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Computer Methods and Programs in Biomedicine 169 (2019) 59–69

Contents lists available at ScienceDirect

Computer Methods and Programs in Biomedicine

journal homepage: www.elsevier.com/locate/cmpb

Geometrical features for premature ventricular contraction recognition

with analytic hierarchy process based machine learning algorithms

selection

Bruno Rodrigues de Oliveira a , ∗, Caio Cesar Enside de Abreu b , Marco Aparecido Queiroz Duarte c , Jozue Vieira Filho d

a Department of Electrical Engineering, São Paulo State University (UNESP), Ilha Solteira, Brazil b Department of Computing, Mato Grosso State University (UNEMAT), Alto Araguaia, Brazil c Department of Mathematics, Mato Grosso do Sul State University (UEMS), Cassilândia, Brazil d Telecommunication and Aeronautic Engineering, São Paulo State University (UNESP), São João da Boa Vista, Brazil

a r t i c l e i n f o

Article history:

Received 22 August 2018

Revised 24 November 2018

Accepted 24 December 2018

Keywords:

Electrocardiogram analysis

Premature Ventricular Contraction

Geometrical features

a b s t r a c t

Background and Objective: Premature ventricular contraction is associated to the risk of coronary heart

disease, and its diagnosis depends on a long time heart monitoring. For this purpose, monitoring through

Holter devices is often used and computational tools can provide essential assistance to specialists. This

paper presents a new premature ventricular contraction recognition method based on a simplified set of

features, extracted from geometric figures constructed over QRS complexes (Q, R and S waves).

Methods: Initially, a preprocessing stage based on wavelet denoising electrocardiogram signal scaling is

applied. Then, the signal is segmented taking into account the ventricular depolarization timing and a

new set of geometrical features are extracted. In order to validate this approach, simulations encompass-

ing eight different classifiers are presented. To select the best classifiers, a new methodology is proposed

based on the Analytic Hierarchy Process.

Results: The best results, achieved with an Artificial Immune System, were 98.4%, 91.1% and 98.7% for

accuracy, sensitivity and specificity, respectively. When artificial examples were generated to balance the

dataset, the recognition performance increased to 99.0%, 98.5% and 99.5%, employing the Support Vector

Machine classifier.

Conclusions: The proposed approach is compared with some of latest references and results indicate its

effectiveness as a method for recognizing premature ventricular contraction. Besides, the overall system

presents low computation load.

© 2018 Elsevier B.V. All rights reserved.

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. Introduction

The health of an individual is mainly associated to its heart

ealth. There are several diseases that affect the sinus rhythm,

hich is considered as normal heartbeat, and produce what is

alled arrhythmia. One of them is the Premature Ventricular Con-

raction (PVC), which are premature heartbeats originating from

he ventricles. In order to assess the heart health, the most com-

on clinical examinations are those that employ Electrocardio-

ram (ECG) analysis. An ECG records the electrical heart activity

∗ Corresponding author. Department of Electrical Engineering, São Paulo State niversity (UNESP), Brasil Avenue 56, Ilha Solteira, Brazil.

E-mail addresses: [email protected] (B.R.d. Oliveira), [email protected]

C.C.E.d. Abreu), [email protected] (M.A.Q. Duarte), [email protected] (J. Vieira

ilho).

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ttps://doi.org/10.1016/j.cmpb.2018.12.028

169-2607/© 2018 Elsevier B.V. All rights reserved.

riggered by the atria and the ventricles, from electrodes placed

n the body surface. It is mainly composed by P, Q, R, S, T and

waves, and by PR, ST and QT intervals, according to Fig. 1 . P

ave and QRS complex represent the atrial and ventricular depo-

arization, respectively, and T wave represents the ventricular repo-

arization, whereas the atrial repolarization is hidden by the QRS

omplex due to its low amplitude.

The membrane of the cardiac cells has resting and action poten-

ial. When the depolarization threshold is overcome the action po-

ential is triggered [1] , resulting in the atrial and ventricular con-

ractions. The PVC is a result of three possible effects: reentry, trig-

ered activity and abnormal impulse formation [2] . Although some

atients may suffer from PVC episodes without realizing them (e.g.

ue to external factors such as food and medication), increasing

heir occurrence frequency can lead to hemodynamic problems [3] .

VC episodes occurrence is common in some patients with heart

https://doi.org/10.1016/j.cmpb.2018.12.028http://www.ScienceDirect.comhttp://www.elsevier.com/locate/cmpbhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.cmpb.2018.12.028&domain=pdfmailto:[email protected]:[email protected]:[email protected]:[email protected]://doi.org/10.1016/j.cmpb.2018.12.028

60 B.R.d. Oliveira, C.C.E.d. Abreu and M.A.Q. Duarte et al. / Computer Methods and Programs in Biomedicine 169 (2019) 59–69

Fig. 1. ECG waves and intervals.

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diseases or those that already had a myocardial infarction. For the

first group, PVC prevalence is associated to the risk of sudden

death [4] . Prevalence of PVC was detected in some studies cited by

Latchamsetty and Bogun [2] . In a study with 301 middle-aged (55

to 58 years old) men, 62% had some of the ventricular arrhythmias,

including PVC. For those people with higher risk of coronary heart

disease, PVC was more frequent. In another study, carried out with

122,043 men in this majority young and healthy, from 16 years old

to over 50, the PVC occurrence was less than 1%. Latchamsetty and

Bogun in [2] highlighted that prevalence of PVC depends on the

screening duration and type. In general, PVC occurs in approxi-

mately 50% of the population when the 24/48-hour Holter mon-

itoring is considered. As a consequence, for a simple ECG, the PVC

occurrence in the whole population is close to 1%. Therefore, com-

putational systems are essential for the analysis of long-term ECG

obtained by Holter monitoring.

The problem of PVC recognition is very complex because its

pattern is quite changeable, even for the same patient. An example

is shown in Fig. 2 , where a segment from record 207 from MIT-

BIH [11,12] database with different PVC (V label) waveforms is pre-

sented.

Many researches have considered automatic arrhythmia recog-

nition by using different methodologies, but just a few ones have

been focused on PVC. Li et al. [5] proposed an approach based on

template-matchings, considering the morphological differences be-

tween ventricular depolarization (QRS complex) and repolarization

phases. Principal Component Analysis and linear regression were

used by Hadia et al. [6] to detect PVC and Normal heartbeat. Zarei

et al. [7] proposed a strategy based on the variation of principal

directions provided by Principal Component Analysis, by means of

the construction of a matrix with non-PVC beats and the replace-

ment of one of these beats by a PVC beat, obtaining a new matrix.

