arrhythmia classification using support vector machine -alexis pena

8/12/2019 Arrhythmia Classification Using Support Vector Machine -Alexis Pena

1/36

CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

ARRHYTHMIA CLASSIFICATION USING SUPPORT VECTOR MACHINE

A graduate project submitted in partial fulfillment of the requirements

For the degree of Master of Science

in Electrical Engineering

By

Alexis Pena

August 2013


2/36

ii

The graduate project of Alexis Pena is approved:

__________________________________ _________________________

Benjamin F Mallard Date

__________________________________ _________________________

Dr. Ali Amini Date

__________________________________ _________________________

Dr. Xiyi Hang, Chair Date

California State University, Northridge


3/36

iii

TABLE OF CONTENTS

Signature page.ii

Abstract...iv

Introduction..1

Support Vector Machine .8

Feature extraction ..........12

Numerical Experiment.......14

Discussion......22

Bibliography .....23

Appendix....24


4/36

iv

ABSTRACT

ARRHYTHMIA CLASSIFICATION USING SUPPORT VECTOR MACHINE

By

Alexis Pena

Master of Science in Electrical Engineering

The number one cause of death in the United States is heart disease (1). 67% of heart

disease death is brought on by sudden cardiac death. Most of these cases are due to an

abnormal electrical triggering of the heart which disrupts blood circulation that lead to

immediate death if electrical shock therapy is not applied. Automatic arrhythmia analysis

helps speed up the defibrillation therapy to correct the disruption in the electrical system.

Implantable defibrillators analyze every heart beat and proper classification is the key to

saving thousands of lives every year. In my project, I approached automatic arrhythmia

analysis through support vector machine classification (SVMs). I analyze time series

ECG heartbeat files from multiple subjects with various arrhythmias, as well as normal

heartbeats with no arrhythmias. The heartbeat signals are extracted into individual beats

and classified using SVM. The performance of the SVM is evaluate through multiple

kernel modification, including higher order dimension analysis and compared to achieve

the best classification accuracy rate. Finally, the wavelet transform is taken of the

individual signals to maintain enough features while compressing and reducing the

sample size to classify each signal with a high accuracy rate. Through my numerical

experiments I conclude that SVM provides fast and accurate arrhythmia classification

allowing automatic analysis without human oversight.


5/36

1

INTRODUCTION

A healthy human heart pumps about 2,000 gallons of blood through all of our veins and

arteries every single day. It carries oxygen and nutrients to every cell in our body. With

an average of 100,000 heart beats per day, (2) it is one of the hardest working organs in a

human body. The heart beats because of the small electrical current generated by the

cardiac conduction system. An electrocardiogram, ECG is a noninvasive procedure that

records the electrical activity of the heart over a period of time. The morphology of a

heartbeat can provide many detail of a patient. We can determine the cause of symptoms

of heart disease, such as dizziness, fainting or shortness of breath. We can check the

health of the heart when other conditions are present, such as diabetes, high cholesterol,

high blood pressure, or cigarette smoking. And we can check the maintenance of

mechanical devices, such as a pacemaker working in combination with other organs

throughout the rest of the body. An ideal heart beat has five deflections.

Figure 1. QRS complex wave with P and T wave.

The ECG will record the electrical activity that comes from depolarization and

repolarization of the heart muscle cells when the atria and ventricles contract. The P wave

results from atrial depolarization which spreads from the SA node throughout the atria

and pumps blood through the open valves from the atria into both ventricles. The time


6/36

2

between the P and Q wave is when the signal arrives at the atrioventricular (AV) node

and allows the hearts left and right ventricles to fill with blood. The Q wave results from

when the signal arrives at the bundle of His and is divided into left and right bundle

branches. The signal leaves the bundle branches through the Purkinje fibers and spreads

across the hearts ventricles causing them to contract which pushes the blood though the

pulmonary value into the lungs and through the aortic valve to the rest of the body . The

left ventricles contracts first immediately followed by the right, this is marked by the R

wave and S wave respectively. After the signal passes, the ventricles relax and await the

next signal. The T wave marks the point when the ventricles are relaxing.

