ORIGINAL ARTICLE

Automatic identification of epileptic EEG signals through binary
magnetic optimization algorithms

Luı́s A. M. Pereira1 • João P. Papa2 • André L. V. Coelho3 • Clodoaldo A. M. Lima4 •

Danillo R. Pereira2 • Victor Hugo C. de Albuquerque3

Received: 2 November 2016 / Accepted: 17 June 2017 / Published online: 28 June 2017

� The Natural Computing Applications Forum 2017

Abstract Epilepsy is a class of chronic neurological

disorders characterized by transient and unexpected

electrical disturbances of the brain. The automated anal-

ysis of the electroencephalogram (EEG) signal can be

instrumental for the proper diagnosis of this mental con-

dition. This work presents a systematic assessment of the

performance of different variants of the binary magnetic

optimization algorithm (BMOA), two of which are

introduced here, while serving as feature selectors for

epileptic EEG signal identification. In this context, the

optimum-path forest classifier was adopted as a classifi-

cation model, whereas different wavelet families were

considered for EEG feature extraction. In order to

compare the performance of the improved BMOA vari-

ants against the traditional one, as well as other meta-

heuristic techniques, namely particle swarm optimization,

binary bat algorithm, and genetic algorithm, we employed

a well-known EEG benchmark dataset composed of five

classes of EEG signals (two of which comprising normal

patients with eyes open or closed, and the remaining

comprising ill patients with different levels of epilepsy).

Overall, the results evidenced the robustness of the pro-

posed BMOA and its variants.

Keywords Feature selection � Epilepsy � EEG signal

classification � Magnetic optimization algorithm �
Metaheuristics � Optimum-path forest

1 Introduction

Broadly speaking, epilepsy can be defined as a medical

condition related to the occurrence of seizures, which

affect a variety of mental and physical functions of an

individual. In short, the term ‘‘epilepsy’’ encompasses a

number of different neurological syndromes characterized

by transient and unexpected electrical disturbances of the

brain [4]. In epileptic patients, the brain’s normal electrical

activity is disrupted by overactive electrical discharges,

causing a temporary communication problem among nerve

cells [3]. It is estimated that epilepsy is the third most

common neurological disorder in the USA, being around

50–65 million people worldwide affected by such class of

syndrome. Besides, the mortality rate is two to three times

higher among people with epilepsy, which is fair enough

for increasing the investments on novel methodologies and

computational devices for the early and correct diagnosis

of this medical condition.

& João P. Papa

papa@fc.unesp.br

Luı́s A. M. Pereira

luismartinspr@gmail.com

André L. V. Coelho

acoelho.albuquerque@unifor.br

Clodoaldo A. M. Lima

c.lima@usp.br

Danillo R. Pereira

danilopereira@unoeste.br

Victor Hugo C. de Albuquerque

victor.albuquerque@unifor.br

1 Instituto de Computação, Universidade Estadual de

Campinas, Campinas, SP, Brazil

2 Departamento de Computação, UNESP - Univ Estadual

Paulista, Bauru, SP, Brazil

3 Programa de Pós-Graduação em Informática Aplicada,

Universidade de Fortaleza, Fortaleza, CE, Brazil

4 Escola de Artes, Ciências e Humanidades, Universidade de

São Paulo, São Paulo, SP, Brazil

123

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One of the most reliable examinations for the proper

diagnosis of seizures and epilepsy is the well-known

electroencephalogram (EEG) [3], which records the brain’s

electrical activity as a series of traces, each of them cor-

responding to a different region of the brain. However, the

visual inspection of the EEG signals for the detection of

normal, interictal, and ictal activities in the patient’s brain

is usually a time-consuming and error-prone task due to the

huge volumes of EEG segments that have to be analyzed.

Therefore, the adoption of computer-based techniques for

the purpose of tackling epilepsy diagnosis via EEG signal

classification has been actively pursued in the last dec-

ades [8]. Besides, since EEG signals are nonlinear and

dynamic in nature [1], there has been a growing interest in

applying nonlinear signal analysis techniques, such as

those based on wavelets, entropy, fractal, and chaos the-

ory [37], for studying the behavior of these signals and also

to extract relevant and condition-discriminatory informa-

tion from them.

In order to assess the pros and cons of different machine

learning approaches to cope with the epilepsy diagnosis

problem, several prominent works have recently employed

different configurations of the EEG dataset made available

by Andrzejak et al. [1, 2]. This benchmark dataset is

composed of five classes in total (two of which comprising

normal patients with eyes open or closed, and the

remaining comprising ill patients with different levels of

epilepsy), whose full discrimination is very hard to

achieve. In this context, Subasi [26–28] employed some

variants of artificial neural networks (ANN) and also

mixture-of-experts (ME) models aiming to discriminate

between seizure and seizure-free profiles. In [27], in par-

ticular, the author reported 94.5% of accuracy rate

achieved by ME models while discriminating solely classes

A and E, which was a score better than that achieved by

single multilayer perceptron (MLP) neural networks

(93.2%). The specificity and sensitivity values reported for

the ME and MLP models were, respectively, 94%/92.6%

and 95%/93.6%. ME models induced with wavelet coeffi-

cients have also been considered by Übeyli [33], even

though, in that work, the performance of the models was

measured over three sets of the EEG dataset (namely sets

A, D, and E). The total classification accuracy achieved by

the ME network structures was 93.17% [33].