Bazi et al. [8] extracted the features using the Wavelet Transform

at four levels and the S-Transform to compute QRS duration and

RR interval. Liu et al. [9] inserted a new set of features based on

Lyapunov exponents and their derivative. Adnane and Belouchrani

[10] evaluated an approach for QRS detection based on wavelet co-

Fig. 2. Example of different PVCs for record 207 of MIT-BIH database. V, R and L

fficients to obtain an h value representing the sum of coefficients

rom Haar wavelet transform at levels 3 and 4, which is compared

o a threshold value to determine whether the clusters belong to

he PVC or Normal beat.

In the present work, it is proposed a PVC recognition method

ased on a completely new set of features extracted from a geo-

etrical viewpoint. Each QRS complex is projected onto the Carte-

ian plane, where the initial QRS complex sample is the plane ori-

in. A triangle, whose vertices are the origin and the maximum

nd minimum of the QRS complex, is built on the plane. An in-

ircle is designed for this triangle and twelve measurements from

hese two geometric figures are calculated, also including differ-

nces of maximum/minimum projections on the horizontal and

ertical axis. This approach is unprecedented, since the most com-

on features are based on measures from RR-intervals, duration

nd amplitude of the PQRST-waves, according to Luz et al. [11] .

n the other hand, there are classes of methods that take use

f domain transformation techniques, such as Wavelet and Fourier

ransforms, or advanced decomposition processes such as Princi-

al Component Analysis, in order to extract features [11] . However,

hese methods are more computationally intensive than the one

roposed here.

Aiming to highlight the contributions by this work, eight differ-

nt types of machine learning algorithms were implemented and

he results show that the efficiency in classification performance

s clearly due to the new set of features, even considering some

nfluence of the algorithm. In order to select the best classifiers,

new methodology based on Analytic Hierarchy Process (AHP) is

roposed. Main contribution in this aspect is related to the propo-

ition of a new conversion function responsible to convert numer-

cal differences to Saaty‘s scale, aiming the suitable AHP execution.

Simulations were performed using two datasets from two MIT-

IH [12] databases. In addition of using real data, balanced datasets

omposed by synthetic QRS complexes from averaged PVC heart-

eats were used. The proposed method is also confronted with a

ataset that simulates QRS complexes misdetection. Furthermore,

verall results are compared with the ones obtained from refer-

nce methods cited previously.

The remainder of this paper is organized as follows: in

ection 2 , dataset description, evaluation measures, foundations

nd proposed approach are described; in Sections 3 and 4 results

re respectively presented and discussed; finally, conclusions are

resented in Section 5 .

. Materials and methods

.1. Dataset description

Two classical databases provided by Goldberger et al.

12,13] were chosen for the PVC heartbeats recognition: MIT-

IH Arrhythmia Database (ARDB) and MIT-BIH ST Change Database

STDB). They are composed by 48 half-hour ECG recordings and 28

arying lengths, respectively, all of them are sampled at 360 Hz.

nly recordings from the main lead were considered. According

labels are PVC heartbeats, left and right bundle branch block, respectively.

B.R.d. Oliveira, C.C.E.d. Abreu and M.A.Q. Duarte et al. / Computer Methods and Programs in Biomedicine 169 (2019) 59–69 61

Table 1

Datasets description.

Name Recordings Normal PVC

DS1 101, 106, 108, 109, 112, 114, 115, 116, 118, 119, 122, 124, 201, 203, 205, 207, 208, 209, 215, 220, 223, 230 38,087 3683

DS2 100, 103, 105, 111, 113, 117, 121, 123, 200, 202, 210, 212, 213, 214, 219, 221, 222, 228, 231, 232, 233, 234 36,428 3219

DS3 300 to 327 75,019 322

Total 71 150,534 7224

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o Association for the Advancement of Medical Instrumentation

AAIM) recommendations, recordings 102, 104, 107 and 217 from

RDB, which are composed by paced heartbeats, were discarded

14] . The remainders were split into training (DS1) and test (DS2)

atasets. An additional validation dataset (DS3), obtained from

TDB, is used to evaluate the proposed features robustness on

ew test items. Recordings from these datasets are described in

able 1 .

It is noteworthy that DS1 and DS2 datasets used in this work

re the same as in the studies conducted by Li et al. [5] and Zarei

t al. [7] . Furthermore, DS3 dataset is used only in the validation

hase. Normal and PVC heartbeats are those labeled as N and V in

he MIT-BIH databases, respectively.

.2. Evaluation measures

In order to assess the performance of the proposed approach,

everal classical evaluation measures are employed. They are based

n the amount of true positives TP , true negatives TN , false posi-

ives FP and false negatives FN classifications obtained in the test

hase: accuracy A cc = ( TP + TN )/( TP + TN + FP + FN ); sensitivity e = TP /( TP + FN ); specificity S p = TN /( TN + FP ); positive predic-ion P + = TP /( TP + FP ); negative prediction P − = TN /( TN + FN );nd AUC (Area Under Curve) relating to Receiver Operating Charac-

eristic Curve (ROC curve) supported by a true positive rate versus

alse positive rate plot [15] .

In this work, positive classifications are those belonging to the

VC class. It is important to highlight that sensitivity and speci-

city measures are the recall measures for positive and negative

alues, respectively [15] . The measures mentioned before ensure an

ccurate assessment for the proposed approach, since training, test

nd validation datasets are unbalanced, i.e., there exist more Nor-

al than PVC heartbeats. This unbalance still justifies the construc-

ion of artificial QRS complexes in order to balance the datasets in

ection 3.4 .

.3. Machine learning algorithms

Machine learning algorithms are widely used for data classifi-

ation. Therefore, in this work some of them are briefly discussed

nd applied. Furthermore, a new methodology based on AHP is

roposed to select the top three studied machine learning algo-

ithms that lead to the best PVC classifiers [15–23] .

.3.1. k-Nearest neighbors

k -Nearest Neighbors ( k -NN) is one of the simplest algorithms

or data classification. It is an instance-based learning algorithm

ecause it labels a new sample presented by computing the dis-

ance among it and samples previously stored in the training

hase. The class assigned to the test item is chosen based on a

ajority vote approach. The most voted class, amongst the k near-

st neighbors, is then assigned to classification [15] .

.3.2. Multinomial naive Bayes

Bayesian classification algorithms are broadly used in pattern

ecognition and they are based on Bayes rule which considers

oint, conditional and marginal probabilities [16] . These probabilis-

ic classifiers assume that the samples are generated by a mixture

odel where each class is a component from this mixture [16,17] .

aive Bayes is one of these algorithms. This model is supported by

he independence assumption about the probability distribution,

hich indeed reduces its complexity. A variant of this algorithm

s the so-called Multinomial Naive Bayes, for which the probability

istribution is multinomial [16,17] .

