ECG arrhythmia classification based on logistic model tree

doi:10.4236/jbise.2009.26058

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Vol.2, No.6, 405-411 (2009)

doi:10.4236/jbise.2009.26058

JBiSE

ECG arrhythmia classification based on logistic model

tree

V. Mahesh1, A. Kandaswamy2, C. Vimal2, B. Sathish2

1Department of Information Technology, PSG College of Technology, Coimbatore, India; 2Department of Bio-Medical Engineering,

PSG College of Technology, Coimbatore, India.

Email: vm@ity.psgtech.ac.in; hod@bme.psgtech.ac.in; vimalfu@gmail.com; satfrd@gmail.com

Received 6 May 2008; revised 25 May 2009; accepted 9 June 2009.

ABSTRACT

This paper presents a diagnostic system for

classification of cardiac arrhythmia from ECG

data, using Logistic Model Tree (LMT) classifier.

Clinically useful information in the EC G is found

in the intervals and amplitudes of the charac-

teristic waves. Any abnormality in the wave

shape and duration of the wave features of the

ECG is considered as arrhythmia. The ampli-

tude and duration of the characteristic waves of

the ECG can be more accurately obtained using

Discrete Wavelet Transform (DWT) analysis.

Further, the non-linear behavior of the cardiac

system is well characterized by Heart Rate

Variability (HRV). Hence, DWT and HRV tech-

niques have been employed to extract a set of

linear (time and frequency domain) and non-

linear characteristic features from the ECG

signals. These features are used as input to the

LMT classifier to classify 11 different arrhyth-

mias. The results obtained indicate an impres-

sive prediction accuracy of 98%, validating the

choice and combined use of the current popular

techniques (DWT and HRV) for cardiac ar-

rhythmia classification. The system can be de-

ployed for practical use after validation by ex-

perts.

Keywords: ECG; Arrhythmia; Wavelet Transform;

HRV Analysis; Feature Extraction

1. INTRODUCTION

Electrocardiography is a commonly used, non-invasive

procedure for recording electrical changes in the heart.

The record, which is called an electrocardiogram (ECG

or EKG), shows the series of waves that relate to the

electrical impulses which occur during each beat of the

heart. The information present in the ECG characteristic

wave peaks and time intervals between them are impor-

tant. The waves in a normal record are named P, Q, R, S,

and T and follow in alphabetical order. Any abnormal

change in the shape and variation of time intervals is

conside red as arrhythmia.

Detection of abnormal ECG signals is a critical step in

administering aid to patients. Arrhythmias can occur in a

healthy heart and be of minimal consequence. They may

also indicate a serious problem and lead to heart disease,

stroke or sudden cardiac death. Cardiac arrhythmia is

one of the major causes of sudden death. To detect the

presence of arrhythmia, patients are hooked to cardiac

monitors in hospitals. This requires continuous monitor-

ing by the physicians. Visual inspection is tedious and

physician dependent. Computer programs have been

developed to help in this visual analysis by providing

condensed printouts. This again requires meticulous

study by the physician to identify arrh ythmia. To cater to

large number of patients, to eliminate subjective inaccu-

racies and to aid the physician in the diagnosis several

methods for automated arrhythmia detection have been

developed in the past few decades to attempt simplify

the monitoring task and improve diagnostic efficiencies.

In pursuit of arrhythmia detection and classification

work, many computer techniques have been developed.

Notably, Palreddy et al. employed a multiple-classifier

architecture composed of Self Organizing Maps (SOM)

and Learning Vector Quantization (LMQ) to classify

premature ventricular contraction (PVC) beats and the

non-PVC beats [1]. Babak Mohammadzadeh-Asl et al

used both lin ear and non-linear p arameter extracted from

heart rate signals with multilayer feed forward neural

networks to classify only five types of arrhythmias [2]. J.