On the other hand, the paper of Tzallas et al. [31, 32]

presents a methodology whereby selected segments of the

EEG signals (maybe with different sizes) are analyzed

using time–frequency methods, and then several features

are extracted for each segment representing the energy

distribution in the time–frequency plane. These features are

used as input to a feedforward neural network, which

provides the final classification. In order to evaluate the

methodology, the authors generated four different

classification problems, none of which, however, involving

the five classes at the same time, and the results achieved in

terms of overall accuracy ranged from 97.72 to 100%.

Nunes et al. [21] carried out a simple application of the

optimum-path forest classifier [23, 24] to diagnose patients

with epilepsy via EEG signal classification using four types

of wavelet functions for feature extraction, being the Coi-

flets as the most accurate ones.

Lima et al. [14–16] evaluated the potentials of several

kernel-based learning machines, such as support vector

machines (SVM) and relevance vector machines (RVM), in

the task of automatic discrimination of epileptic from non-

epileptic EEG signals. The performance levels obtained by

the kernel machines were contrasted in terms of predictive

accuracy, sensitivity to the kernel function/parameter

value, and sensitivity to the type of features extracted from

the signal. For this purpose, several types of features

extracted from the EEG signal, including statistical values

derived from the discrete wavelet transform, Lyapunov

exponents, and combinations thereof, were considered.

Overall, the results evidenced that all considered kernel

machines were competitive in terms of accuracy, and the

choice of the kernel function and parameter value, as well

as the choice of the feature extractor, are really critical

decisions to be taken into account.

In this paper, we focus our attention on one specific step

of the whole classification process that was not deeply

investigated in the aforementioned works, i.e., the step of

selecting the optimal subset of discriminatory features

extracted from the EEG signal. In a nutshell, feature

selection, also known as variable or attribute selection, is

the task of selecting a subset of relevant features for

inducing a classifier model [9, 10]. The central assumption

when using a feature selection technique is that the data

contain many redundant or irrelevant features. While

redundant features are those which provide no more

information than the currently selected features, irrelevant

features provide no useful information at all. Even though

the theme of feature selection has been much researched in

the last years, it is noticeable that only a few works have

given some attention to the study of the impact of this step

in the context of EEG signal classification.

The paper of Ocak [22], for instance, is an exception,

where the use of a genetic algorithm-based (GA) EEG

feature selector was investigated. In the proposed scheme,

normal and epileptic EEG segments were decomposed into

various frequency bands through a wavelet packet

decomposition. Then, approximate entropy values of the

wavelet coefficients at all nodes of the decomposition tree

were used as candidate features to characterize the pre-

dictability of the EEG data within the corresponding fre-

quency bands. Finally, the GA was used to find the subset

of features that maximizes the classification performance

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of an EEG classifier based on learning vector quantization

(LVQ). It was particularly demonstrated in [22] that, if the

GA was not used for the optimal feature selection, the good

classification accuracies achieved by the LVQ classifier

would drop noticeably.

In this paper, our emphasis is on the investigation of the

potentials of a recently introduced population-based

metaheuristic technique, named as magnetic optimization

algorithm (MOA) [30], to serve as selector of optimal EEG

features extracted by different wavelet families. Since the

feature selection task is computationally intractable for

even moderate sizes of feature sets [9, 10], the analysis of

the performance of different metaheuristic algorithms for

performing this task is readily justified [39]. Moreover,

since the feature selection task can be regarded as a binary

optimization problem, different variants of the binary

magnetic optimization algorithm (BMOA) [18] have been

considered in this study, two of which are introduced here.

We compared MOA-based algorithms against GA, particle

swarm optimization (PSO) [17, 38], and binary bat algo-

rithm (BBA) [19], being the experiments conducted over

the aforementioned EEG benchmark dataset.

The remainder of the paper is organized as follows. In

Sect. 2, we outline the main steps behind the BMOA

variants considered. Section 3 formalizes the steps of the

proposed feature selection methodology, while Sect. 4

characterizes the EEG dataset and the wavelet basis used as

feature extractors. Section 5 presents how the computa-

tional experiments were set up, while Sect. 6 is devoted to

assess the performance of the techniques for EEG signal

classification, taking into account the impact of the dif-

ferent feature selectors. Finally, Sect. 7 states conclusions.

