used. Therefore, our comparisons are in the context of the predictability, accuracy, and ease of – learning of these algorithms. The former two capabilities are signiﬁcant in diagnosing and treating ECGabnormalities while the latter facilitates the practical use of our ECG diagnostic device.
2.3. Proposed approach
We have proposed system, which has two stages. In the ﬁrst stage, dimension of ECG Arrhythmia datasetthat has 279 features is reduced to 4 features using principal component analysis. In the second stage, we usedLS-SVM classiﬁer to diagnosis of ECG Arrhythmia. The block diagram of proposed system is shown in Fig. 1.
2.3.1. Principal component analysis (PCA)
PCA was used to make a classiﬁer system more eﬀective. For this aim, before classifying, PCA method wasused for dimensionality reduction of ECG Arrhythmia dataset. Therefore, ECG Arrhythmia dataset was rep-resented a vector consists of 279 attributes. PCA is based on the assumption that most information about clas-ses is contained in the directions along which the variations are the largest. The most common derivation of PCA is in terms of a standardized linear projection, which maximizes the variance in the projected space [10].For a given
p
-dimensional data set
X
, the
m
principal axes
T
1
,
T
2
,
...
,
T
m
, where 1
6
m
6
p
, are orthonormalaxes onto which the retained variance is maximum in the projected space. Generally,
T
1
,
T
2
,
...
,
T
m
can begiven by the
m
leading eigenvectors of the sample covariance matrix
S
¼ ð
1
=
N
Þ
P
N i
¼
1
ð
x
i
l
Þ
T
ð
x
i
l
Þ
, where
x
i
2
X
,
l
is the sample mean and
N
is the number of samples, so that
ST
i
¼
k
i
T
i
;
i
2
1
;
...
;
m
;
ð
1
Þ
ECG Arrhythmia Dataset that has279 attributes Dimensionality Reduction using Principles Component Analysis (PCA)Classification of ECG Arrhythmia using Least Square Support Vector Machine (LSSVM) Detection of ECG Arrhythmia that has 15 attributes
Fig. 1. The block diagram of proposed system.900
K. Polat, S. Gu¨ nes
/ Applied Mathematics and Computation 186 (2007) 898–906
where
k
i
is the
i
th largest eigenvalue of
S
. The
m
principal components of a given observation vector
x
i
2
X
aregiven by
y
¼ ½
y
1
;
y
2
;
...
;
y
m
¼ ½
T
T1
x
;
T
T2
;
...
;
T
T
m
¼
T
T
x
:
ð
2
Þ
The
m
principal components of
x
are decorrelated in the projected space. In multi-class problems, the varia-tions of data are determined on a global basis, that is, the principal axes are derived from a global covariancematrix:
b
S
¼
1
N
X
K j
¼
1
X
N
j
i
¼
1
ð
x
j
^
l
Þð
x
j
^
l
Þ
T
;
ð
3
Þ
where
^
l
is the global mean of all the samples,
K
is the number of classes,
N
j
is the number of samples in class
j
;
N
¼
P
K j
¼
1
N
j
and
x
ji
represents the
i
th observation from class
j
. The principal axes
T
1
,
T
2
,
...
,
T
m
are thereforethe
m
leading eigenvectors of
b
S
:
b
ST
i
¼
^
k
i
T
i
;
i
2
1
;
...
;
m
;
ð
4
Þ
where
^
k
i
is the
i
th largest eigenvalue of
b
S
. An assumption made for feature extraction and dimensionalityreduction by PCA is that most information of the observation vectors is contained in the subspace spannedby the ﬁrst
m
principal axes, where
m
<
p
. Therefore, each srcinal data vector can be represented by its prin-cipal component vector with dimensionality
m
[11].
2.3.2. Least square support vector machine (LSSVM)
In this section we ﬁrstly mention about SVM classiﬁer after that LSSVM related to SVM.
2.3.2.1. Support vector machines (SVMs).
SVM is a reliable classiﬁcation technique, which is based on the sta-tistical learning theory. This technique was ﬁrstly proposed for classiﬁcation and regression tasks by [12].As shown in Fig. 2, a linear SVM was developed to classify the data set which contains two separable clas-ses such as {+1,
1}. Let the training data consist of
n
datum (
x
1
,
y
1
),
...
