FINDING NEW EASI ECG COEFFICIENTS

Improving EASI ECG Model using Various Regression Techniques

Wojciech Oleksy and Ewarystk Tkacz

Silesian University of Technology, Gliwice, Poland

Keywords: EASI, ECG, Multilayer perceptron, SMO, Artificial neural network, Linear regression, Pace regression.

Abstract: Main idea of this study was to increase efficiency of the EASI ECG method introduced by Dover in 1988

using various regression techniques. EASI was proven to have high correlation with standard 12 lead ECG.

Apart from that it is less susceptible to artefacts, increase mobility of patients and is easier to use because of

smaller number of electrodes. Multilayer Perceptron (Artificial Neural Network), Support Vector Machine

Regression (with Sequential Minimal Optimization algorithm), Linear Regression and Pace Regression

methods were used to improve the quality of the 12-lead electrocardiogram derived from four (EASI)

electrodes. Hundreds of ANNs with different learning rates and number of hidden layers were built and

tested using data from PhysioNet and also data that were artificially generated. Next SMO Regression

method with few different kernels (polynomial, normalized polynomial and RBF), Linear Regression and

Pace Regression method were tested on the same dataset. All computed results were compared with those

obtained using classic EASI ECG method described by Dover. Computation of Root Mean Squared Error

and Correlation Coefficient was performed to measure the overall result of a given method. Obtained results

show that various regression methods could be used to increase the performance of EASI ECG method and

thus make it more popular.

1 INTRODUCTION

In 1988 Dower and his team introduced EASI ECG

system, which derives standard 12 lead ECG using

only 5 electrodes. The E electrode is on the sternum

while, the A and I electrodes are at the left and right

mid-auxiliary lines, respectively. The S electrode is

at the sternal manubrium. The fifth electrode is a

ground and is typically placed on one or the other

clavicle, see Fig 1. EASI was proven to have high

correlation with standard 12 lead ECG, as well as

with Mason-Likar 12-Lead ECG. Apart from that it

is less susceptible to artifacts, it increase mobility of

patients, it is easier and faster to use because of

smaller number of electrodes. What is more, smaller

number of electrodes reduces cost of a device. The

electrodes are positioned over readily identified

landmarks which can be located with minimal

variability, independent of the patient’s physique,

assuring high repeatability. The electrode placement

make the chest largely unencumbered, allowing

physical or imaging examination of the heart and

lungs without removing the electrodes.

2 PROBLEM DESCRIPTION

In the classical approach introduced by Dower,

using the EASI lead configuration, 3 modified

vectorcardiographic signals are recorded from the

following bipolar electrode pairs:

- A-I (primarily X, or horizontal vector component)

- E-S (primarily Y, or vertical vector component)

- A-S (containing X, Y, plus Z, the anteriorposterior

component)

Each of the 12 ECG leads is derived as a weighted

linear sum of these 3 base signals using the

following formula:

derive

= a(A – I) + b(E – S) + c(A – S) (1)

where L represents any surface ECG lead and a, b,

and c represent empirical coefficients. These

coefficients, developed by Dower, are positive or

negative values, accurate to 3 decimal places, which

result in leads very similar to standard leads.

Our idea to improve EASI ECG performance

was to find new model used for 12 ECG leads

calculation. To do that we treated the system as a

black box with 4 input variables: E, A, S, I and 12

406

Oleksy W. and Tkacz E..

FINDING NEW EASI ECG COEFFICIENTS - Improving EASI ECG Model using Various Regression Techniques.

DOI: 10.5220/0003788404060409

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 406-409

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Lead placement for the EASI system (A) and the Mason-Likar (B) 12-lead electrocardiogram.

output variables: I, II, III, aVR, aVL, aVF, V1, V2,

V3, V4, V5, V6 and we used various regression

techniques to build a model.

3 USED METHODS

Four different regression methods were tested to find

a best fitting model, namely Artificial Neural

Network (ANN), Support Vector Regression with

Sequential Minimal Optimization algorithm used,

Linear Regression and Pace Regression.

3.1 Artificial Neural Network

ANN is a system inspired by the operation of

biological neural networks, in other words, is an

emulation of biological neural system. We used

Multilayer Perceptron (MLP) to build the model.

The Multilayer Perceptron method was proven by

the Cybenko theorem to be a universal function

approximator. It uses a backpropagation technique to

train the network. In our experiments MLP used a

sigmoid activation function:













1+









(2)

where y

is the output of the ith node (neuron) and v

is the weighted sum of the input synapses.

Activation function determine whether or not a

neuron fires. The multilayer perceptron consists of

three or more layers (an input and an output layer

with one or more hidden layers) of nonlinearly-

activating nodes. Each node in one layer connects

with a certain weight w

to every node in the

following layer. Learning in the network is done by

changing connection weights after each piece of data

is processed, based on the amount of error in the

output compared to the expected result. To obtain

the best model hundreds of different networks were

built, with different values of learning rate and

various number of hidden layers (nodes).

3.2 Support Vector Regression

The Support Vector algorithm is a nonlinear

generalization of the Generalized Portrait algorithm

developed in Russia in the sixties. As such, it is

firmly grounded in the framework of statistical

learning theory, or VC theory, which has been

developed over the last three decades by Vapnik and

Chervonenkis. Due to this industrial context, SV

research has up to date had a sound orientation

towards real-world applications. Initial work focused

on OCR (optical character recognition). Within a

short period of time, SV classifiers became

competitive with the best available systems for both

OCR and object recognition tasks. We tested three

kernels for SV regression:

- The RBF kernel.

- The polynomial kernel.

- The normalized polynomial kernel.