.3.3. Voted perceptron

Perceptron is a popular algorithm for binary linear classification

roposed by Rosenblatt [18,19] and supported on the McCulloch-

itts’s nonlinear neuron [19] . Essentially, the perceptron structure

onsists of data input, summing node, which computes a linear

ombination, and the output, which is produced by the hard lim-

ter function [19] . The synaptic weights (elements of the linear

ombination) are updated, according to a convergence rule, un-

il the computed output is equal to the desired output. Percep-

ron pattern recognition uses linear combination from the synap-

ic weights and the data input to compute an output for a new

xample. Freund and Schapire [18] proposed a more sophisticated

lgorithm based on Perceptron, named Voted Perceptron. In this

lgorithm, at each iteration, a list of all prediction vectors is main-

ained and a weight of such vectors is computed considering the

umber of iterations with no changes while a new mistake is not

enerated. Lastly, prediction is calculated through weighted major-

ty vote.

.3.4. Multilayer perceptron

Multilayer Perceptron (MLP) is a class of feed-forward artificial

eural network with at least three layers of nodes. Therefore, the

asic MLP configuration consists of input, intermediary (hidden)

nd output layers [19] . The number of hidden layers and nodes per

ayer are defined by means of simulations and depends essentially

n the data complexity. It is noteworthy that each node, except for

he ones in the input layer, is a neuron with nonlinear activation

unction. In our implementation, supervised learning was carried

ut with the back-propagation learning algorithm [19] .

.3.5. Support vector machines

Support Vector Machines (SVM) constitutes a class of super-

ised learning binary classifiers and thus discriminates between

wo possible classes. Classification task is made by means of the

onstruction of a linear hyperplane to separate the two classes of

ata. The optimal separating hyperplane is selected based on the

aximization of the margin (distance) between the two classes.

ue to data complexity, it is not always possible to create a linear

ata separation in the input data space. Therefore, space transfor-

ation by means of kernels is often used. Such an approach trans-

orms the input data space in a higher dimension space, and the

onlinearly separable data in the input space become linearly sep-

rable in the new space [20] .

.3.6. Radial-basis functions network

In contrast to a neural network structure, the Radial-basis Func-

ions (RBF) network has only three layers: input, hidden, and out-

ut [19] . In the hidden layer lies the main distinction, due to the


Table 2

Saaty’s scale. Converts verbal judgments to nu-

meric.

Verbal scale Importance

Equal importance 1

Somewhat more importance 3

Much more important 5

Very much more important 7

Absolutely more important 9

Intermediate value (weaker) 2, 4, 6, 8

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nonlinearly mapping from the input space to a higher dimension

space through radial basis functions (usually a Gaussian function).

In this layer, an unsupervised learning is performed using the k -

means algorithm, which determines the parameters of the func-

tions (or kernels). The basis of this approach is the Cover’s theo-

rem, which states that nonlinear pattern recognition is more likely

to be linearly separable in a high-dimensional space [19] . The out-

put layer is linear and trained in a supervised manner.

2.3.7. Random forest

Tree-based predictors are widely employed in data classification

problems, especially in environments where some expert knowl-

edge is available, since this structure can be easily interpreted and

validated. One disadvantage of such predictors is data-overfitting

[22] , which makes their implementation questionable in many sit-

uations, because it reduces their general predictive capacity. To

overcome this problem and improve prediction, the Random For-

est algorithm is an alternative that maintains the same tree model

structure, but combining these predictors to generate a better over-

all model, where each tree is constructed from a random vector

which is sampled independently, whose probability distribution is

the same for all the trees in the forest [23] .

2.3.8. Artificial immune system

Artificial Immune Systems (AIS) constitutes a relatively recent

approach in the artificial intelligence field that connects con-

cepts from biological immune system to computational concepts

by means of metaphors. In other words, researchers in the AIS field

look to the biological immune system as inspiration on how to

solve problems in engineering and computer science [24] . Some of

these biological concepts, such as the distinction among molecules

from our own cells and foreign molecules (the negative selection

concept); the duplication of B-cells able to recognize an antigen

and thus stimulating the production of antibodies (the clonal se-

lection concept); some of these clones will compete with the origi-

nal ones and those with higher affinity may become a memory cell

(affinity maturation concept); they have natural learning properties

which may be used to advantage in machine learning systems [24] .

The AIS used in this work is the one proposed by Watkins, Tim-

mis and Boggess [25] . Classification process performed by this AIS

is based on the development of a set of memory cells generated in

the training stage, capable of classifying data. Each memory cell is

iteratively presented with each test item for stimulation. Then, sys-

tem’s classification is determined by the most stimulated memory

cells in a k nearest neighbor way: the class with higher number of

stimulated memory cells is assigned to the test item.

2.4. Analytic Hierarchy Process (AHP)

AHP is a method for decision-making based on multiple crite-

ria. It has been used in many areas to assist the decision mak-

ers in complex and extremely important problems, such as: per-

sonal, educational, manufacturing, political, engineering, industry,

governmental [26] , judiciary [27] and machine learning algorithms

selection [28–30] .

Proposed by Saaty [31] , in order to perform an AHP, firstly a

decision process is modeled as a hierarchy. At the top is the goal,

right below is the criterion and in the bottom, the alternatives rep-

resenting the choices available. After problem modeling, the alter-

natives and criteria are pairwise compared with respect to some

criterion at the level before the hierarchy. For each comparison, it

is attributed a value from the Saaty’s scale, according to Table 2 .

The result of these comparisons is a square pairwise matrix

= ( a ij ) n × n , n ≥ 2:

(h ) k

=

⎡ ⎢ ⎢ ⎢ ⎣

1 a (h ) 12

· · · a (h ) 1 n

1 /a (h ) 12

1 · · · a (h ) 2 n

. . . . . .

. . . . . .

1 /a (h ) 1 n

1 /a (h ) 2 n

· · · 1

⎤ ⎥ ⎥ ⎥ ⎦ , (1)

here a (h ) i j

= w (h ) i

/w (h ) j

represents the judgment with respect to al-

ernative i over alternative j in relation to some criterion in the

ierarchy level h ; w (h ) i

> 0 , ∀ i, h ; n is the amount of alternativesnd k = 1, 2, 3, �� is used to identify the matrices. The elementsn the normalized eigenvector w (h )

k = [ w (h )

1 w (h )

2 · · · w (h ) n ] T , associ-

ted to the principal eigenvalue λmax , are the weights that ex-lain the local importance of one alternative over another. It is

amed local priority vector and is obtained by solving the system

(h ) k

w (h ) k

= λmax w (h ) k subject to w (h ) T k

[ 1 1 · · · 1 ] T = 1 [32] . Aiming toggregate all local judgments in a unique priority, it is necessary to

ompute the global priority vector v = [ v 1 v 2 … v n ] T . Each elementn v is given by:

p = o ∑

l=1 s (

h −1 ) l

t ( h )

pl , p = 1 , · · · , n, (2)

here s ( h −1 ) l

is the l -th criterion weight in relation to the goal, t (h ) pl

s the local priority of the alternative p with respect to the l -th

riterion, and o is the amount of criteria. After obtaining vector v ,

t must be normalized by computing v norm = v / ‖ v ‖ 1 , where ‖ v ‖ 1 =

r | v r | is the l 1 -norm. AHP is used in this work to the best PVC classifier choice, con-

idering each evaluation measure as a criterion and the alterna-

ives as the own classifiers. In this way, global priority vector has

n itself the preferences order to choose the classifiers. The best

lassifier is related to the greater element in v norm .