2 Magnetic optimization algorithm

The electromagnetic force concept is one of the four fun-

damental interaction forces in nature. In this interaction

force, the force intensity concerning two electromagnetic

particles is inversely proportional to the distance between

them, i.e., the greater the distance, the smaller the inter-

action force. Based on this definition, Tayarani and

Akbarzadeh [30] proposed a new metaheuristic algorithm

called magnetic optimization algorithm (MOA), which

models a system of magnetic particles (agents) that seek

for a solution in a search space using their magnetic fields,

i.e., their fitness values, to interact with each other. The

mathematical definitions of MOA are summarized as

follows:

• Initially, MOA starts randomly placing all agents in the

search space. Each agent is modeled as a solution

vector xi 2 Rd, where i denotes the i-th agent, and xdi
stands for its position at d-th dimension.

• At each iteration of the algorithm, the solution vectors

are evaluated, and their respective fitness values are

stored in Bi, which denotes the magnetic field value of

the particle i.

• The mass Mi of each agent is given by:

Mi ¼ aþ qBi; ð1Þ

where a and q are constant parameter values.

• The interaction force between two particles i and j at

dimension d is given as follows:

Fd
ij ¼ Bi

xdj � xdi

Dðxj; xiÞ
; ð2Þ

in which Dð�; �Þ is a distance function.

• The acceleration, velocity, and the position of each

agent are updated, respectively, by:

adi ¼
Fd
i

Mi

; ð3Þ

vdi ðt þ 1Þ ¼ hvdi ðtÞ þ adi ð4Þ

and

xdi ðt þ 1Þ ¼ xdi ðtÞ þ vid; ð5Þ

where t is the iteration step and h�Uð0; 1Þ.
Tayarani and Akbarzadeh [30] also proposed a lattice

where each agent can be influenced by the magnetic field

from its neighborhood, being possible to determine the

total force acting over each particle. However, this sort of

lattice provides low and limited interactions, since an agent

can interact with its immediate neighbors only (four

neighborhoods) [18].

2.1 Binary MOA

Mirjalili and Hashim [18] proposed a binary version of the

original MOA (BMOA) aiming to tackle binary optimiza-

tion problems. In addition, they introduced a fully con-

nected topology, in which all particles are connected and

can interact to each other, thereby improving the short-

comings of the four-neighborhood lattice topology. Here-

after, we will refer to BMOA configured with a four-

neighborhood lattice as BMOA1, whereas BMOA2 refers

to the one with fully connected topology.

In order to restrict the new particle’s position to only

binary values, the authors employed a hyperbolic tangent

function [18]:

Sðvdi ðtÞÞ ¼ tanhðvdi ðtÞÞ
�
�

�
�: ð6Þ

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Equation (6) can be rewritten as:

xdi ðt þ 1Þ ¼
:ðxdi ðtÞÞ if Sðvdi ðt þ 1ÞÞ[ r;

xdi ðtÞ otherwise

(

ð7Þ

in which :ð�Þ means the binary complement operator and

r�Uð0; 1Þ. To provide a good convergence rate, the

velocity was limited to jvdi ðt þ 1Þj\vmax, where vmax was

set to 6.

2.2 Improving BMOA

Although BMOA2 has demonstrated more interaction

benefits than BMOA1, the particles suffer from the

attraction of bad ones, which may cause the loss of the

previous good solution. As such, we propose here two new

variants of the BMOA algorithm:

1. In the first variant, named as BMOA3, we model the

interaction between good and bad particles, so that only

particles with a good magnetic field can attract particles

with bad magnetic ones. Therefore, a particle i with a

magnetic fieldBi will attract a particle j only ifBi [Bj (in

case of maximization problems). Thus, the resultant force

Fj over a bad particle j is formed by the attraction from

particles with better magnetic fields than Bj.

2. The second variant, called BMOA4, uses the same

interaction strategy employed by BMOA3; however, it

allows that some good particles be attracted by some

bad ones, as follows:

Bj � bestB

Bj � Bi

[ r or Bj [Bi: ð8Þ

However, these conditions may introduce the same

problem as in BMOA2, i.e., losing good solutions. In

order to avoid this problem, we introduce a vector y to

store the best local position of each particle i. Thus, we

update yi only if the new solution xiðt þ 1Þ achieves a
better solution. These procedures are similar to those

presented in [12], but for a different approach.

3 Feature selection methodology

In this section, we present the methodology used to eval-

uate the proposed variants of BMOA. The main idea is to

allow a fair unbiased mean recognition rate computation

together with a proper subset of suitable features. In order

to accomplish with such deals, let us introduce some

important definitions. Let Z be a labeled dataset, such that

Z ¼ Z1 [ Z2 [ Z3 [ Z4, in which Z1, Z2, Z3, and Z4

stand for the training, learning, validating, and test sets,

respectively. Roughly speaking, the main goal of a meta-

heuristic-based feature selection approach is to employ

some classifier’s recognition rate to be part of the fitness

function (wrapper approaches). In this work, we use the

training and learning sets to guide the search process onto

the solution space (‘‘Learning process’’ module in Fig. 1).