3.3 Linear Regression

The next regression technique used was a classic

linear regression. In general this technique fits a

linear model to a set of data. Because the model

generated is a linear model this approach is simple

and easy to use, which makes this approach

extensively used in practical applications.

3.4 Pace Regression

Last method used was Pace Regression method.

Pace Regression improves on classical ordinary least

squares (OLS) regression by evaluating the effect of

FINDING NEW EASI ECG COEFFICIENTS - Improving EASI ECG Model using Various Regression Techniques

407

each variable and using a clustering analysis to

improve the statistical basis for estimating their

contribution to overall regression. As well as

outperforming OLS, it also outperform – in a

remarkably general sense – other linear modelling

techniques in the literature, including subset

selection procedures, which seek a reduction in

dimensionality that falls out as a natural byproduct

of pace regression.

4 RESULTS

4.1 Improved Model

Based on results obtained from all tested methods

one linear model was generated:

 = 0.2143 × E + 0.1146 × A

−1.0935 × S + 0.7287 × I − 3.0685

(3)

 = −0.1298 ×  + 0.5988 × 

−1.6804 ×  + 2.3043

(4)

 = −0.0845 ×  − 0.1195 ×  + 0.4929

×  + 0.9408 ×  + 0.7811

(5)

 = −0.0302 ×  + 0.083 ×  + 0.0718

×  − 1.7402 × 

+ 1.0043

(6)

 = 0.1992 ×  + 0.1561 ×  − 1.0576

×  − 0.1414 ×  − 2.5664

(7)

 = 0.2295 ×  + 0.0731 ×  − 1.1295

×  + 1.5988 × 

−3.5707

(8)

1 = 0.6344 ×  + 0.0799 ×  + 0.501

×  + 0.4933 × 

+ 4.0389

(9)

2 = 1.0836 ×  − 0.095 ×  + 0.5252

×  −1.249 × 

+ 13.6635

(10)

3 = 0.7993 ×  + 0.2801 ×  + 0.0881

×  − 2.3115 × 

+ 5.0573

(11)

4 = 0.368 ×  + 1.2349 ×  + 0.0869

×  − 1.1872 ×  − 2.2414

(12)

5 = 0.1384 ×  + 1.5578 ×  + 0.0865

×  + 0.3616 ×  + 0.024

(13)

6 = 0.0362 ×  + 1.2552 ×  − 0.1469

×  + 0.706 × 

−1.2352

(14)

4.2 Results Comparison

Each model calculation was 10 fold cross validated.

All results are based on data from PhysioNet

database and also on data that were artificially

generated according to the following equations

(described in the paper “Investigation Of A Transfer

Function Between Standard 12-Lead ECG And

EASI ECG”):

E = 6.4073889 × II 4.58091464 × aVR +

4.4236590 × aVF + 1.4023342 × V1 –

0.2316670 × V2 + 0.63803224 × V3

0.3104148 × V4 0.5253245 × V5 + 0.7453142

× V6

(15)

A = 0.1205489 × I + 0.1440902 × aVL

0.07460267 × V1 – 0.005248586 × V2 +

0.04413031 × V3 0.001846735 × V4 +

0.14529887 × V5 + 0.5326776 × V6

(16)

S = 0.9615144 × II + 0.07950829 × aVL +

0.21000511 × aVF – 0.096557012 × V1 +

0.3608502 × V2 0.32692627 × V3 +

0.252434208 × V4 + 0.04650518 × V5

0.1318653 × V6

(17)

I = 0.1494002 × I 0.24593780 × aVL

0.003465868 × V1 – 0.1516211491 × V2 +

0.2637671 × V3 0.17090946 × V4 +

0.03756737 × V5 0.10936146 × V6

(18)

Calculated models were compared with results

obtained using classical Dower approach and also

with Improved EASI Coefficients described in the

paper “Improved EASI Coefficients: Their

Derivation, Values, and Performance” by Dirk Q.

Feild, Charles L. Feldman, and B. Milan Horacek.

To determine performance of all systems, for each of

them correlation coefficient (Table 1) and root mean

squared error (Table 2).

4.3 Tables

Table 1: Correlation coefficients comparison.

Obtained

Model

EASI Dower

approach

Improved EASI

Coefficients

aVF 0,939 0,984 0,776

aVL 0,966 0,955 0,922

aVR 0,984 0,985 0,966

I 0,985 0,971 0,973

II 0,964 0,994 0,894

III 0,941 0,963 0,786

V1 0,99 0,882 0,849

V2 0,984 0,968 0,872

V3 0,975 0,971 0,751

V4 0,971 0,981 0,851

V5 0,992 0,977 0,97

V6 0,997 0,888 0,985

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

408

Table 2: Root Mean Squared Error comparison.

Obtained

Model

EASI Dower

approach

Improved EASI

Coefficients

aVF 27,45 28,41 66,29

aVL 22,02 35,45 34,22

aVR 16,03 31,86 55,3

I 18,01 40,75 42,47

II 26,13 32,57 78,2

III 31,41 37,19 60,03

V1 21,01 99,24 86,42

V2 40,54 177,75 119,61

V3 46,62 120,25 141,69

V4 55,6 144,6 129,96

V5 24,66 119,93 49,9

V6 10,77 93,17 33,1

5 CONCLUSIONS

Above results show that the best performance was

obtained for the linear model built using regression

techniques. Second best model was one created by

Dower. Surprisingly low performance was observed

for model that uses improved EASI coefficients.

Further work in the topic of improving EASI

ECG coefficient using various regression techniques

should be continued.

ACKNOWLEDGEMENTS

This work was supported by the European

Community from the European Social Fund.

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http://www.physionet.org/challenge/2007/data/

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