Any changes from a normal heart beat may indicate a problem with the patient. A patient

with atrial premature complexes, APC will have a reduced p wave. In this paper, the

following arrhythmia groups have been considered: Normal Sinus Rhythm (NOR), Atrial

Premature Contractions (APC), Ventricular premature complexes (VPC), Left Bundle

Branch Block (LBBB) and Right Bundle Branch Block (RBBB). An atrial premature

contraction (APC) is a heart rhythm disorder that involves a premature firing of the

atrium (3), its feels like an extra heartbeat. On an ECG, APC will have a reduce P wave.


7/36

3

Figure 2. ECG of a heart beat with APC

A ventricular premature complex (VPC) is perceived as a skipped beat, with a sensation

feeling of palpitations in the chest. On an ECG, VPC is identifiable when the P wave is

closer to the QRS complex. You will also see a longer duration from the T wave to the

next QRS complex (4).

Figure 3. ECG of a heart beat with VPC


8/36

4

In Left bundle branch block, (LBBB) the left ventricle contracts later than the right

ventricle. On an ECG, the T wave is deflected opposite compared to a normal sinus

rhythm.

Figure 4. ECG of a heart beat with LBBB

Right bundle branch block, (RBBB) is the result when the right ventricle is not activated

by the current charge traveling through the right bundle branch. During this time, the left

ventricle is operating normal. On an ECG graph we can see a slurred S wave as well as a

widen QRS complex (5).


9/36

5

Figure 5. ECG graph showing a heartbeat with RBBB

In a normal heart beat we can see the P wave, QRS complex and the S wave.

Figure 6. ECG of a normal heart beat.

Comparing the 4 arrhythmias to the normal heart beat, we can clearly distinguish the

features that give the ECG its unique characteristics for each arrhythmia. A trained

cardiologist can diagnose various arrhythmias just by looking at the ECG of a patient.

This method is not very practical since the cardiologist cannot monitor the patient at all


10/36

6

times. A holter monitor is used to record the hearts activities for at least 24 hours and

later analyzed. In 24 hours, the holter monitor will record about 100,000 heartbeats

making it a tedious task to do without computer help. The computational analysis of the

ECG signals gives an output with a tally of the unique recorded heart beats. The field of

arrhythmia classification is continuously evolving. There are several techniques for

providing classification. Shape based matching algorithms using Fourier transform are

used for classification from ECG printouts (6). In pattern recognition, k-nearest neighbor

and neural networks provide similar approaches to that of SVM. Morphological pattern

recognition is the leading method for accurate classification among ECG signals. I

propose using the integrated software for support vector classification, libsvm to do

multiclass classification with a multi-order polynomial kernel to provide a high accuracy

rate of 99.6% in arrhythmia classification. I take advantage of SVMs simplicity.

Through minimal code and lack of computational expenses, I incorporated arrhythmia

analysis that could be used in implantable devices to save thousands of lives each year. In

this paper I explain the mathematical background and methods of support vector machine

and feature extractions to bring an understanding of classification. I explain the method

of gaining the ECG signals and how training and testing of the datasets was completed

using matlab. In chapter 5, procedure i go into detail of how each heartbeat was

separated, grouped and label into a single matrix file. A 10-fold cross validation was

performed to achieve the best kernel function for a high accuracy rate within

classification. A feature extraction process was performed with wavelet transform in

matlab to reduce the signal data while maintaining enough features to perform

classification without a drop in accuracy. In the proceeding chapter, I clarify the results of


11/36

7

classification and conclude with an overview of the projects expectation and how the

results were met.