Therefore, the idea is to train a classifier over Z1 for further

Fig. 1 Pipeline of the proposed feature selection methodology

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classification of Z2 (for each search agent), being the

recognition rate over the latter set used as the fitness

function. As one can realize, we need a fast and effective

classifier, since we need to perform the training step fol-

lowed by the classification of the learning set every time an

agent changes its position. Therefore, we opted to employ

the supervised optimum-path forest (OPF) classi-

fier [23, 24], which is a parameter-free technique that has

been used for several applications.

The above procedure, which outputs the selected subset

of features that maximizes the OPF accuracy over Z2, is

then conducted 10 times with randomly generated training

and learning sets. Thus, one has at the final of the process,

10 subsets of selected features, being now the main goal to

choose the best one. Such step is conducted by the

‘‘Threshold’’ module in Fig. 1: we employed a threshold-

based approach to find out the final subset of features,

being such threshold value ranged from 10 to 90%, with

steps of 10%. A threshold value of T%, for instance, means

we selected the features that appeared at least T% on that

10 subsets outputted over the 10 executions of the

‘‘Learning process’’ module in Fig. 1. The selected features

for that threshold, i.e., T%, are then used to train OPF for

further classification of the validating set (Z3). Therefore,

if we perform the above procedure for each threshold

within the range ½10%; 90%�, we obtain a curve that rep-

resents the recognition rate over Z3 for each threshold

value. The final subset of features is the one which maxi-

mizes the accuracy of such curve, being such subset used to

train OPF for further classification of the unseen testing set

(Z4). Notice the test set has not been used so far, i.e., it has

been employed for assessing the effectiveness of the final

subset of features only.

Figure 1 illustrates our proposed methodology to select

the subset of features that best represents EEG signals. We

used 30% of the original dataset for Z1, 20% for Z2, 20%

for Z3, and 30% for Z4. These percentages were set up

empirically.

We also compared the MOA-based approaches against a

mutual information (MI) filter-based method [20]. The best

MI model was chosen by selecting the features percentage

among ½10%; 20%; . . .; 90%� with the highest mutual

information. For this purpose, Z1 was employed as the

training set and Z2 [ Z3 as the validating sets. Thereafter,

the OPF classifier was trained on Z1 to classify Z4.

4 Dataset description

In this work, we evaluate the performance of BMOA and

its variants in the context of automatic epilepsy diagnosis.

The complete dataset consists of five sets (denoted as A–

E), which contains 100 single-channel EEG segments of

23.6s. These segments were selected and cut out from

continuous multi-channel EEG recordings after visual

inspection for artifacts due to muscle activity or eye

movements. All EEG signals were recorded with the same

128-channel amplifier system using an average common

reference. The data were digitized at 173.61 Hz sampling

rate with 12 bit analog-to-digital resolution, and the band-

pass filter settings were 0.5340 Hz (12 dB/oct). The data

are made available by Andrzejak et al. [1, 2].

The signals from folds A and B were obtained

extracranially from surface EEG recordings of five healthy

individuals with eyes open and closed, respectively. Notice

the sets C, D, and E were originated from an EEG archive

of pre-surgical diagnosis. The EEG signals from five

patients were selected, all of whom had achieved complete

seizure control after resection of one of the hippocampal

Table 1 Parameter setting of the metaheuristic algorithms

Technique Parameters

BBA a ¼ 0:9, c ¼ 0:9

BGA pm ¼ 0:1

BMOA a ¼ 0:9, q ¼ 4:8

BPSO c1 ¼ 2:0, c2 ¼ 2:0, w ¼ 0:9

Table 2 Mean recognition rates

considering OPF over the

original (baseline) testing set

Accuracy (%) F-measure Precision Recall

A B C D E A B C D E A B C D E

Coif2 64 63 70 55 39 92 55 74 57 42 93 73 67 53 37 90

Coif3 70 70 74 61 56 91 64 72 65 55 100 77 77 57 57 83

Coif4 68 58 74 67 45 95 56 78 59 52 97 60 70 77 40 93

Db2 61 69 60 43 41 85 65 70 42 46 76 73 53 43 37 97

Db3 60 65 51 46 48 87 56 71 48 45 84 77 40 43 50 90

Db4 60 72 51 59 42 71 64 62 47 56 86 83 43 80 33 60

Sym2 62 73 64 42 46 84 61 74 44 45 92 90 57 40 47 77

Sym3 59 66 58 41 48 81 65 64 41 44 83 67 53 40 53 80

Sym4 59 72 52 54 33 84 65 58 48 38 92 80 47 63 30 77

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formations, which was therefore correctly diagnosed to be

the epileptogenic zone. Signals in the folds C and D were

sampled intracranially in seizure-free intervals from five

patients. While the signals in fold C were captured from the

hippocampal formation of the opposite hemisphere of the

brain, those from fold D were extracted directly from the

epileptogenic zone. Finally, fold E contains signals

obtained intracranially and related to the seizure activity.

