Separation Method of Atrial Fibrillation Classes with High Order

Statistics and Classification using Machine Learning

Luís Fillype da Silva

, Jonathan Araújo Queiroz

, Caroline Vanessa

, Allan Kardec Barros

Gean Carlos Lopes

and Letícia Cabral

Departament of Eletrical Engineering, Federal University of Maranhão, Av. dos Portugueses, São Luís, Brazil

Department of Nursing, Faculdade Santa Terezinha, São Luis, Brazil

lcabralcorreia@gmail.com

Keywords: ECG, Machine Learning, High Order Statistics, Signs Classification.

Abstract: The electrocardiogram (ECG) is an exam that presents a graphical representation of the electrical activity of

the heart. Through it, it is possible to observe the rhythm of heart beats, the number of beats per minute, in

addition to enabling the diagnosis of various arrhythmias. This article aims to develop a classification model

based on the beats of three groups of individuals: with atrial fibrillation, intra-atrial fibrillation and normal

sinus rhythm. The methodology of extraction of characteristics based and adapted to classify Atrial

Fibrillation and its subtype, Intracardiac Atrial Fibrillation. The classifications were carried out in three-

dimensional space in two stages: with the application of Principal Component Analysis (PCA) and without

application of it, through Artificial Neural Networks (ANN), Support Vector Machines (SVM) and K-nearest

Neighbors (KNN), obtaining accuracy of 93% to 99%.

1 INTRODUCTION

Atrial fibrillation (AF) as being a supraventricular

arrhythmia characterized by disorganized atrial

electrical activity, secondary to multiple foci of atrial

depolarization (Neto et al., 2018).

Despite recent advances in the treatment of AF,

patients with this heart disease still have high

mortality. This is because there are other ways that

AF. It has been widely used due to the nature of its

observations, as shown: the complex electrical pattern

observed during AF can be explained with several

waves that propagate along several routes along the

atria; the available data also support a focal

mechanism, according to which conductors, located

mainly in the pulmonary veins, trigger and support

the spread of electrical activity in the atria (Richter et

al., 2010). Thus, ECG is essential to predict, detect

and diagnose various heart problems, aiding in its

diagnosis (Queiroz et al., 2017).

Works such as that of Kachuee et. al. (2018)

proposes a method based on deep convolutional

neural networks for the classification of heartbeat,

capable of accurately classifying five different

arrhythmias. Hullah et. al. (2020) performs a

classification of 8 types of arrhythmia also using

convolutional neural networks. In Queiroz et al.

(2017) studied the variability of heartbeat and

provided an automatic diagnosis method for heart

disease. Alhusseini et al. (2020) developed a

convolutional neural network to train 100,000 AF

image grids. There are still methods in the literature

that classify ECG signals, as proposed in Ma et al.

(2020), using the RR interval for this classification of

Atrial Fibrillation.

This paper studies and proposes a method of

extracting the heartbeat of all ECGs from the bases

used, grouping 3 groups: individuals with signs of

Atrial Fibrillation, Intracardiac Atrial Fibrillation and

healthy, using high-order Statistics, and subsequently

performing the classification in three Machine

Learning algorithms.

2 THEORY

2.1 ECG

The ECG is essential two main types of information.

First, in medicine, the cardiologist can measure the

284

Fillype da Silva, L., Queiroz, J., Vanessa, C., Barros, A., Lopes, G. and Cabral, L.

Separation Method of Atrial Fibrillation Classes with High Order Statistics and Classiﬁcation using Machine Learning.

DOI: 10.5220/0010325402840291

In Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2021) - Volume 4: BIOSIGNALS, pages 284-291

ISBN: 978-989-758-490-9

time intervals of the ECG to determine how long the

electrical wave takes to pass through the heart's

electrical conduction system. This information find

out to find out if electrical activity is regular or

irregular, fast or slow. Second, by measuring the

strength of electrical activity, the cardiologist is able

to find out if parts of the heart are too large or

overloaded (Ebrahimi et al., 2020).

Figure 1: ECG.