12/36

8

SUPPORT VECTOR MACHINE

Binary classification starts with some input data used for training:

, , , , 1,1 2.1

with the goal of finding the function,, , that can best approximate thefunction . The training data is considered linearly separable if the data can beseparated with a linear hyperplane,

, 2.2

There could be many different hyperplanes that could linearly separate the training data

but there is one hyperplane that has the biggest gap between the two data called the

maximum margin hyperplane. The maximum margin hyperplane must satisfy the

following condition:

1 2.3

while having the minimal norm:

2.4


13/36

9

Figure7.Maxmarginhyperplane

In figure 7 we see the separation of the two data points, H1 and H2 by the hyperplane, H.The distance from H to H1 is:

| |||||

1||||

2.5

And from H1 to H2 is:

2||||2.6


14/36

10

If the training data cannot be linearly separated, we can use a soft margin hyperplane,

which allow misclassification through the slack variable,while still maximizing themargin. We need to minimize:

2.7

under constraints:

1 0 2.8

The optimal separating hyperplane for the separable and non-separable case is through

finding the saddle point of the lagrangian:

, , , 1 2.9

0, 0

Since, and is the maximum point of:

, , 2.10

0, 0

The separating hyperplane is:

2.11

In SVM, we sometimes need to map input vectors non-linearly into a high dimensional

feature space. Having multiple inputs increases complexity of classification thus mapping


15/36

11

into high feature space allows for a better decision surface. Using polynomial kernel

allows for better classification:

, 1 ,

1, 2.12

where d is the degree of the polynomial.

We can perform the kernel trick of replacing every dot product by the nonlinear

polynomial kernel function to create our nonlinear classifier. A kernel trick allows us to

map observations from a general set D into an inner product space S which only requires

dot products between the vectors in S. The kernel trick permits high-dimensional dot

products to be computed within the original space.

In order to do a multi-class classifier, we perform multiple binary classifications to

reduce the single multiclass problem (7). There are two general approaches in multiclass

classification, one-versus-all and one-versus-one classification. In a one-versus-all

strategy, a single classifier is trained per class that separates it from all the other classes.

The prediction with the highest confidence is chosen after predicting each binary

classifier. In a one-versus-one strategy, classification is done where every classifier

assigns the instance to one of the two classes, the assigned class gets one vote and

increases over time, in the end the class with the most votes determines that moments

classification.


16/36

12

FEATURE EXTRATION

In discrete wavelet transform, the signal, is passed through a low pass filter withimpulse response

resulting in the convolution (8):

3.1

The signal is also decomposed simultaneously using a high pass filter. The outputs are

the approximation and detail coefficients from the low and high pass filter respectively

(9):

2 Low-pass filter output 3.2

2 High-pass filter output 3.3

The result is one half the time resolution due to the decomposition.

Figure 8. Filter analysis

The decomposition is repeated and cascaded to create a filter bank.


17/36

13

Figure 9. 3 level filter bank of decomposition

Creating the decomposition in reverse is called reconstruction. The detail and

approximation coefficients are upsampled by two at every level and passed through a

low-pass and high-pass filter.

Figure 10. 3 level filter bank of reconstruction

The process of decomposition and reconstruction allows for de-noising and compression

of the signal while maintaining the unique features without affecting the accuracy rate of

classification (10).


18/36

14

NUMERICAL EXPERIMENTS

The ECG files were acquired from PhysioNet.org. PhysioNet offers free web access to

large collections of recorded physiologic signals (PhysioBank) and related open-source

software (PhysioToolkit) (11). From the website, twenty records were downloaded from

twenty different patients. The records that were captured were one hour in length from

patients as young as 24 years old to 87 years old. The files were in .mat format and came

with an annotation file for each ECG. The annotation files marked each heart beat and

assigned a label on the R peak of the QRS complex wave and based on the category of

the arrhythmia, it was given a letter. The letter identified each arrhythmia within the ECG

signal. Matlabwas the software of choice for its numerical computing environment (12).

The files were uploaded into matlab with a software extension package called libsvm.

Libsvm is integrated software for support vector classification that supports multi-class

classification (13). Feature extraction was done through matlab via the wavelet

decomposition.