.5. Wavelet denoising

Discrete Wavelet Transform (DWT) implementation is based on

digital filter bank in a tree structure, where low (approximation

avelet coefficients) and high (detail wavelet coefficients) frequen-

ies are successively separated. Originally proposed by Donoho

33] , for denoising purposes, the wavelet thresholding method con-

ists in applying the DWT on the original signal and modifying de-

ail coefficients with absolute values under a certain threshold. In

ther words, it is accepted as noisy coefficients those ones with

bsolute values under the estimated threshold. This procedure is

fficient due to the DWT characteristics [33] . The way as the noisy

oefficients will be modified depends on the thresholding func-

ion choice. Hard thresholding is used in this work, since it has

resented better results [34] . Its formulation is defined as follows

33] :

ˆ =

{Y [ k, n ] if | Y [ k, n ] | > δ

0 if | Y [ k, n ] | ≤ δ ,


Fig. 3. Proposed approach overview. Fs is the sampling rate.

Table 3

Parameters configuration for the classifiers.

Name Label Parameters configuration

Random forest RF 90 trees

k -Nearest neighbors KNN k = 3. Euclidean distance Multinomial Naive Bayes MNB None

Support Vector Machine SVM Linear Kernel. Use shrinking heuristic. γ = 1/12 and cost c = 10 Multilayer Perceptron MLP One hidden layer with 8 units. Learning rate equal to 0.3. Backpropagation learning

algorithm. 500 epochs

Radial basis function network RBF k-Means with 40 clusters.

Voted Perceptron VP 10 iterations and 34,169 perceptrons.

Artificial Immune System AIS Affinity threshold, clonal rate, hypermutation rate, k-nearest neighbor, stimulation

value and B-cells equal to 0.2, 10, 2, 3, 0.9 and 150, respectively.

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here Y [ k, n ] is the n -th wavelet coefficient at the k -th scale,

= 1, 2, ��, N, k = 1, 2, �� and ˆ Y is the signal Y attenuated ver-ion. The threshold is estimated as δ = σ

√ 2 lo g 2 N , where N is the

ength of Y and σ is the noise standard deviation. After filter-banknalysis, and wavelet coefficient thresholding, a denoised signal is

btained by applying the inverse DWT.

.6. A PVC recognition approach

Supported by a new set of features which are extracted from

geometric viewpoint, a PVC recognition approach is proposed by

eans of six steps, described in Fig. 3 .

First, raw ECG signal is read and then segmented, taking the

-peak location and the standard cardiac cycle duration (0.75 sec-

nds). In the present implementation, annotations provided by

IT-BIH databases about R-peaks localization are used. For each

btained segment, the wavelet denoising method is applied, and

hen it is scaled in order to keep zero mean and unit variance. This

reprocessing step ensures better results because it standardizes

ata. After this step, an approximated QRS complex is obtained

egmenting it to the standard width of the QRS complexes, i.e.,

.12 seconds. After QRS complex segmentation, proposed features

re extracted and used to the training and test/validation of the

lassifiers. In the following subsections, a detailed discussion en-

ompassing the steps of the proposed method is provided.

.6.1. Preprocessing

In the preprocessing step, a denoising procedure based on

avelet thresholding is performed, according to Section 2.5 . In this

pproach, Y and ˆ Y are noisy and denoised ECG signal segments,

espectively, and σ = std ( Y [0: 10]), i.e., ten first samples standardeviation. Besides denoising high frequency noise, approximation

oefficients in the last level are reduce to zero, aiming baseline

andering removal [35] . DWT decomposition is performed in five

evels. Next, this ECG signal segment is scaled by means of equa-

ion: ˜ Y = ( ̂ Y − ˆ Y ) / σ ˆ Y , where ˜ Y is the denoised scaled ECG signalegment, ˆ Y and σ ˆ Y are the average and the standard deviation of

he denoised ECG signal segment ˆ Y .

.6.2. Segmentation and training

After obtaining a denoised scaled ECG signal segment, a new

egmentation is performed considering 0.6 seconds forward and

ackward from R-peak, resulting in a 44-sample segment. This pro-

edure returns an ˜ Y = [ ̃ Y 1 , · · · , ̃ Y 44 ] signal. On this segmented sig-al, proposed features described in Table 4 are calculated. Thus,

˜ is mapped into a space of features with fewer dimensions. This

apping is f : � 44 → � 12 where f ( ̃ Y ) = [ a 1 , · · · , a 12 ] is the featureattribute) vector to be used as input to a machine learning algo-

ithms. Considering that the main motivation in this research is the

roposition of a new way to get consistent features for PVC recog-

ition, eight classifiers encompassing different learning approaches

ere used in the simulations. In Table 3 , their main configurations

re summarized. Those configurations were defined by means of

xhaustive experiments in order to obtain better results, using DS1

nd DS2 datasets in training and test phases, respectively.


Table 4

Features description.

Equation Description

a 1 = ‖ v 1 ‖ Triangle side a 2 = ‖ v 2 ‖ Triangle side a 3 = ‖ v 1 − v 2 ‖ Triangle side a 4 = ‖ ( v 1 x + v 2 x , v 1 y + v 2 y ) ‖ /3 Triangle center of mass a 5 = θ = arccos( v 1 ∗v 2 / a 1 a 2 ) Angle between a 1 and a 2 a 6 = a 1 a 2 sin ( θ )/2 Triangle area a 7 = 2 a 1 / p Incircle radius a 8 = ‖ ( a 2 v 1 x + a 3 v 2 x , a 2 v 1 y + a 3 v 2 y ) ‖ / p Incenter a 9 = 2 πa 7 Length of the incircle a 10 = πa 2 7 Incircle area a 11 = p x = | v 1 x − v 2 x | Distance between projections on the x -axis a 12 = p y = | v 1 y − v 2 y | Distance between projections on the y -axis

Fig. 4. Modeling of the proposed geometric characteristics: (a) Standard non-PVC heartbeat. (b) Standard PVC heartbeat.