These signals were selected from all recording sites of the

brain exhibiting ictal activity. We consider here the whole

dataset of 500 EEG segments, each one with 4096 samples,

as employed in [34].

5 Experimental design

This section describes the main steps involved in our

experimental procedures. We compared the MOA-based

approaches against three other feature selection techniques:

binary bat algorithm (BBA) [25], binary particle swarm

optimization algorithm (BPSO) [6], and binary genetic

algorithm (BGA) [13].

• Parameter setting: Table 1 presents the parameters

employed for each metaheuristic technique. Notice we

used 30 agents with 100 iterations for all techniques.

These parameters were set based on previous

experiments.

• Statistical evaluation: In order to give more support for

our conclusions, we carried out two round of statistical

tests. Firstly, we performed the nonparametric Fried-

man test, which was used to rank the algorithms for

each dataset separately. In case of Friedman test to

provide meaningful results to reject the null-hypothe-

sis (h0: all techniques are equivalent), then we can

perform a post hoc test. For this purpose, we perform

the Nemenyi test [20], which allows us to verify

whether there is a critical difference (CD) among

techniques. The results of the Nemenyi test can be

represented in a simple diagram, in which the average

ranks of the methods are plotted on an horizontal axis,

Table 3 Mean recognition rates and number of selected features considering BMOA variants over the testing set

BMOA1 BMOA2 BMOA3 BMOA4

Acc (%) #Selected features Acc (%) #Selected features Acc (%) #Selected features Acc (%) #Selected features

Coif2 71 16 71 24 69 39 69 20

Coif3 70 7 72 11 75 18 81 13

Coif4 76 31 71 4 76 34 75 24

Db2 67 24 61 22 73 8 67 10

Db3 69 11 73 11 69 12 69 15

Db4 69 16 72 16 71 26 72 14

Sym2 66 8 62 7 68 4 71 6

Sym3 67 14 58 20 61 22 69 10

Sym4 66 12 67 16 67 10 67 22

Bold values indicate the most accurate techniques

Table 4 Mean recognition rates and number of selected features considering BBA, BGA, BPSO, and MI on test set

BBA BGA BPSO MI

Acc (%) #Selected features Acc (%) #Selected features Acc (%) #Selected features Acc (%) #Selected features

Coif2 69 20 72 16 66 18 72 32

Coif3 72 11 78 22 80 24 80 28

Coif4 78 10 76 33 75 31 72 16

Db2 69 33 67 6 67 15 64 8

Db3 64 25 75 16 66 15 68 8

Db4 64 4 68 15 68 8 60 8

Sym2 63 14 64 15 68 4 66 8

Sym3 65 14 54 21 69 11 62 16

Sym4 67 6 66 14 64 16 65 8

Bold values indicate the most accurate techniques

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where the lower average rank is better. Furthermore,

the groups with no significantly difference are then

connected. More about these procedures can be found

in Demšar [5].

• Performance measures: in order to assess the perfor-

mance of the feature selection techniques, four well-

known measures were employed: standard accuracy,

F-measure, precision, and recall. Since we are dealing

with a problem with multiple classes, the three latter

measures were calculated for each class separately.

• Fitness function: as the reader may have noticed, our

methodology (Sect. 3) requires a fast training and

classification steps. In this fashion, we employed the

OPF classifier, since it is a nonparametric and very

robust classifier. Thus, for each iteration of the

optimization techniques, the fitness function is calcu-

lated as the accuracy [24] of the OPF classifier on the

learning set.

• Platform: it is important to highlight that all experi-

ments were carried out on a PC Intel� Core i7 Q740

1.73GHz with 3GB RAM running Ubuntu 10.04 as

operational system.

In order to extract discriminatory features from raw

EEG data, the discrete wavelet transform (DWT) was

employed in this work [29, 36]. The basic idea underlying

wavelet analysis consists in expressing a signal as a linear

combination of a set of localized functions, which are

obtained by shifting, contracting, and dilating one partic-

ular prototype function, called a mother wavelet [11]. The

decomposition of the signal leads to a set of values,

referred to as wavelet coefficients.