2.2 Machine Learning

Within the innovations of data science, Machine

Learnine is a class of techniques and research area

that allows computers to learn as humans and to

extract or classify patterns. Machines may also be

able to analyze more data sets and extract data

resources that humans may not be able to do. This

technique allows the creation of algorithms that can

learn and make predictions. In contrast to rule-based

algorithms, AM takes advantage of greater exposure

to large and new data sets and has the ability to

improve and learn from experience, such as Neural

Networks, K-nearest Neighbors (Choy et al. 2016).

2.2.1 Artificial Neural Network

Artificial Neural Networks (ANN), better known as

neural networks, as complex structures

interconnected by simple processing elements

(neurons), which have the ability to perform

operations, such as calculations in parallel, for data

processing and knowledge representation (Haykin,

2001).

The author also stresses the properties and

capabilities that make ANN potentially useful are:

non-linearity: an artificial neuron can use linear or

non-linear functions; Input-Output mapping: based

on examples of input and output, the ANN is able to

adapt to minimize the mapping error. Among the

known structures of these models, we have the MLP

(Multilayer Perceptron), which, in general, has an

input layer, one or more hidden layers and an output

layer. See Figure 2 for the MLP model.

Figure 2: MLP model.

In this paper, MLP was used with hyperparameter

of 3 neurons in the input layer, 2 layers with 100

neurons, and 3 neurons in the output layer.

2.2.2 K-Nearest Neighbors (KNN)

KNN is one of the prospective statistical

classification algorithms used to classify objects

based on training examples closest to the plane.

According to the authors, it is a slow algorithm, due

to the model or real learning not being performed

during the training phase. In this case, this set is used

only to fill a sample of the space with instances whose

class is known. At this stage, the vector and class

labels of the user-defined constant training samples, a

query or test point (unlabeled vector), and the data are

classified by assigning a label, which is the most

recurrent among the K samples training courses

closer to that consulted point (Noi and Kappas ,2018).

In this paper, KNN with K settings equal to 10

was used for the classification of heart disease.

2.2.3 Support Vector Machine (SVM)

SVM as a powerful method to build a classifier. This

method aims to create a decision boundary between

two classes that makes it possible to predict the labels

of one or more feature vectors. For the authors, this

decision frontier, known as a hyperplane, is oriented

so that it is as far as possible from the closest data

points for each of the classes present. Such closer

points are called support vectors, giving rise to the

method name (Huang et al., 2017).

In this way, the ideal hyperplane can then be

defined as that which separates the data and

maximizes the margin, respecting the following

equations (Huang et al., 2017).

w𝑥



𝑏  0

)

w𝑥



𝑏  1

)

Separation Method of Atrial Fibrillation Classes with High Order Statistics and Classiﬁcation using Machine Learning

285

wxᵀ + 𝑏 ≤ −1

(3)

In the above equations, w represents the values of

the weights, x the input vector and the bias value.

Being the Equation (1) representing the optimal

hyperplane, the Equations (2) e (3) parameterizing the

data that represents the classes. The explanatory

Figure 3 follows.

Figure 3: SVM model.

2.2.4 Principal Component Analysis (PCA)

PCA as a statistical technique that aims at condensing

information from a large set of variables correlated

into some variables ("main components"), while not

wasting the variability present in the data set. For the

authors, the main components are derived as a linear

combination of the variables in the data set, with

weights chosen so that these components necessarily

become uncorrelated. Each component contains new

information about the data set and is ordered so that

the first components account for most of the

variability (Ramon et al., 2006).

Demonstrating the importance of this technique,

including ECG signs, PCA is used to deal with

several problems in ECG analysis, such as data

compression, beat detection and classification, noise

reduction, separation signal and resource extraction

(Ramon et al., 2006).

In this paper, PCA is not used to reduce

dimensionality, but to not correlate the data, as

described in (Haykin, 2009).

2.2.5 High-order Statistics

In the early 1990s, in particular, there was an increase

in interest in High Order Statistics and its

applications. The application of cumulants in several

fields of knowledge was verified, such as sonar,

biomedicine, data processing, image reconstruction,

etc (Borelli, 2018).

These statistics provide more information than is

available simply provided through the mean and

variance of a process. Thus, it can be said that they

allow a better way to discriminate processes. So, to

better understand and start an approach beyond the

variance and average of the sets, using the skewness

and kurtosis of the data.