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2.6.3. Proposed features

As outlined previously, the main motivation for this paper is the

proposition of new features based on a geometric viewpoint able

to recognize PVC heartbeats. In other words, proposed features aim

to explain the QRS complex morphology by building geometric fig-

ures that represent its waveform in a suitable way. Therefore, each

QRS complex is projected onto the Cartesian plane. Afterward, a

triangle is built by fixing the fiducial points R and S as two vertices

and the third vertex at the origin of the plan, which corresponds

to the beginning of the QRS complex segment. Furthermore, a cir-

cle (incircle) inscribed in this triangle is also built. This approach

starts a new way to design attributes from ECG waveforms based

on geometric figures, representing them in a simplified manner.

Note that unlike state-of-the-art methods, the proposed method

does not only consider the amplitude and width (duration) of the

ECG characteristics waves, but also the relation among them, in a

linear and a nonlinear way.

After building these geometric figures, the measures presented

in Table 4 are calculated. In the proposed approach, it is assumed

that triangles from abnormal heartbeats suffer some distortion in

relation to the ones from normal heartbeats, since the respective

QRS complexes differ in amplitude and position. Consequently, the

incircle is also modified. Specifically for PVC heartbeats, the mini-

mum of the QRS complex tends to be larger than in normal beats.

This is due to the fact that PVC is characterized by a gain in R

and S waves’ amplitude, generating a distortion in the QRS com-

plex morphology [3] . Such morphology depends on the origin of

the ectopic heartbeat. If it occurs at the right ventricle, PVC has a

eft bundle branch block (LBBB) morphology, since the right ventri-

le depolarization occurred before the left ventricle. It makes the

RS complexes predominantly positive [4] . Such occurrence com-

licates the Normal heartbeat recognition, since the LBBB and Nor-

al heartbeats may be coincident [36] .

Fig. 4 , (a) and (b), shows examples of standard waveforms for

ormal heartbeat and PVC, respectively. Variables v 1 and v 2 ( v ′ 1 nd v ′

2 ), are vectors whose coordinates, in y -axis, are the QRS com-

lex waveform global maximum and minimum, respectively. p y nd p x ( p

′ y and p

′ x ) are the differences between the coordinate pro-

ections of vectors v 1 and v 2 ( v ′ 1 and v ′ 2 ) in the respective axis. Theriangle center of mass (barycenter) is represented by c ( c ′ ). Thencircle is tangent to each side of the triangle. Finally, the features

btained by this modeling are discriminated in Table 4 , where “∗”s the vector product, p is triangle perimeter, ‖ · ‖ and | · | are theuclidean norm ( l 2 -norm) and absolute value, respectively.

Although the geometric figures summarize the QRS complexes

aveforms and so the features only explain these forms, it is em-

hasized that the projections on the x -axis are regarded as tim-

ng features, since they are related to positions of the local fiducial

oints of the QRS complexes. It is important because such timing

nformation is relevant for classification, as verified by Bazi et al.

8] . On the other hand the projections on the y -axis represent the

agnitude information. It is noteworthy that features a 1 ,…, a 12 are

f simple computation and do not require any kind of transforma-

ion or complicated decomposition process.

Finally, as can be seen in Fig. 4 , QRS complexes for normal

Fig. 4 (a)) and PVC ( Fig. 4 (b)) beats are different, since PVC config-


Fig. 5. Proposed AHP model to choose a classifier.

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res distortions in the QRS. Therefore, the twelve geometric char-

cteristics proposed, provide a set of comparisons which will help

classifier to distinguish between the two QRS waveforms.

.6.4. Classifiers selection

In order to select the best classifiers and take into account

he performance of all measures simultaneously, an AHP based

pproach is proposed. The proposed AHP model is illustrated in

ig. 5 . Note, from this figure, that evaluation measures and classi-

ers (alternatives) are located in the hierarchy levels 1 and 2, re-

pectively. At level h = 2, from left to right, each classifier is com-ared to another in relation to some measure at the top level, re-

ulting in differences among the scores evaluated by the function

n (3) . Each of the evaluated scores is an element in the pairwise

omparison matrix, from which the local priority vector t (2) is ob-

ained according to Section 2.4 . Therefore, for each measure there

ill be a pairwise comparison matrix.

On the other hand, at level h = 1, since the measures are notompared in the experiments and the most important measures

re those related to the PVC heartbeats identification, the elements

n the local priority vector s (1) were set as 1 for the measures re-

erring to positive classes, and 0.5 for negative classes. Therefore,

he pairwise comparison matrix is not required at level one. In this

ay, s (1) = [1 1 0.5 1 0.5 1] is related to the measures A cc , P + , P − , e , S p and AUC , respectively, which after normalization, mentioned

n Section 2.4 , it is close to s (1) = [0.15 0.15 0.07 0.15 0.07 0.15],onsidering only two decimal places.

Since the judgments are made in an automatic way, a function

s proposed to replace the decision maker action, which converts

he objective measures scores to the Saaty’s scale:

d pq = c p − c q , where p, q = 1 , · · · , 8 and p = q, mpq = � | d pq | κ� , where m = 1 , · · · , 6 and κ > 0 ,

( δmpq ) =

⎧ ⎪ ⎨ ⎪ ⎩

1 if δmpq < 1 9 if δmpq > 1 1 / δmpq if d pq < 0 δmpq otherwise

,

(3)

here c p and c q are values from measure m obtained by the clas-

ifiers p and q , respectively. x returns the smallest integer greater

han or equal to x . The constant κ can be adjusted to increasehe weight of the difference | d pq |. For example, in the comparisons

mong three distinct classifiers p, q 1 and q 2 , if d p q 1 = 0 . 001 and p q 2 = 0 . 1 and κ = 10, then in both cases conversion function( δmp q 1 ) = ( δmp q 2 ) = 1 . Therefore, both alternatives are equally

referable, i.e., the classifier p has the same preference over q 1 and

2 . In order to increase function sensitivity, setting κ = 16, for in-tance, the new results are ( δmp q 1 ) = 1 and ( δmp q 2 ) = 2 . There-ore, the last result means that p classifier is more preferred over

2 than over q 1 . In this work, κ = 20 presents appropriated resultsor comparisons.

In the global priority vector calculation, given by Eq. (2) , for hi-

rarchy proposed model, note that indices l = 1, 2, …, 6 and p = 1, 2,, 8 index the lists { A cc , P + , P − , S e ,S p ,AUC } and {RF, KNN, MNB,

SVM, MLP, RBF, VP, AIS}, representing measures and classifiers,

espectively. For each measure pairwise comparison matrix a lo-

al priority vector t (2) l

∈ � p is obtained. This vector contains theriority of an alternative over another. In order to calculate the

lobal priority of the p -th alternative in relation to the l -th cri-

erion (measure) the summation in Eq. (2) is applied.