19/36

15

The annotation files were manually imported one by one into matlab and the datasets

entered into matrixes. Based on the arrhythmia needed, which was searched by a single

letter indicating the arrhythmias, (A = APC, V=PVC, L=LBBB, R=RBBB, N=Normal)

all the categories were grouped and saved as a separate .mat file. The procedure was

repeated for each patient file. Next the hour long ECG file was loaded into matlab and

with a sampling rate on 360 and the annotation time stamp, each labeled heart beat was

extracted. The result was a 301 sample heart beat that included the P wave, QRS complex

and T wave from start to finish. The second matlab script file combined all the groups

into one giant training file containing 5400 heart beats in a 5400 by 301 matrix. The

appropriate training labels were assigned and SVM classification was produce with the

libsvm package. The test file was created in similar fashion as the training dataset but

with only 2036 samples. Libsvm offers multiple types of kernel functions. In this paper

we only look at Linear, polynomial 2nd

order, 3rd

order and 4th order. The cost of the

kernel varies from 10-3

to 10+3

and the best value was calculated using a 10-fold cross

validation. The gamma in the kernel function was also manipulated with the 10-fold cross

validation. After the first classification on the original signal files, feature extraction was

performed to reduce the number of samples in the ECG. Having fewer samples gives us

the ability to run faster analysis, while maintaining a small memory size. The samples in

the ECG signal were reduced from 301 to 154, 80, 43, 25, 16, 11, and 9 in a seven level

reconstruction.


20/36

16

Figure 11. ECG graph of original 301 sample vs. level 5 feature extraction with 25

samples

Using the small sample size, SVM classification was redone for each step and my

algorithm maintained a high accuracy.

To evaluate the performance of the classifier, we first setup the kernel function for linear

classification by setting the kernel flag options with -t 0 and the cost parameter at 10-3

.

After training and testing, our accuracy was 99.26%. Next we try changing the cost to C

= 10-2

and C = 10-1

up until C = 103and the accuracy remained the same at 99.26%

To properly visualize the classification performance and compare the accuracy, a

confusion matrix was computed. The results conclude that not only is the high accuracy

valid, its performance to properly classify the test data is efficient with regards to

providing true positive classification.

The next step in classification was to change the kernel function to polynomial in second

order. This is done by setting the option flag with -t 1 d 2. The d is for setting the

degree or order of the classifier. We did the testing by changing the cost uniformly from


21/36

17

C = 10-3

to C = 103. After training and testing the dataset, our results were similar to

linear classification, 99.26%. Changing the order of classification from 2nd

order to 3rd

and 4th

order had no effect on accuracy, which remained at 99.26%. Computing a

confusion matrix yield the same results for the linear kernel, therefore table 2 and 3 could

be associated with a polynomial kernel.

Table 1. Accuracy on testing results

C 10-3

10-2

10-1

100

101

102

103

Linear 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

2ndOrder 99.26%

99.26% 99.26% 99.26% 99.26% 99.26%

99.26%

3rd

Order 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

4th

Order 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Table 2. Confusion Matrix

Actual/Predicted APC PVC LBBB RBBB Normal

APC 74 1 0 0 1

PVC 0 106 0 0 1

LBBB 0 10 481 0 0

RBBB 0 0 0 625 0

Normal 1 1 0 0 735


22/36

18

Table 3. Table of confusion

True Positive False Negative False Positive True Negative

APC 74 2 1 1959

PVC 106 1 12 1917

LBBB 481 10 0 1545

RBBB 625 0 0 1411

Normal 735 2 2 1297

Our next focus was to evaluate how well feature extraction reduced a signal file while

maintaining the important characteristics. In a 7 level feature extraction, 301 samples are

reduce and trained and tested for each level and the accuracy recorded. First Linear

classification was performed. For the first 3 levels, the features were reduced from 301

samples to 157, 80 and 43, and the accuracy remained unchanged at 99.26%. The results

are listed in Table 2. Varying the cost also had no change. On the fourth level, where the

features were reduced to 25 samples, the accuracy went down to 99.17%. Adjusting the

Cost from C = 10-3

to 103also had no effect on accuracy. But changing the cost to C = 10

-

4gave us an accuracy of 99.12%, and C = 10

-5increase it to 99.26%, the same accuracy

rate as our first evaluation with 301 samples. The accuracy rate of level 6 with only 11

features was 97.84% and 95.04% on level 7 with only 9 samples! Changing the cost does

have some slight effect on accuracy. The rest of the feature extraction results can be

viewed on tables 3 through 5.