While conducting the experiments for this paper, we

have also considered different wavelet families with dif-

ferent orders and parametrization factors. However, due to

the lack of space, we focus our analysis here on the Coiflets

(Coif) order 2–4, the Symlet (Sym) order 2–4, and Dau-

bechies (Db) order 2–4 [7, 14]. Therefore, 40 feature val-

ues were extracted from each of the 500 data patterns

available in the dataset. The chosen features are related to

the well-known statistics calculated over the wavelet

coefficients in each or adjacent sub-bands, i.e., minimum,

maximum, mean, standard deviation, power, absolute

mean, and ratio of absolute mean [14, 27, 33, 35].

Fig. 2 Nemenyi statistical test considering the accuracy results

Fig. 3 Nemenyi statistical test considering the F-measure results

Fig. 4 Nemenyi statistical test considering the precision results

Fig. 5 Nemenyi statistical test considering the recall results

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6 Results and discussion

In this section, we present the results obtained using the

proposed approaches. In order to provide a baseline for

comparison purposes, we evaluated the performance of

OPF classifier over the original datasets, i.e., without fea-

ture selection. For such experiment, we employed only the

training and testing sets, since the learning and validating

sets were used for feature selection purposes (Sect. 3).

Notice the training and test sets were the same as the ones

used in the feature learning process.

Table 2 shows the OPF classifier results over the orig-

inal datasets (baseline), as well as Tables 3 and 4 display

the recognition rates concerning the feature selection

approaches. Notice that improvements on the accuracies

after feature selection for all datasets can be observed. In

regard to the Coif3 dataset, for instance, BMOA1 achieved

the same results as the OPF classifier, but it has selected

only seven features. The same behavior can be observed for

Db2 and Sym2 datasets, in which BMOA2 presented the

same OPF results, but it has selected 22 and 7 features,

respectively. If we consider the Sym3 dataset, BMOA2 was

the only technique that did not surpass the performance of

the OPF classifier.

Figures 6 and 7 depict the curves generated by the

‘‘Threshold’’ module described in Fig. 1. Roughly speak-

ing, one can observe that all techniques have presented

similar behavior concerning variations on the threshold

value. In addition, the great majority of the datasets have

been better described with a threshold greater or equal than

50%, which means there might be an inferior bound for the

feature selection problem. However, as the threshold

increases, it does not imply the accuracy will also increase.

Additionally, its is important to shed light over that BMOA

(b)(a)

(d)(c)

Fig. 6 Accuracy rates over the validating set considering Coif2, Coif3, Coif4, and Db2 datasets

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(b)(a)

(d)(c)

(e)

Fig. 7 Accuracy rates over the validating set considering Db3, Db4, Sym2, Sym3, and Sym4 datasets

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variants obtained the best results in four out nine datasets,

and also they achieved the same recognition rate as BPSO

and BBA for Sym3 and Sym4 datasets, respectively.

If we consider Coif2 dataset, for instance, BMOA1 was

the best technique with 80.95% of accuracy (considering

a threshold of 50%), as displayed in Fig. 6a. In addition,

BMOA3 selected the 60% of the features that maximized

the classification rate for Coif3 dataset (Fig. 6b). Finally,

for Coif4 dataset, BMOA2 and BBA were the best per-

formers with 77.14% of accuracy and a threshold equal to

70%. In case of Db datasets, for Db2, BMOA3 and

BMOA4 achieved the same accuracy rates, but with a

different threshold: 60 and 70%, respectively. For Db3

dataset, BMOA2 achieved 69.52% of recognition rate

considering a threshold of 60%. For Db4 dataset, BMOA4

maximized the accuracy measure with a threshold of

60%, reaching 75.23%. Considering Sym2 dataset,

BMOA4 was the best performer achieving 73.33% of

accuracy (threshold of 70%), and for Sym3 and Sym4,

BPSO and BBA achieved the best accuracy rates of 76.19

and 74.28%, respectively.

From Tables 3 and 4, it is possible to observe the pro-

posed BMOA4 has been the most accurate technique in five

out nine datasets, being them: Coif3, Db4, Sym2, Sym3

and Sym4. These results show us that the BMOA4 inter-

action mechanism provides better convergence rates than

the other BMOA variants. Among the other algorithms,

BPSO was the best performer in four out of nine datasets. It

also achieved a great result over the Coif3 dataset with

accuracy equal to 80%, being slightly less accurate than

BMOA4. Nevertheless, BMOA4 has selected less features

than BPSO.