It should be noted that the AHP methodology proposed in this

ork is grounded on the conversion function in (3) , which trans-

ates the dissimilarity among objective measures related to the

lassifiers to the Saaty’s scale. This function is irrelevant regard-

ng the computational load, since it is composed by simple math-

matical operations. Although a consistency index is often used in

HP framework, in this work it is replaced by an automatic con-

ersion function in such a way that the subjectivity is purged. In

ecision-making problems, the inconsistency arises due to subjec-

ive human judgments, when an alternative A 1 is preferable over

2 , and A 2 over A 3 , but A 3 is preferable over A 1 , characterizing the

ack of transitivity among the alternatives. It results in an inconsis-

ent matrix to which there exists an associated consistency ratio,

ccording to Saaty [31] . This fact is observed in Khanmohammadi

nd Rezaeiahari [29] , where this ratio is calculated because an ex-

ert’s knowledge was incorporated to obtain the priorities in the

erformance measures.

In contrast to this proposal, Kou and Wu [30] use the AHP

ethod together associated to other decision-making methods,

uch as TOPSIS, VIKTOR, PROMETHEE II and GRA, to sort the clas-

ifiers. In Khanmohammadi and Rezaeiahari [29] , AHP method is

ncorporated to the expert’s knowledge and used to establish the

eights of performance measures, which in turn ranks the classi-

ers. However, the performance measures are not specifically com-

ared to each other. Finally, in Jaya and Tamilselvi [28] the perfor-

ance is computed by win-loss tables from the paired t -test and

he priority vectors are calculated in the same way as proposed

ere.

Although AHP has been used in machine learning problems, as

utlined above, the proposed approach in this paper (according to

ig. 5 ) is original. It is preferable to others, since it depends only on

he AHP method and the conversion function, which is easy to cal-

ulate. In addition, due to the ability to link classifiers to objective

easures, this approach can be used in the models ensemble con-

truction. Thus, facing a large number of classifiers, the best ones

an be selected to compose the ensemble according to several ob-

ective measures in an automated way.

. Results

In order to verify the proposed characteristics robustness, ex-

eriments encompassing several classifiers with different learn-


Table 5

Results 1 considering DS1 and DS2 datasets for training and test, respectively.

Cls A cc P + P − S e S p AUC Confusion Matrix

T N F P

F N T P

RF 0.972 0.827 0.985 0.833 0.985 0.963 35 , 866 562

539 2680

KNN 0.968 0.804 0.983 0.805 0.983 0.928 35 , 797 631

623 2596

MNB 0.970 0.819 0.984 0.821 0.984 0.945 35 , 841 587

571 2648

SVM 0.976 0.978 0.976 0.721 0.999 0.860 36376 52

898 2321

MLP 0.967 0.778 0.985 0.835 0.985 0.955 35 , 662 766

530 2689

RBF 0.971 0.912 0.976 0.724 0.994 0.977 36 , 204 224

888 2331

VP 0.970 0.953 0.971 0.665 0.997 0.831 36 , 322 106

1079 2140

AIS 0.984 0.857 0.992 0.911 0.987 0.949 35 , 938 490

287 2932

Avg ± σ 0.972 ± 0.005 0.866 ± 0.069 0.982 ± 0.006 0.789 ± 0.075 0.989 ± 0.006 0.926 ± 0.049

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ing approaches are carried out. This phase is performed into four

stages: 1) General experiments: all classifiers are used in the

dataset training and test. It ensures overall performance and en-

ables to choose the best classifiers, besides providing the classi-

fiers parameters which are used later in the other experiments;

2) Selection of the classifiers: the top three classifiers are selected

by the AHP method, based on the proposed conversion function

(3) ; 3) Deviation in the QRS complex location: for the best classi-

fiers, new tests are performed considering the characteristics ex-

tracted from DS2 dataset modified by the insertion of deviations

in R-peak locations, in order to verify its robustness to misdetec-

tion; and 4) Artificial heartbeats: aiming to balance the datasets

and provide more PVC instances for model learning, some artifi-

cial heartbeats are constructed and the cross-validation approach

is implemented, avoiding misleading performance due to overfit-

ting, for both databases described in Section 2.1 .

3.1. General experiments

Table 5 shows the classification performance on test dataset

(DS2). Classifiers and their configurations were presented in

Table 3 . Some measures are calculated separately for Normal and

PVC heartbeats, indicated by the superscript initials.

3.2. Selecting the classifiers

By means of the AHP method and conversion function (3) , the

pairwise comparison matrices and their respective priority vectors

are obtained, according to expressions (4) –(9) with respect to P + ,S e and AUC measures. Matrices for A cc , P − and S p measures andtheir priority vectors have all elements equal to 1.0 and 0.1, respec-

tively. For these measures, such results mean that there is no pref-

erence among the classifiers.

P + =

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

1 1 1 1 / 4 1 1 / 2 1 / 3 1 1 1 1 1 / 4 1 1 / 3 1 / 3 1 / 2 1 1 1 1 / 4 1 1 / 2 1 / 3 1 4 4 4 1 4 2 1 3 1 1 1 1 / 4 1 1 / 3 1 / 4 1 / 2 2 3 2 1 / 2 3 1 1 2 3 3 3 1 4 1 1 2 1 2 1 1 / 3 2 1 / 2 1 / 2 1

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(4)

1 σ , Avg and Cls mean standard deviation, average and classifier, respectively.

Bold results are the best.

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2 = [ 0 . 071 0 . 062 0 . 071 0 . 265 0 . 060 0 . 166 0 . 208 0 . 093 ] T (5)

e =

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

1 1 1 3 1 3 4 1 / 2 1 1 1 2 1 2 3 1 / 3 1 1 1 2 1 2 4 1 / 2 1 / 3 1 / 2 1 / 2 1 1 / 3 1 2 1 / 4 1 1 1 3 1 3 4 1 / 2 1 / 3 1 / 2 1 / 2 1 1 / 3 1 2 1 / 4 1 / 4 1 / 3 1 / 4 1 / 2 1 / 4 1 / 2 1 1 / 5 2 3 2 4 2 4 5 1

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(6)

4 = [ 0 . 151 0 . 125 0 . 136 0 . 061 0 . 151 0 . 061 0 . 037 0 . 273 ] T (7)

UC =

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

1 1 1 3 1 1 3 1 1 1 1 2 1 1 2 1 1 1 1 2 1 1 3 1 1 / 3 1 / 2 1 / 2 1 1 / 2 1 / 3 1 1 / 2 1 1 1 2 1 1 3 1 1 1 1 3 1 1 3 1 1 / 3 1 / 2 1 / 3 1 1 / 3 1 / 3 1 1 / 3 1 1 1 2 1 1 3 1

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(8)

6 = [ 0 . 153 0 . 138 0 . 145 0 . 063 0 . 145 0 . 153 0 . 054 0 . 145 ] T (9)

In order to aggregate all results, from Eq. (2) and taking the

ocal priority vectors values, the global priority vector is

norm = [ 0 . 123 0 . 115 0 . 119 0 . 125 0 . 120 0 . 123 0 . 111 0 . 161 ] T(10)

.3. Deviation in the QRS complex location

The proposed method is dependent on the QRS complex or R-

eak location, in the same way that the baseline methods. There-

ore, some deviation at this location is expected to damage the

rediction accuracy [11] . To verify the robustness in relation to

uch deviations, for each R-peak location a random number from


Table 6

Results 2 considering artificial deviations in R-peak locations.