23/36

19

Table 4. Feature extraction on linear kernel

Linear kernel

10-3

10-2

10-1

100 10

1 10

2 10

3

Level 1 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 2 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 3 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 4 99.17% 99.17% 99.17% 99.17% 99.17% 99.17% 99.17%

Level 5 98.62% 98.67% 98.58% 98.72% 98.67% 98.67% 98.53%

Level 6 97.94% 98.08% 97.69% 97.84% 97.59% 97.79% 97.69%

Level 7 96.02% 95.78% 95.87% 95.04% 95.24% 95.73% 95.14%

Table 5. Feature extraction on 2nd order kernel

2

nd

order polynomial kernel

10-3

10-2

10-1

100 10

1 10

2 10

3

Level 1 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 2 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 3 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 4 99.07% 99.07% 99.07% 99.07% 99.07% 99.07% 99.07%

Level 5 98.82% 98.82% 98.82% 98.82% 98.82% 98.82% 98.82%

Level 6 98.43% 98.33% 98.33% 98.38% 97.54% 98.28% 97.54%

Level 7 97.3% 97.05% 93.27% 96.76% 95.92% 95.92% 96.41%


24/36

20

Table 6. Feature extraction on 3rd order kernel

3rd


10-3

10-2

10-1

100 10

1 10

2 10

3

Level 1 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 2 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 3 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 4 99.07% 99.07% 99.07% 99.07% 99.07% 99.07% 99.07%

Level 5 98.77% 98.77% 98.77% 98.77% 98.77% 98.77% 98.77%

Level 6 98.08% 98.08% 98.08% 98.08% 98.08% 98.08% 98.08%

Level 7 97.05% 96.66% 97.45% 97% 96.56% 97.25% 96.76%

Table 7. Feature extraction on 4th order kernel

4th


10-3

10-2

10-1

100 10

1 10

2 10

3

Level 1 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 2 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 3 99.31% 99.31% 99.31% 99.31% 99.31% 99.31% 99.31%

Level 4 99.07% 99.07% 99.07% 99.07% 99.07% 99.07% 99.07%

Level 5 98.92% 98.92% 98.92% 98.92% 98.92% 98.92% 98.92%

Level 6 97.99% 97.99% 97.99% 97.99% 97.99% 97.99% 97.99%

Level 7 96.91% 96.66% 96.86% 96.71% 96.94% 96.66% 96.51%


25/36

21

The results from all 4 tables show a small variance in accuracy when changing the Cost

or the kernel type. The best result was from the 4th

order polynomial after level 3 feature

extraction for a rate of 99.31% and the worst was the 2nd

order polynomial at level 7 for a

rate of 93.27%


26/36

22

DISCUSSION

In my paper I describe the effects of support vector machine classification on ECG signal

for arrhythmia classification and seven level feature extractions. Classification was done

with matlab and libsvm software package to import twenty hour long ECG signal files

and analyze and collect each heart beat into its appropriate category. Once categorize and

labeled, the heart beats were trained and classification testing was done on a second set of

arrhythmias and the accuracy rate recorded. Several kernel functions were used,

including linear and high order polynomials to provide better classification. The results

show the high accuracy effectiveness of SVM on ECG signals. Through proper feature

extraction, we were able to reduce the sample set on each heart beat from 301 samples to

9 samples while maintaining a high accuracy rate. A reduction of samples will reduce the

memory size and processing time of classification without the cost of accuracy.

ECG signals are very important because of their noninvasive approach to diagnose

various heart conditions. We can help treat heart disease and prevent problems from

forming through early detection. My paper brought forth the ease of arrhythmia detection

through SVM classification. The feature reduction ability will allow low memory usage

to incorporate such SVM algorithms into mobile devices to be readily available to more

patients who can self-monitor their own heartbeat.


27/36

23

BIBLIOGRAPHY

1.Deaths:PreliminaryDatafor2011.Hoyert,yDonnaL.6,2012,Vol.61.

2.AmericanHeartAssociation.[Online][Cited:April1,2013.]www.americanheart.org/.

3.ECGPedia.org.[Online][Cited:March15,2012.]

http://en.ecgpedia.org/wiki/Atrial_Premature_Complexes.