3 MATERIALS AND METHOD

In Figure 4, the methodology used in this article is

illustrated. The used databases were defined,

separating them into 3 groups: signs of individuals

with AF, individuals with intra-cardiac AF and

individuals with normal sinus rhythm. The database

signs were pre-processed.

Figure 4: Methodology.

Then, the features represented by high-order

statistics were selected, applying the PCA, generating

new data. Data with PCA and without PCA were

placed as input for classifiers, in order to investigate

the difference in classifications in both approaches.

3.1 Database

The Intracardiac Atrial Fibrillation Database, MIT-

BIH Atrial Fibrillation Database and The MIT-BIH

Normal Sinus Rhythm Database data sets, both

available in Goldberger et al. 2000, were used. The

database of signs of patients with AF contains 23

records, all of which are used in this analysis. The

signal database of patients with intra-cardiac AF

contains 8 patients, all of which are used. From the

database of individuals with normal sinus rhythm, 18

patients were used.

3.2 Pre-processing

ECG signs characteristic of the DII lead were

acquired. The entire duration of the signal, sampled at

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286

a frequency of 256 Hz, was used to extract the beats

of each patient for analysis and subsequent extraction

of features.

After that, each selected signal was segmented to

obtain the respective beat, as proposed by Queiroz et

al. (2017). Thus, the beats of each group were

grouped, generating three matrices, one for each

group of individuals, as described in the equations

below.

𝑀 



𝐵𝑛,𝑎 𝐵𝑛,𝑏…𝐵𝑛,𝑧



(4)

where n represents the number of beats, equal to 190,

and a to z represents the total of all columns of all

beats. Concomitant to this, the mean of its set was

subtracted from the sign, dividing the result by

Shannon's entropy, given by the Equation (5).

𝑍  𝑀 

∑













∑

 











(5)

where p represents the probability associated with

each beat, and Z represents the new matrix associated

with the concatenation of the beats.

3.3 Feature Extraction

The extraction methodology was adapted using high-

order statistics, proposed by Queiroz et al. (2017). A

vector was obtained for each of the associated

statistics: variance, kurtosis and asymmetry, which

will be the inputs of the classifiers, represented by

𝜎





, 𝜅



and 𝜆



, respectively. The equations that

describe such statistics are described in Equation (6),

(7) and (8), where E(x) represents the Expected value.

𝜎





 𝐸𝑋



  𝐸𝑋



(6)

𝜆



𝐸𝑋  𝐸



𝑋



𝜎







(7)

𝜅



𝐸𝑋  𝐸



𝑋



𝜎







(8)

3.4 Evaluation Metrics

In this article, the values of accuracy, sensitivity and

specificity, described by Equation (9), (10) and (11),

were used to verify the performance of the classifiers.

In the equations, TP corresponds to the number of

true positives, TN to true negatives, FP to record false

positives and FN to classify false negatives.

𝐴

𝑐𝑐𝑢𝑟𝑎𝑐𝑦 

𝑇𝑃  𝑇𝑁

𝑇𝑃  𝐹𝑁  𝑇𝑁  𝐹𝑃

𝑥 100

(9)

𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 

𝑇𝑃

𝑇𝑃  𝐹𝑁

𝑥 100

(10

)

𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 

𝑇𝑁

𝑇𝑁  𝐹𝑃

𝑥 100

(11

)

3.5 Cross-validation

Cross validation is a technique to assess the

generalizability of a model, based on a set of data. In

this article, the data is divided using the holdout

method, which consists of dividing the data into 70

and 30 at random. 70% of the patients were used for

training, 30% for testing and k-fold equal to 7.

3.6 Dataset Builded

The construction of the data set was carried out as

follows. A column was created for each statistic,

representing the variance, skewness and kurtosis of

each beat. A label was also created, column 4 of the

data set, which represents the class belonging to the

respective beat. This class has a value of 1 for a

healthy, 2 for intracardiac AF and 3 for AF. See

Figure 6 below.

Figure 5: Data examples.

4 RESULTS

This paper analyzed the beats extracted from the ECG

for patients with normal sinus rhythm, AF and signs

from individuals with intra-cardiac AF, in order to

classify them.