Cls A cc P + P − S e S p AUC Confusion Matrix Pri

T N F P

F N T P

SVM 0.976 0.977 0.976 0.721 0.999 0.860 36374 54

897 2322

0.35

RBF 0.967 0.853 0.976 0.724 0.989 0.958 36 , 147 402

889 2330

0.33

AIS 0.945 0.622 0.986 0.857 0.955 0.901 34 , 771 1657

491 2728

0.32

Avg ± σ 0.962 ± 0.013 0.917 ± 0.147 0.979 ± 0.004 0.767 ± 0.063 0.981 ± 0.018 0.906 ± 0.040

Table 7

Five folds cross-validation results using real and artificial PVC heartbeats from DS1 and DS2 datasets.


T N F P

F N T P

SVM 0.990 0.995 0.985 0.985 0.995 0.990, 36253 175 0.33

547 35881

RBF 0.987 0.987 0.988 0.988 0.987 0.998 35951 477 0.33

430 35998

AIS 0.982 0.981 0.984 0.984 0.981 0.982 35735 693 0.33

588 35840

Avg ± σ 0.986 ± 0.003 0.987 ± 0.005 0.985 ± 0.001 0.985 ± 0.001 0.987 ± 0.005 0.990 ± 0.006

Table 8

Five folds cross-validation results using real and artificial PVC heartbeats from DS3 dataset.


T N F P

F N T P

SVM 0.942 0.907 0.985 0.987 0.899 0.943 34417 3875 0.30

513 37779

RBF 0.977 0.975 0.980 0.980 0.975 0.978, 37335 957 0.36

755 37537

AIS 0.945 0.953 0.938 0.937 0.954 0.945 36512 1780 0.34

2431 35861

Avg ± σ 0.954 ± 0.015 0.945 ± 0.028 0.967 ± 0.021 0.968 ± 0.022 0.942 ± 0.032 0.955 ± 0.016

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he set { ± 1, ±2, ��, ± 5} is added. This procedure is done onlyn test dataset (DS2). It is equivalent to diverting the QRS complex

ocation in up to five samples, according to Ye and Kumar [37] . In

ractice, this experiment simulates errors in the QRS complex de-

ector algorithms. Results for the top three classifiers are presented

n Table 6 .

.4. Balanced datasets

Results presented so far are provided by experiments conducted

n unbalanced datasets (see Table 1 ), since there are more in-

tances of Normal than PVC heartbeats. In order to overcome this

rawback, it is proposed to generate artificial PVC heartbeat in-

tances. Therefore, two PVC heartbeats are randomly chosen and

veraged among all available, generating a new PVC heartbeat.

his procedure results in 36,428 Normal heartbeats and 36,428

VC, where 29,526 are artificial, for DS1 and DS2 datasets. For

S3 dataset there are considered 38,292 Normal heartbeats and

8,292 PVC, where 37,970 are artificial. The classification stage is

erformed considering the cross-validation method [38] , with five

olds to avoid models overfitting. It is noteworthy that, in this ex-

eriment, different heartbeats from a same patient can be used for

he classifiers training and test instead of what was done with un-

alanced datasets. Table 7 shows results considering the recordings

rom DS1 and DS2 datasets. Table 8 shows results only for DS3

2 Columns “Cls” and “Pri” mean Classifier and Priority, respectively.

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ataset aiming to validate the performance obtained in the last ex-

eriments, using classifiers configurations described in Table 3 , but

ow, on a validation dataset.

. Discussion

Analyzing the classifiers average results in Table 5 , it is noted

hat 86.6% of positive and 98.2% of negative examples are cor-

ectly classified. For SVM and AIS, these results are higher, 97.8%

nd 99.2%, respectively. Taking into account overall performances,

t is noted that the AIS is the best, but it is worse than SVM with

espect to P + and S p measures, close to 12.8% and 1.2%, respec-ively. It is also noteworthy that SVM generates less false positives

han the other classifiers, whereas AIS produces less false nega-

ives. In addition, RBF presents the greater AUC result, around 2.8%

nd 11.7% higher in relation to AIS and SVM classifiers, respec-

ively. By taking the measures separately, it is not clear which is

he best classifier absolutely. For example, AIS presents most mea-

ures higher than SVM, however the positive prediction for PVC

eartbeats recognition and specificity are larger for SVM. For this

eason, AHP is used to rank them.

Analyzing the pairwise comparison matrices and their respec-

ive priority vectors, according to expressions (4) –(9) , from P + easure, matrix (4) and vector (5) , it is concluded that SVM clas-

ifier is the best, with priority of 0.265 (4-th column in vector (5) )

nd since all values are integers, greater than or equal to one (4-

h row in matrix (4) ). Therefore, SVM is preferable over the others,


Table 9

Comparing the proposed method with baseline methods.

Approach PVC Beats Classifier A cc P + P − S e S p

Liu et al. [9] 2400 LVQ neural network 0.99 0.92 – 0.90 –

Bazi et al. [8] 7117 Gaussian process 0.96 – – 0.97 0.96

Hadia et al. [6] – k -NN – – – 0.93 0.93

Adnane and Belouchrani [10] 1540 Threshold coefficients 0.98 0.92 – 0.97 0.98

Li et al. [5] 3213 Template matching 0.98 0.81 0.99 0.93 0.99

Zarei et al. [7] 3220 Principal directions 0.99 0.86 – 0.96 –

Proposed - Table 5 3219 AIS 0.98 0.85 0.99 0.91 0.98

Proposed - Table 7 36,428 SVM 0.99 0.99 0.98 0.98 0.99

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except to VP classifier, since the value P + 4,7 (the element locatedin the fourth row and seventh column) is equal to one. Likewise,

VP is the second best, with priority of 0.208 and having on the

7-th row all integer values. These results are consistent with those

in the Table 5 , since SVM and VP classifiers obtained better results

for P + . In relation to S e measure, from expressions (6) and (7) , AIS clas-

sifier is the best again. The preference over VP classifier is five (el-

ement S e 8,7 ), since VP classifier got the lowest value of all the mea-

sures, which is 0.665 ( Table 5 , row 8 and column 9). In addition,

this preference is the highest value obtained.