4.JatinDave,MD,MPH.VentricularPrematureComplexes.http://emedicine.medscape.com/.

[Online]Nov.12,2012.

5.FrankG.Yanowitz,M.D.RBBB.ECGlearningcenter.[Online]2006.http://ecg.utah.edu/.

6.T.,SyedaMahmood.ShapebasedMatching.EngineeringinMedicineandBiologySociety.

2007.

7.Duan,KaiBoandandKeerthi,S.Sathiya.WhichIstheBestMulticlassSVMMethod?An

EmpiricalStudy.ProceedingsoftheSixthInternationalWorkshoponMultipleClassifierSystems.

2005.

8.Akansu,AliN.andHaddad,RichardA.Multiresolutionsignaldecomposition:transforms,

subbands,andwavelets.Boston,MA:AcademicPress,1992.

9.Mallat,S.AWaveletTourofSignalProcessing,2nded.1999.

10.HoTattWeiandJeoti,V.AwaveletfootprintsbasedcompressionschemeforECGsignals.

2004.

11.PhysioNet.[Online][Cited:September5,2012.]www.physionet.org.

12.Matlab.[Online][Cited:October2,2011.]http://www.mathworks.com/products/matlab/.

13.ChihChungChangandChihJenLin.Libsvm.[Online][Cited:September2012,2012.]

http://www.csie.ntu.edu.tw/~cjlin/libsvm/.

14.LIBSVM:ALibraryforSupportVectorMachines.Lin,ChihChungChangandChihJen.Taipei,

Taiwan:s.n.,2001.


28/36

24

APPENDIX

Matlab code

%%clcclose

clear

load('sapc1.mat');

a1 = poi2;load('sapc2.mat');

a2 = poi2;

load('spvc1.mat');p1 = poi2;

load('spvc2.mat');

p2 = poi2;load('spvc3.mat');

p3 = poi2;

load('slbbb1.mat');

l = poi2;load('srbbb1.mat');

r = poi2;

load('snor1.mat');n1 = poi2;

load('snor2.mat');

n2 = poi2;



%%

train = [a2(1:300,:); p2(1:400,:); l(1:2000,:); r(1:1200,:); n2(1:1500,:)];

labels = [ones(300,1); 2*ones(400,1); 3*ones(2000,1); 4*ones(1200,1); 5*ones(1500,1)];

model = svmtrain(labels, train, '-t 1 -d 4 -c .001 ');

test = [a2(301:376,:); p2(401:507,:); l(2001:2491,:); r(1201:1825,:); n2(1501:2237,:)];tlabels = [ones(76,1); 2*ones(107,1); 3*ones(491,1); 4*ones(625,1); 5*ones(737,1)];

%test = [a1(1:76,:); p2(401:428,:); p1; p3; l(2001:2491,:); r(1201:1825,:); n1(1:737,:)];

[predicted_label, accuracy, dec] = svmpredict(tlabels, test , model);

%% Coefficients of approximations at level 1


29/36

25

ca1 = mdwtdec('r',train,7,'sym4');

ca1t = mdwtdec('r',test,7,'sym4');train2 = mdwtrec(ca1,'ca',1);

test2 = mdwtrec(ca1t,'ca',1);

model2 = svmtrain(labels, train2, '-t 1 -d 4 -c .001');[predicted_label, accuracy, dec] = svmpredict(tlabels, test2 , model2);

%% Coefficients of approximations at level 2train3 = mdwtrec(ca1,'ca',2);


model3 = svmtrain(labels, train3, '-t 1 -d 4 -c 1000 ');[predicted_label, accuracy, dec] = svmpredict(tlabels, test3 , model3);


train4 = mdwtrec(ca1,'ca',3);

test4 = mdwtrec(ca1t,'ca',3);model4 = svmtrain(labels, train4, '-t 1 -d 4 -c .001 ');

[predicted_label, accuracy, dec] = svmpredict(tlabels, test4 , model4);


train5 = mdwtrec(ca1,'ca',4);test5 = mdwtrec(ca1t,'ca',4);

model5 = svmtrain(labels, train5, '-t 1 -d 4 -c 1000 ');


%% Coefficients of approximations at level 5train6 = mdwtrec(ca1,'ca',5);










model8 = svmtrain(labels, train8, '-t 1 -d 4 -c .01 ');



30/36

26

Figure 12. QRS complex wave with P and T wave.