,(
x
n
,
y
n
),
x
2
R
n
and
y
2
{+1,
1}. Toseparate these classes, SVMs have to ﬁnd the optimal (with maximum margin) separating hyperplane so thatSVM has good generalization ability. All of the separating hyperplanes are formed with
D
ð
x
Þ ¼ ð
w
x
Þ þ
w
0
ð
5
Þ
Fig. 2. The structure of a simple SVM.
K. Polat, S. Gu¨ nes
/ Applied Mathematics and Computation 186 (2007) 898–906
901
and provide following inequality for both
y
= +1 and
y
=
1.
y
i
½ð
w
x
i
Þ þ
w
0
P
1
;
i
¼
1
;
...
;
n
:
ð
6
Þ
The data points which provide above formula in case of equality are called the support vectors. The clas-siﬁcation task in SVMs is implemented by using of these support vectors.Margins of hyperplanes obey following inequality:
yk
D
ð
xk
Þk
w
k
P
C
;
k
¼
1
;
...
;
n
:
ð
7
Þ
To maximize this margin (
C
), norm of
w
is minimized. To reduce the number of solutions for norm of
w
,following equation is determined.
C
k
w
k ¼
1
:
ð
8
Þ
Then formula (9) is minimized subject to constraint (6).
1
=
2
k
w
k
2
:
ð
9
Þ
When we study on the non-separable data, slack variables
n
i
, are added into formula (6) and (9). Instead of formulas (6) and (9), new formulas (10) and (11) are used.
y
i
½ð
w
x
i
Þ þ
w
0
P
1
n
i
;
ð
10
Þ
C
X
ni
¼
1
n
i
þ
1
=
2
k
w
k
2
:
ð
11
Þ
Since srcinally SVMs classify the data in linear case, in the nonlinear case SVMs do not achieve the classi-ﬁcation tasks. To overcome this limitation on SVMs, kernel approaches are developed. Nonlinear input dataset is converted into high dimensional linear feature space via kernels. In SVMs, following kernels are mostcommonly used.
•
dot product kernels:
K
(
x
,
x
0
) =
x
Æ
x
0
;
•
polynomial kernels:
K
(
x
,
x
0
) = (
x
Æ
x
0
+ 1)
d
; where
d
is the degree of kernel and positive integer number;
•
RBF kernels:
K
(
x
,
x
0
) = exp(
k
x
x
0
k
2
/
r
2
); where
r
is a positive real number.In our experiments
r
is selected 10,000.
2.3.3. LSSVM (least squares support vector machines)
LSSVMs are proposed by [13]. The most important diﬀerence between SVMs and LSSVMs is that LSSVMsuse a set of linear equations for training while SVMs use a quadratic optimization problem [14]. While formula(11) is minimized subject to formula (10) in Vapnik’s standard SVMs, in LSSVMs formula (13) is minimized
subject to formula (12).
y
i
½ð
w
x
i
Þ þ
w
0
¼
1
n
i
;
i
¼
1
;
...
;
n
:
ð
12
Þ
1
=
2
k
w
k
2
þ
C
2
X
ni
¼
1
n
2
i
:
ð
13
Þ
According to these formulas, their dual problems are built as following:
Q
ð
w
;
b
;
a
;
n
Þ ¼
1
=
2
k
w
k
2
þ
C
2
X
ni
¼
1
n
2
i
X
ni
¼
1
a
i
f
y
i
½ð
w
x
i
Þ þ
w
0
1
þ
n
i
g
:
ð
14
Þ
Another diﬀerence between SVMs and LSSVMs is that
a
i
(Lagrange multipliers) are positive or negative inLSSVMs but they must be positive in SVMs. Information in detailed is found in [13,14].
2.4. The performance evaluation of LSSVM on the diagnosis of ECG Arrhythmia 2.4.1. Classiﬁcation accuracy
In this study, the classiﬁcation accuracy for the dataset was measured according to Eq. (15):
902
K. Polat, S. Gu¨ nes
/ Applied Mathematics and Computation 186 (2007) 898–906

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