For the classification stage, matrices were

generated, where each column is represented by

variance, skewness and kurtosis, respectively. Such

matrices were the inputs of the KNN, SVM and ANN

classifiers to verify which classification algorithm has

greater accuracy, sensitivity and specificity. The

results were compared with PCA in the data sets and

Separation Method of Atrial Fibrillation Classes with High Order Statistics and Classiﬁcation using Machine Learning

287

without the application of the same. See below in

Figure 6, Figure 7 and Figure 8.

Figure 6: Classifiers Accuracy.

Figure 7: Classifiers Sensibility.

Figure 8: Classifiers Specificity.

5 DISCUSSION

5.1 Data without PCA

In his work, Ma et al. (2020) used the RR interval for

the classification, obtaining an accuracy of 98.3%. In

another study, the same authors also used the RR

interval, classifying with CNN-LSTM, obtaining an

accuracy of 97.21%. Alhusseini et al. (2020)

developed a CNN applied to images of 35 patients,

who made decisions similar to that of specialists, with

95% accuracy. Khriji et al. (2020) used ANN to

classify three differents types of heart diseases too,

obtaining 93.1% of accuracy. In this work, the

approach of extracting features of the beats was used,

with high order statistics, obtaining an accuracy of

98.95 % for ANN.

In Figure 9, 10, 11, the analysis without PCA

shows that the AF data are quite grouped, as they are

the same heart disease, but with different analysis

approaches.

Figure 9: Beats expressed by Variance and Skewness.

Figure 10: Beats expressed by Variance and Kurtosis.

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Figure 11: Beats expressed by Skewness and Kurtosis.

Figure 12: Beats expressed by Variance, Skewness and

Kurtosis.

Separations that use variance as features present a

good representation and achieve high accuracy in

relation to other combinations. This is because

kurtosis can be an appropriate approach to measure

sparse signs, such as the ECG, as discussed in

Queiroz et. al. (2017). It is also inferred from Figure

6 that exemplifies the construction of the dataset, that

the data sets have variance and kurtosis very different

from each other, justifying this result.

5.2 Data with PCA

To improve the representation of these features, the

PCA was then used to rotate these data, resulting in

Figure 14.

As seen in Figures 14, 15, 16, and 17, the results

of the classifications with the use of the PCA were

better and confirmed by the metrics of evaluation of

the algorithms themselves, described in Equations 9,

10, and 11.

Figure 13: Beats expressed by Variance and Kurtosis with

PCA.

Figure 14: Beats expressed by Variance and Skewness with

PCA.

Figure 15: Beats expressed by Skewness and Kurtosis with

PCA.

Separation Method of Atrial Fibrillation Classes with High Order Statistics and Classiﬁcation using Machine Learning

289

Figure 16: Beats expressed by Variance, Skewness and

Kurtosis with PCA.

SVM performed better due to its easy parameter

definition. For ANN, on the other hand, it is necessary

to estimate and define these values very well

empirically to ensure convergence and generalization

capacity. That is, to achieve the best result, it is

necessary to test several different architectures,

increasing or decreasing the number of hidden layers,

making variations in the learning rates, momentum

and number of training periods.

KNN, on the other hand, because it has a slow

training and it is also necessary to estimate the

number of K, this algorithm had a performance below

the others used.

6 CONCLUSIONS

In this paper, the effectiveness of using high-order

statistics to extract characteristics and classify heart

disease, such as atrial fibrillation, was reinforced. In

addition, the use of data modification was shown,

showing a difference in the performance of the

original data and the rotated data in ECG signs. It is

also concluded that although they are the same

pathology, computationally FA and intracardiac FA

have different features. It can also be concluded that

the use of the entire beat instead of the RR interval

can be a good methodology to solve this problem.

In future works, different cardiovascular diseases

can be studied in the methodology and techniques can

be used to improve the pre-processing, as well as

apply other classifiers to evaluate the metrics, and to

test hyperparameters of the classification algorithms.

ACKNOWLEDGEMENTS

We thank CNPQ, the Biological Signal Processing

Laboratory of the Federal University of Maranhão

(UFMA) and BIOSIGNALS for the opportunity to try

to publish science.

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