Lee et al. proposed a wavelet based approach along with

Linear Discriminant Analysis (LDA) for classifying only

five types of arrhythmias using multilayer perceptron

classifier [3]. Chazal et al. has proposed a method for

automatic classification of heartbeats using ECG mor-

phology, heartbeat interval features and RR intervals to

discriminate only five different beat types [4]. Dingfie et

al. classified only six arrhythmias using autoregressive

V. Mahesh et al. / J. Biomedical Science and Engineering 2 (2009) 405-411

406

modeling and Generalized Linear Model (GLM) [5].

Linh et al. selected the Hermite Function Expansion as

the feature extraction method to represent the QRS com-

plex. They proposed a fuzzy neural network where Her-

mite coefficients served as the features to classify only

seven different types of arrhythmias [6]. Kannathal et al.

used three non-linear parameters as inputs to the pro-

posed ANF classifier for classification of only ten dif-

ferent types of arrhythmias [7]. Kadbi et al. used wavelet

parameters along with RR interval and Form Factor as

inputs to an ANN classifier to discriminate only ten dif-

ferent arrhythmias [8].

In clinical domains, one has to face the problem of

developing classifiers that are able to deal with nonlinear

discrimination between classes, incomplete or ambigu-

ous input patterns, and suppression of false alarms. It is

necessary to develop new detection schemes with a high

level of accuracy, or equivalently, low false-positive and

false-negative statistics, for them to be useful in practical

applications. In this direction a new approach based on

Logistic Model Tree classifier is presented in this paper.

LMT is a recent addition to decision trees that replace

the terminal nodes of a decision tree with logistic regres-

sion functions. This has the advantage of producing de-

cision trees that are more comprehensible, have higher

accuracy, and have higher fidelity than previous decision

tree extraction algorithms [9].

2. DATA SOURCE AND CONTENT

ECG data for use in this classification work has been

collected from the MIT-BIH arrhythmia database as

published in Physionet, a site dedicated to data for vari-

ous diseases and their study [10]. The database contains

48 recordings, each containing two 30-min ECG lead

signals (denoted A and B). In 45 recordings, lead A is

modified-lead II and for the other three is lead V5. Lead

B is lead V1 for 40 recordings and is either lead II, V2,

V4 or V5 for the other recordings. Twenty-three records,

numbered from 100 to 124 with some numbers missing,

serve as a representative sample of routine clinical re-

cordings and the remaining twenty-five records, num-

bered from 200 to 234 again with some numbers missing ,

contain complex ventricular and supraventricular ar-

rhythmias. In this work, ECG signals from Modified

Lead II (MLII) leads are chosen. Prior to recording, the

ECG signals in these records have been sampled at a

frequency of 360Hz and preprocessed to remove noise

due to power-line interference, muscle tremors, spikes

etc. This database was selected because it contains a

variety of beat types. Another reason for considering this

database was its use in other studies and thus compari-

son of results can be performed. One minute segments of

each beat type were extracted from the records for fur-

ther processing. This work focused on several important

arrhythmia types such as Paced beat (P), Atrial prema-

ture beat (A), Right bundle branch block beat (R), Left

bundle branch block beat (L), Ventricular escape beat (E),

Ventricular flutter wave (!), premature ventricular con-

traction (V), Fusion of ventricular and normal beat (F),

Fusion of paced (f), Blocked Atrial Premature Beat (x)

and the Normal beat segment (Normal). The number of

segments extracted for each type from the database re-

cords is given in Table 1.

3. FEATURE EXTRACTION

The main objective of the feature extraction process is to

derive a set of parameters that best characterize the sig-

nal. These parameters, in other words, should contain

maximum information abou t the signal. Hence the selec-

tion of these parameters is an important criterion to be

considered for proper classification. Arrhythmia classi-

fication, therefore, involves determination of several

characteristic features of the ECG signal. This work ex-

plores a combination of linear (time and frequency do-

main) and non-linear characteristic features of the ECG

signal. The Discrete Wavelet Transform has been used to

obtain the amplitude and duration of the characteristic

waves of the ECG from which a set of time-domain pa-

rameters are derived. The DWT is also used to obtain the

RR interval time series. Heart Rate Variability (HRV)

helps in understanding the non linear behavior of the

cardiac system. Using the RR series a set of non linear

paramete rs are al so derived.