Table 5 F-measure, precision

and recall rates over the testing

set considering BMOA variants

BMOA1 BMOA2 BMOA3 BMOA4

A B C D E A B C D E A B C D E A B C D E

F-measure

Coif2 64 80 68 52 92 67 70 70 54 90 63 71 70 46 92 63 64 72 55 89

Coif3 79 77 58 50 88 68 69 70 63 90 71 75 65 67 95 83 84 75 67 95

Coif4 84 90 59 51 95 69 72 62 64 91 77 88 62 58 95 83 84 61 50 97

Db2 73 67 56 50 85 68 60 50 45 85 84 90 49 46 87 75 72 49 49 90

Db3 78 86 46 45 94 81 78 56 59 91 74 70 55 54 92 70 73 60 52 92

Db4 77 71 64 48 83 85 73 64 48 87 81 71 62 51 88 76 78 66 54 87

Sym2 73 66 51 48 90 73 59 49 40 87 81 77 46 49 86 77 80 54 56 85

Sym3 74 68 45 54 90 63 63 35 41 87 63 63 42 45 89 78 72 50 52 87

Sym4 67 71 59 50 84 68 68 65 53 84 67 72 57 46 93 65 66 65 57 85

Precision

Coif2 69 80 63 54 90 67 67 67 64 88 57 77 64 55 93 63 74 64 60 85

Coif3 76 81 59 47 93 66 76 70 61 90 69 76 72 64 94 77 89 76 67 97

Coif4 81 88 61 52 97 65 75 73 56 96 75 90 61 59 97 77 89 59 54 97

Db2 73 70 59 50 78 73 60 54 41 84 81 88 57 50 78 76 71 52 48 88

Db3 88 92 55 37 91 83 79 62 51 96 83 74 60 46 88 79 70 63 49 90

Db4 75 62 69 54 86 84 70 58 60 87 78 72 54 62 93 79 70 62 58 96

Sym2 70 62 56 50 90 70 61 52 40 84 83 75 50 46 89 71 74 64 59 84

Sym3 72 66 52 52 90 67 63 33 43 84 71 55 44 46 87 74 68 59 54 84

Sym4 67 69 58 50 89 69 66 60 56 89 70 71 51 48 96 62 68 58 65 86

Recall

Coif2 60 80 73 50 93 67 73 73 47 93 70 67 77 40 90 63 57 83 50 93

Coif3 83 73 57 53 83 70 63 70 67 90 73 73 60 70 97 90 80 73 67 93

Coif4 87 93 57 50 93 73 70 53 73 87 80 87 63 57 93 90 80 63 47 97

Db2 73 63 53 50 93 63 60 47 50 87 87 93 43 43 97 73 73 47 50 93

Db3 70 80 40 57 97 80 77 50 70 87 67 67 50 63 97 63 77 57 57 93

Db4 80 83 60 43 80 87 77 70 40 87 83 70 73 43 83 73 87 70 50 80

Sym2 77 70 47 47 90 77 57 47 40 90 80 80 43 53 83 83 87 47 53 87

Sym3 77 70 40 57 90 60 63 37 40 90 57 73 40 43 90 83 77 43 50 90

Sym4 67 73 60 50 80 67 70 70 50 80 63 73 63 43 90 67 63 73 50 83

Bold values indicate the most accurate techniques

S1326 Neural Comput & Applic (2019) 31 (Suppl 2):S1317–S1329

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Figure 2 displays the statistical test concerning the

accuracy results. Clearly, one can observe the proposed

BMOA approaches (i.e., BMOA4 and BMOA3) have been

placed as the two top best techniques (from right to left),

though all techniques have been considered similar to each

other, except the baseline provided by OPF (i.e., without

feature selection).

Similarly, Figs. 3, 4, and 5 depict the statistical tests

concerning the F-measure, precision and recall results.

Notice all performance measures placed the proposed

approaches as the best ones, tough all being similar to each

other concerning the statistical test, excepting the baseline

provided by OPF. Roughly speaking, we can argue the

proposed approaches are suitable for feature selection, and

the neighborhood information can really improve the

results (Figs. 6, 7).

In regard to the F � measure results (Table 5), which is

the harmonic average between precision and recall mea-

sures, BMOA variants have achieved the highest values for

classes A, B, and C, since such classes are well separated by

kernel machines in general (please, refer to [14]). The pro-

posed BMOA4 has been the one with the highest accuracy

over class D, followed by BMOA1 and BMOA2 that

achieved the best results over classes B (a tie with BPSO can

be observed) and A, respectively. In addition, BBA has

obtained the best accuracy considering class D. For the sake

of comparison purposes, Table 6 displays the F-measure

values concerning the techniques compared in this work.