Lastly, from matrix in (8) and vector in (9) , it is concluded that

RBF and RF are the best in terms of AUC measure, with priority of

0.153 (first and 6-th rows in (9) ), followed by AIS, MNB and MLP,

with the same priority.

Considering that the elements in global priority vector v norm ,

given by (10) , are ordered as RF, KNN, MNB, SVM, MLP, RBF, VP

and AIS, the top three classifiers, from the best to the worst, are

AIS, SVM and RBF, with 16.12%, 12.53% and 12.39% of priority, re-

spectively. This selection is consistent with the results presented in

Table 5 , taking into account bold values.

Comparing the respective results shown in Table 5 and Table 6 ,

it is observed that AIS and RBF present worse performances. There

was a decrease mainly in the positive class measures. Mean-

while, SVM maintained the same performance, getting only two

more false positives and one more false negative. RBF only main-

tained P − and S e measures. On the other hand, AIS presented inTable 6 all scores lower than those obtained in Table 5 . In general,

AIS presents the worse performance, according to priority vector

(last column of Table 6 ). Nevertheless, AIS presented lower false

negative alarms in both experiments. Therefore, these results en-

sure that the proposed geometrical features robustness, using SVM,

facing a QRS complex misdetection.

Overall results shown in Table 7 make clear a significant im-

provement in comparison with previous results on unbalanced real

data. RBF classifier yet keeps first position with respect to AUC

measure. Furthermore, it overcomes AIS in relation to the other

measures, but only from the third decimal place on. Finally, SVM

obtained better results for a larger amount of measures. Even so,

AHP tool provides the same priority values for these classifiers. It is

justified because the relative difference among measurements ob-

tained by each classifier is very low.

On the other hand, results obtained from balanced STDB

database are worse than the ones obtained by ARDB in relation

to all measures. Partly, it can be explained due to lower amount

of PVC instances in STDB, which prevents further generalization

by the classifiers. Note that the decreases, comparing results in

Table 7 with the ones in Table 8 , for P + and P − , are on average4.2% and 1.8%, respectively. Another circumstance comprising these

decreases refers to the classifiers parameters, since they are stipu-

lated from ARDB database and are adjusted for it.

Ultimately, the proposed approach is compared with baseline

methods. Note from Table 9 that some researches did not report

a

ll performance measures used in evaluations. Furthermore, each

elected paper used different classifiers. However, the goal in this

ork is to evaluate the proposed geometrical features, and thus,

he classifier that provides best results. It is also worth noting that

he reported papers and the present work used the same database

RDB, but different dataset recordings.

Regarding Normal heartbeats recognition, it is noted from

able 9 that the proposed approach performed at least equal to

aseline methods, being superior when compared to Hadia et al.

6] , Bazi et al. [8] and Adnane and Belouchrani [10] in relation

o specificity measure. When considering PVC heartbeats recog-

ition results, the last two rows in Table 9 , the proposed ap-

roach overcome all methods in relation to P + and S e measures.roadly speaking, the proposed method obtained less false positive

nd negative alarms than the most of baseline methods. Note still

hat the artificial dataset used in the simulations by the proposed

ethod, in relation to PVC heartbeats, is larger than those used

y the baseline methods. For the real dataset it is also larger, ex-

ept to Bazi et al. [8] and Zarei et al. [7] . Moreover, cross-validation

ethod implemented for the artificial dataset avoids model over-

tting, which generally overestimates performance.

. Conclusion

In this paper a new set of features based on geometrical fig-

res extracted from QRS complexes for PVC recognition was pre-

ented, opening a new way to design features looking for geomet-

ical aspects from ECG waveforms, aiming to represent them in a

imple and low cost manner. The proposed mathematical model

apped the signal, obtained after a preprocessing stage, into a

pace of reduced dimension. The new features were built from

irtual triangles and incircles constructed over each QRS complex,

onsidering their fiducial points. Results obtained from extensive

imulations indicated that the proposed approach performed the

est in terms of specificity (98.7%) and sensitivity (91.1%) measures

valuated on DS2 dataset, using an AIS classifier. Using balanced

ataset by means of artificial PVC heartbeats insertion, the results

ere improved to 99.5% and 98.5% in terms of positive prediction

nd sensitivity, respectively. Applying this approach to another bal-

nced dataset (DS3), the obtained results were 97.5% for specificity

nd 98.0% for sensitivity. In general, for accuracy measure, the pro-

osed approach is as good as the baseline methods, being better

han two of them. Furthermore, the proposed features are not sen-

itive to errors of detection in QRS complexes in up to five samples,

hen using an SVM classifier.

In addition to a new set of features, this paper has reported

n a new methodology based on AHP in order to select the best

lassifier supported by consistent criteria. This methodology can be

xtended to any research in the field of machine learning, being

seful mainly in the construction of ensemble of models. This is a

urther topic to be investigated.

In future works it is intended to get other geometrical figures

onstructed over T waves, making possible the recognition of other

rrhythmia types, besides the improvement in performance. In ad-


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ition, validation of the proposed features on more databases will

e performed, as well as the setting of a single classifier in order

o obtain the best parameters to achieve higher results.

onflict of interest statement

There are no conflicts of interest.

cknowledgments and declarations

Authors would like to thank Coordination for the Improvement

f Higher Education Personnel ( CAPES ) and the Department of

lectrical Engineering of the State University of São Paulo ( UNESP ),

lha Solteira, Brazil. There are no conflicts of interest. The men-

ioned experiments were not directly performed with people, since

CG signals used for tests were artificial or acquired from two MIT-

IH databases.

upplementary materials

Supplementary material associated with this article can be

ound, in the online version, at doi: 10.1016/j.cmpb.2018.12.028 .

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Geometrical features for premature ventricular contraction recognition with analytic hierarchy process based machine learning algorithms selection1 Introduction2 Materials and methods2.1 Dataset description2.2 Evaluation measures2.3 Machine learning algorithms2.3.1 k-Nearest neighbors2.3.2 Multinomial naive Bayes2.3.3 Voted perceptron2.3.4 Multilayer perceptron2.3.5 Support vector machines2.3.6 Radial-basis functions network2.3.7 Random forest2.3.8 Artificial immune system

2.4 Analytic Hierarchy Process (AHP)2.5 Wavelet denoising2.6 A PVC recognition approach2.6.1 Preprocessing2.6.2 Segmentation and training2.6.3 Proposed features2.6.4 Classifiers selection

3 Results3.1 General experiments3.2 Selecting the classifiers3.3 Deviation in the QRS complex location3.4 Balanced datasets

4 Discussion5 ConclusionConflict of interest statementAcknowledgments and declarationsSupplementary materialsReferences

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