3.1. Time-Domain Analysis

For each of the segments extracted from the records, the

characteristic points P, Q, R, S and T are obtained using

Discrete Wavelet T ransform.

3.1.1. Discrete Wavelet Transform (DWT)

The wavelet transform is a convolution of the wavelet

function (t) with the signal x(t). Orthonormal dyadic

discrete wavelets are associated with scaling functions

Table 1. Arrhythmia types classified in proposed method.

Type of Arrhythmia No of Segments Ex-

tracted

Normal 459

P 105

A 123

R 99

L 108

E 18

! 24

V 290

F 16

f 27

x 12

V. Mahesh et al. / J. Biomedical Science and Engineering 2 (2009) 405-411

407

tion A1 respectively. The first approximation A1 is de-

composed again and this process is continued. The de-

composition of the signal into different frequency bands

is simply obtained by successive highpass and lowpass

filtering of the time domain signal. The signal decompo-

sition can be mathematically expressed as follows:

(t). The scaling function can be convolved with the

signal to produce approximation coefficients A. The

wavelet transform of the signal x(t) can be written as:

,().

()

mn tdt

Txt







 (1)

By choosing an orthonormal wavelet basis, m, n (t),

one can reconstruct the original signal [11]. The ap-

proximation coefficients of the signal at scale m and

location n can be rep resented by:

y[k] =x[n].g[2k -n]



(3)

y[k]=x[n].h[2k -n]



(4)

The characteristic points P, Q, R, S and T are obtained

at different decomposition levels as shown in Figure 2.

,().

()

mn tdt

Axt







 (2)  Segment selection

 8-level wavelet decomposition using Daube-

chies 6 wavelet functions

3.1.2. DWT Decomposition

Discrete Wavelet Tr ansform involves decomposition of a

signal by wavelet filter banks. DWT uses two filters, a

low pass filter (LPF) and a high pass filter (HPF) to de-

compose the signal into different scales. The output co-

efficients of the LPF are called approximations while the

output coefficients of the HPF are called details. The

approximations of the signal are what define its identity

while the details only imparts nuance [12].

 Detection of R peak at level 4 using adaptive

threshold value (related to the maximum and

mean values of the signal)

 Determination of R-R interval using R-R dis-

tance

 Detection of Q, S points as local minimum

points at level 0, before and after R wave

 Elimination of the QRS complex from the signal

to obtain other parameters

The DWT decomposition of an input signal x[n] is

schematically shown in the Figure 1 below. Each stage

consists of two digital filters and two downsamplers to

produce the digitized signal. The first filter, g[n] is a

high-pass filter, and the second, h[n] is a low-pass filter.

The downsampled outputs of the first high pass filter and

low-pass filter provide the detail D1 and the approxima-

 Detection of T wave at level 6 and 7 for finding

QT distance

 Detection of P wave at level 6 and 7 for finding

P-R and P-P distance

From the values obtained the following five time-

domain parameters have been calculated:

Feature Meaning Formula

P-P Mean of P-P interval duratio n s. TPP = Pi+1 –Pi , i=1…N – 1

R-R Mean of R-R interval durations. TRR=Ri+1 –Ri , i=1…N – 1

P-R The time duration between successive P and R waves in each beat. TPR=R – Pon-set

QRS Duration The time duration from the beginning of the Q wave to the end o

the S wave. TQRS=TS –TQ

QT Inte rval D uration It is the time from the beginning of the Q-wave to the end of the

T-wave TQT =Toff-set–Q

Figure 1. DWT decomposition.

Openly accessible at

V. Mahesh et al. / J. Biomedical Science and Engineering 2 (2009) 405-411

408

3.2. Frequency Domain Analysis

Time-domain methods are computationally simple but

lack the ability to discriminate between sympathetic and

parasympathetic contributions of HRV. Spectral analysis

is the most popular linear technique used in the analysis

of HRV signals [13]. Spectral power in the high fre-

quency (HF) (0.15–0.4 Hz) band reflects respiratory

sinus arrhythmia (RSA) and thus cardiac vagal activity.