Table 6 F-measure, precision

and recall rates over the testing

set considering BBA, BGA,

BPSO and MI techniques

BBA BGA BPSO MI

A B C D E A B C D E A B C D E A B C D E

F-measure

Coif2 66 73 63 50 90 64 76 72 56 90 64 67 64 45 88 62 88 62 67 93

Coif3 74 72 63 58 93 80 84 66 67 91 82 85 72 67 91 78 85 80 67 93

Coif4 73 82 68 68 98 73 84 73 57 94 80 90 60 50 94 74 86 65 49 97

Db2 70 68 58 51 95 72 77 58 40 86 65 74 54 47 90 60 70 60 50 78

Db4 68 60 55 50 90 85 88 48 57 95 70 71 52 41 94 68 85 59 38 91

Db3 75 79 51 27 81 88 73 57 38 79 80 77 57 39 83 65 56 45 50 91

Sym2 75 64 39 48 92 70 55 54 56 86 76 79 52 39 87 71 77 50 50 79

Sym3 75 74 47 38 85 62 50 36 46 78 78 70 55 55 83 58 62 50 50 88

Sym4 76 80 59 24 91 63 68 60 55 85 61 68 58 51 84 64 64 54 60 89

Precision

Coif2 70 73 58 56 87 73 76 61 65 87 62 73 62 48 84 87 70 70 47 90

Coif3 71 75 63 56 96 74 86 75 62 96 85 81 75 65 93 83 77 67 80 93

Coif4 73 78 71 71 96 69 86 69 61 96 78 90 60 51 96 87 80 37 67 93

Db2 74 69 53 56 91 75 71 59 40 89 72 69 52 52 88 70 70 50 40 93

Db3 73 60 53 47 93 84 93 54 51 94 74 66 54 43 91 77 73 57 37 97

Db4 74 77 48 33 76 82 80 50 50 76 80 75 51 48 83 87 47 67 30 70

Sym2 81 66 41 43 90 67 60 58 50 89 73 76 52 48 84 73 77 40 53 87

Sym3 71 69 47 45 86 64 45 40 43 88 74 67 60 57 83 60 77 50 33 93

Sym4 73 80 51 32 96 63 69 54 60 86 62 66 54 52 92 70 60 67 50 80

Recall

Coif2 63 73 70 46 93 56 76 86 50 93 66 63 66 43 93 72 78 66 55 92

Coif3 76 70 63 60 90 86 83 60 73 86 80 90 70 70 90 81 81 73 73 93

Coif4 73 86 66 66 100 76 83 76 53 93 83 90 60 50 93 80 83 47 56 95

Db2 67 67 63 47 100 70 83 57 40 83 60 80 57 43 93 65 70 55 44 85

Db3 63 60 57 53 87 87 83 43 63 97 67 77 50 40 97 72 79 58 37 94

Db4 77 80 53 23 87 93 67 67 30 83 80 80 63 33 83 74 51 54 38 79

Sym2 70 63 37 53 93 73 50 50 63 83 80 83 53 33 90 72 77 44 52 83

Sym3 80 80 47 33 83 60 57 33 50 70 83 73 50 53 83 59 69 50 40 90

Sym4 80 80 70 20 87 63 67 67 50 83 60 70 63 50 77 67 62 60 55 84

Bold values indicate the most accurate techniques

Neural Comput & Applic (2019) 31 (Suppl 2):S1317–S1329 S1327

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7 Concluding remarks

In this work, we carried the problem of EEG signal clas-

sification by means of four variants of the magnetic opti-

mization algorithm, being two of them proposed in this

work. In addition, three well-known metaheuristic algo-

rithms were considered in this study, namely particle

swarm optimization, binary bat algorithm, and genetic

algorithm.

The proposed BMOA4 variant has prevailed in terms of

effectiveness (accuracy, precision, recall, and F-measure)

measures considering the great majority of datasets, as well

as in terms of the number of selected features. In special,

BMOA4 recognition rate over the features extracted via

Coif-3 wavelets has shown very satisfactory levels of

performance (with accuracy equal to 81%). Besides,

BMOA4 has always prevailed over the other BMOA-based

methods in terms of the discrimination power between

classes C, D, and E.

It is also worth noting the main idea of this work is to

show the importance in considering distinct neighbor-

hood information when dealing with metaheuristic

techniques. The proposed approaches were validated in

the context of feature selection purposes concerning the

task of epileptic identification by means of EEG signals.

Although state-of-the-art results were not achieved,

BMOA approaches seemed to be very much suitable to

the problem, as well as they can also be applied to

different other applications.

Acknowledgements LAMP and JPP are grateful to FAPESP Grants

#2011/14094-1, #2009/16206-1, and #2014/16250-9, respectively,

and also CNPq Grants #303182/2011-3, #470571/2013-6, and

#306166/2014-3. The ALVC and CAML also acknowledge the

sponsorship from CNPq via Grants #475406/2010-9, #304603/2012-

0, 308816/2012-9, and #303182/2011-3. VHCA acknowledges CNPq

for the Grants #470501/2013-8 and #301928/2014-2.

Compliance with ethical standards

Conflicts of interest The authors declare no conflict of interest.

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	Automatic identification of epileptic EEG signals through binary magnetic optimization algorithms
	Abstract
	Introduction
	Magnetic optimization algorithm
	Binary MOA
	Improving BMOA

	Feature selection methodology
	Dataset description
	Experimental design
	Results and discussion
	Concluding remarks
	Acknowledgements
	References