Figure 13. ECG of a heart beat with APC

Figure 14. ECG of a heart beat with VPC


31/36

27

Figure 15. ECG of a heart beat with LBBB

Figure 16. ECG graph showing a heartbeat with RBBB


32/36

28

Figure 17. ECG of a normal heart beat.

Figure 18. Filter analysis

Figure 19. 3 level filter bank of decomposition


33/36

29

Figure 20. 3 level filter bank of reconstruction

Figure 21. ECG graph of original 301 sample vs. level 5 feature extraction with 25

samples


34/36

30

Table 8. Accuracy on testing results

C 10-3

10-2

10-1

100

101

102

103

Linear 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

2ndOrder 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

3rd

Order 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

4th

Order 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Table 9. Confusion Matrix

Actual/Predicted APC PVC LBBB RBBB Normal

APC 74 1 0 0 1

PVC 0 106 0 0 1

LBBB 0 10 481 0 0

RBBB 0 0 0 625 0

Normal 1 1 0 0 735

Table 10. Table of confusion

True Positive False Negative False Positive True Negative

APC 74 2 1 1959

PVC 106 1 12 1917

LBBB 481 10 0 1545

RBBB 625 0 0 1411

Normal 735 2 2 1297


35/36

31

Table 4. Feature extraction on linear kernel

Linear kernel

10-3

10-2

10-1

100 10

1 10

2 10

3

Level 1 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 2 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 3 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 4 99.17% 99.17% 99.17% 99.17% 99.17% 99.17% 99.17%

Level 5 98.62% 98.67% 98.58% 98.72% 98.67% 98.67% 98.53%

Level 6 97.94% 98.08% 97.69% 97.84% 97.59% 97.79% 97.69%

Level 7 96.02% 95.78% 95.87% 95.04% 95.24% 95.73% 95.14%

Table 5. Feature extraction on 2nd order kernel

2nd


10-3

10-2

10-1

100 10

1 10

2 10

3

Level 1 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 2 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 3 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 4 99.07% 99.07% 99.07% 99.07% 99.07% 99.07% 99.07%

Level 5 98.82% 98.82% 98.82% 98.82% 98.82% 98.82% 98.82%

Level 6 98.43% 98.33% 98.33% 98.38% 97.54% 98.28% 97.54%

Level 7 97.3% 97.05% 93.27% 96.76% 95.92% 95.92% 96.41%


36/36

Table 6. Feature extraction on 3rd order kernel

3rd


10-3

10-2

10-1

100 10

1 10

2 10

3

Level 1 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 2 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 3 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 4 99.07% 99.07% 99.07% 99.07% 99.07% 99.07% 99.07%

Level 5 98.77% 98.77% 98.77% 98.77% 98.77% 98.77% 98.77%

Level 6 98.08% 98.08% 98.08% 98.08% 98.08% 98.08% 98.08%

Level 7 97.05% 96.66% 97.45% 97% 96.56% 97.25% 96.76%

Table 7. Feature extraction on 4th order kernel

4th


10-3

10-2

10-1

100 10

1 10

2 10

3

Level 1 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 2 99.26% 99.26% 99.26% 99.26% 99.26% 99.26% 99.26%

Level 3 99.31% 99.31% 99.31% 99.31% 99.31% 99.31% 99.31%

Level 4 99.07% 99.07% 99.07% 99.07% 99.07% 99.07% 99.07%

Level 5 98.92% 98.92% 98.92% 98.92% 98.92% 98.92% 98.92%

Level 6 97.99% 97.99% 97.99% 97.99% 97.99% 97.99% 97.99%

Level 7 96.91% 96.66% 96.86% 96.71% 96.94% 96.66% 96.51%

arrhythmia classification using support vector machine -alexis pena

Documents