Low frequency (LF) (0.04–0.15Hz) power is related to

baroreceptor control and is mediated by both vagal and

sympathetic systems [14]. Hence, the frequency domain

parameter LF/HF, which is the ratio between LF and HF

band powers, is obtained for each segment.

3.3. Non-Linear Analysis

The cardiovascular system is a complex non-linear sys-

tem and is characterized by many complex estimators. In

this classification work the following parameters have

been derived from the RR-interval time series obtained

using DWT.

3.3.1. Spectr al Entropy

The power spectral density (PSD) of a signal is the dis-

tribution of power as a function of frequency. This PSD

can be obtained using Fourier transform. The normaliza-

tion of this PSD yields the probability density function

(PDF) [15]. This PDF has a value in the range

011, 2,...,

pf  (5)



 (6)

The spectral entropy H which describes the complex-

ity of the heart rate variability (HRV) signal is obtained

using Eq.(7).











(7)

Here pf is the probability density function at f. The spec

tral entropy H calculated for each segment is used as one

of the classifying parameters [16].

3.3.2. Detrended Fluctuation Analy sis (DF A )

The Detrended Fluctuation Analysis (DFA) is used to

quantify the fractal scaling properties of short time R-R

interval signals. This technique is a modification of the

root-mean square analysis of random walks applied to

nonstationary signals [17]. The root-mean-square fluc-

tuation of an integrated and detrended time series is

measured at different observation windows and plotted

against the size of the observation window on a log-log

scale. First, the R-R time series (of total length N) is

integrated using the equation:

()( ()))

avg

ykRRi RR





 (8)

where y(k) is the kth value of the integrated series, RR(i)

is the ith inter beat interval and RRavg is the average

inter beat interval over the entire series [18]. Then, the

integrated time series is divided into windows of equal

length, n. In each window of length n, a least squares

line is fitted to the R-R interval data (representing the

trend in that window). The ‘y’ coordinate of the straight

line segments are denoted by yn(k) . Next, we detrend

the integrated time series, yn(k) in each window. The

root mean-square fluctuation of this integrated and de-

trended series is calculated using Eq.(9) for each seg-

ment.

()[() ()]

nyky

N



k (9)

4. LOGISTIC MODEL TREES CLASSIFIER

Logistic Model Trees are a combination of a tree struc-

ture and logistic regression functions to produce a single

decision tree [19,20,21,22]. The decision tree structure

has the logistic regression functions at the leaves. The

leaf node has two child nodes which is branched right

Figure 2. Characteristic points extraction from ECG signal at various decomposition levels.

V. Mahesh et al. / J. Biomedical Science and Engineering 2 (2009) 405-411

409

and left depending on the threshold. If the value of the

attribute is smaller than the threshold it is sorted to left

branch and value of attribute greater than the threshold it

is sorted to right branch as shown in Fi gure 3.

The threshold is usually fixed by Logit Boost method

[19]. Logit Boost uses a ensemble of functions FK to

predict classes 1, . . . , K using M “weak learners”.

() ()



x

(10)

Steps followed for developing the LMT classifier:

 The linear regression function is fitted using the

Logitboost method to build a logistic model.

The Logitboost method uses 5 examples for the

cross validation to determine the best number of

iterations to run, when fitting the logistic regres-

sion function at a node of the decision tree

 The logistic model is built using all data.

 The split of the data at the root is constructed

using the threshold.

 This splitting is continued till some stopping

criterion is met. Here the stopping criterion is 5

examples, since it helps in cross validation for

logitboost method.

 Once the tree has been build it is pruned using

CART-based pruning [19].

Reasons for choosing the Logistic Model Tree classifier:

 Logistic Regression is very good at detecting

linear relationships and then combining those

relationships into an equation that provides the

odds of the dependent variable reaching a par-

ticular outcome, when the various independent

variables are fed into the resulting equation.

 Logistic Regression models are widely used and

they are considered robust and not prone to over

fitting the data.

 These models can be built with high level of

accuracy using little data preparation.

 Logistic Model Trees give explicit class prob-

ability estimates rather than just a classification.

The classification task, depicted in Figure 4, involves

the following steps:

Figure 3. Tree structure of logistic model tree (LMT).

Figure 4. Block diagram of the proposed method.

V. Mahesh et al. / J. Biomedical Science and Engineering 2 (2009) 405-411

410

 One minute segments of each beat type are ex-

tracted from ECG records in the database.

 Each segment is then decomposed using DWT

into various levels for extracting linear time-

domain parameters.

 The different nonlinear parameters are calcu-

lated using their respective formula.

 Both linear and non-linear parameters for all the

segments are combined and a dataset is formed.

 75% of the dataset, called training set, is used

for training the classifier.

 The remaining 25% of the dataset, called test set,

is used for testing the classifier.

5. RESULTS AND DIS CUSSIONS

The objective of any clinical research is to find the rela-

tionship between results and presence of any disease.

For the evaluation of the proposed classifier, a total of

1281 segments, extracted from the MIT BIH arrhythmia

database records were used. Five time-domain, one fre-

quency domain and two non-linear parameters were de-

rived from these segments. These eight parameters along

with the corresponding output class (type of arrhythmia)

forms a feature vector. Thus 1281 feature vectors com-

prise the dataset. 75% of each type from this dataset was

used as the train dataset and the remaining 25% as the

test dataset. The output obtained from the Logistic

Model Tree was used to calculate the accuracy of each

type of beat using Eq.(11)).

Number ofbeatscorrectly classified

Accuracy Totalnumber ofbeats



(11)

The experimental results are presented in Table 2.

Table 2. Performance of the proposed method.

Type of

Arrhythmia No of Segments

Extracted No of Segments for

Training No of Segments for

Testing Correctly

Classified Accuracy %

Normal 459 353 106 102 96.22

P 105 74 31 29 93.54

A 123 95 28 26 92.85

R 99 74 25 25 100

L 108 77 31 31 100

E 18 13 5 5 100

! 24 18 6 6 100

V 290 219 71 70 98.6

F 16 12 4 4 100

F 27 19 8 8 100

X 12 7 5 5 100

Average=98.29

Table 3. Performance comparison of different ECG arrhythmia classifiers.

Work Reference Types Accuracy (%) Feature Extraction Method Classifier

Palreddy [1] 2 98.58% LVQ SOM

Babak [2] 5 99.38% HRV NN

Lee [3] 5 99.48% WT LDA/MLP

Chazal[4] 5 96.87% ECG Morphology/ Interval LDA

Dingfie [5] 6 93.2% AR Modeling GLM

Linh [6] 7 96% HER FNN

Kannathal [7] 10 94.64% HRV ANN

Kadbi [8] 10 90% WT Cascade ANN

Proposed Method 11 98.29% DWT/HRV LMT

V. Mahesh et al. / J. Biomedical Science and Engineering 2 (2009) 405-411

411

Table 3 shows the performance comparison of the

different ECG arrhythmia classifiers. The proposed me-

thod shows comparable performance even when 11 dif-

ferent types of arrhythmias have been considered.

6. CONCLUSIONS

In this paper, the effectiveness of the Logistic Model

Tree classifier for arrhythmia classification has been

demonstrated. The Logistic Model Tree classifier was

fed by the combination of linear and non-linear parame-

ters derived from ECG data using DWT and HRV. The

results indicate that the proposed method employing the

LMT classifier with linear and nonlinear parameters is

effective for classification of cardiac arrhythmias with an

acceptably high accuracy. Compared to other approaches

in the literature cited, the proposed method exploits the

power of HRV and DWT techniques in discriminating 11

different arrhythmia types. Parameters derived from

ECG features and HRV analysis can therefore be used as

a reliable indicator of different types of arrhythmias. The

proposed system, after validation by experts, can serve

as a diagnostic tool and aid the physician in the detection

and classification of cardiac arrhythmias.

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