Fractal dimension undirected correlation graph-based support vector machine model for identification of focal and non-focal electroencephalography signals

Biomedical Signal Processing and Control 54 (2019) 101611

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Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc

Fractal dimension undirected correlation graph-based support vector machine model for identification of focal and non-focal electroencephalography signals Mohammed Diykh a,c , Shahab Abdulla b,∗ , Khalid Saleh d , Ravinesh C. Deo a a

School of Agricultural, Computational and Environmental Sciences, University of Southern Queensland, Australia Open Access College, University of Southern Queensland, Australia c University of Thi-Qar, College of Education for Pure Science, Iraq d School of Mechanical and Electrical Engineering, University of Southern Queensland, Australia b

a r t i c l e

i n f o

Article history: Received 30 October 2018 Received in revised form 12 June 2019 Accepted 11 July 2019 Available online 1 August 2019 Keywords: Fractal dimension Correlation graphs Focal EEG signals Non-focal EEG signals SCA-SVM

a b s t r a c t Recognition of focal (FC) and non-focal (NFC) Electroencephalography (EEG) signals is crucial for clinical diagnosis used to localise and aid in medical treatment of the affected region in the human brain. Developing an artificial intelligence system that can adequately identify these affected regions can support the clinical diagnosis of brain disease. In this study, we develop a new model called a fractal dimension (FD) of the undirected graph (NG) based on a sine cosine driven support vector machine (FD-NG model utilising the SCA-SVM) algorithm for identifying the focal and non-focal EEG signals. Each EEG signal is partitioned into its respective segments and each segment is divided into clusters using a sliding window technique. To reduce the dimensionality of each cluster, a set of best features is extracted. Three types of input features are considered: linear features (LF), statistical features (SF), and features based on time domain (TD). These are investigated and extracted from each cluster. As a result, each EEG signal is represented by a series of reduced segments and is then forwarded to the proposed FD-NG based SCA-SVM model. The model considers each segment as a node and a link is built between each pair of nodes based on their degree of similarity. The FD of graphs are used as inputs to the SCA-SVM model to classify the EEG signal into FC and NFC components. The obtained results, which also demonstrates the practicality of the approach, confirm that the proposed model surpasses the performance of existing state-of- the-art techniques. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction Epilepsy, a chronic neurological syndrome, tends to disturb normal patterns in brain activities due to a sudden discharge of the brain neurons. It is a common disorder by which a group of neurons or the cell nerves operate abnormally causing unusual sensations such as a loss of consciousness, limb movements, and muscle spasms [1,2]. According to the World Health Organization, around 50% of the world’s populations is expected to experience some form of epilepsy in their lifetime [3–5], a statistic that is particularly alarming in terms of the overall health of the affected individual. Most of those cases are, however, found to be in devel-

∗ Corresponding author. E-mail addresses: [email protected] (M. Diykh), [email protected] (S. Abdulla), [email protected] (K. Saleh), [email protected] (R.C. Deo). https://doi.org/10.1016/j.bspc.2019.101611 1746-8094/© 2019 Elsevier Ltd. All rights reserved.

oping countries, and about three out of the four people are not able to access any form of required treatment [6]. Generally, seizures are categorised into two types, namely focal and generalised seizures [7,8]The term focal seizure refers to a partial seizure that affects one region or a group of nerves on one side of the brain, while the generalised seizure involves both sides of the brain. Differentiating between the focal generalised seizure is crucial in the treatment of epilepsy patients, mainly for the recommendation of appropriate medications and treatment. Based on a number of clinical studies, the use of medication does not appear to be an adequate or an ideal treatment for blocking seizure signals in the brain as patients are known to become resistant to epileptic agents. However, patients can undergo a surgical procedure to eliminate affected regions of the brain [9]. Detecting epileptogenic areas is a crucial step in pre-surgical assessments that localise the affected areas in the brain and for a better understanding of the pathophysiology of epilepsy [10,11]. Different clinical techniques, such as ictal video mon-

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itoring, electroencephalography (EEG), structural and functional Magnetic resonance imaging, have been established to diagnose epileptogenic zones. Of these techniques, EEG signals play a dominant role in the discovery and detection of particular zones in the impacted brain. However, visually determining the presence and the type of epilepsy in a patient’s EEG recording, especially long EEG recordings, is a tedious task for clinicians. These limitations of the visual inspection could lead to an accurate diagnose and therefore make the process of EEG analysis somewhat subjective. To address these limitations, a fully automatic and even semi-automatic computer detection technology is necessary to provide the right support to medical experts. As a result of this need, enormous efforts have been made to perform automatic analysis of EEG signals, particularly for identifying the abnormalities in patients’ EEG signals. Much of the research literature focused on analysing EEG signals is based on the use of Fourier transform, wavelet transform (WT) and empirical decompositions (EMD) to distinguish between focal and non-focal EEG signals. For example, the study of Sharma et al. [12] aimed to decompose EEG signals into different frequency bands using tuneable-Q wavelet transform. A set of nonlinear features, namely the k-nearest neighbour entropy, fuzzy entropy, permutation entropy, centred correntropy and bispectal entropies, were extracted and investigated for their suitability as nonlinear input features. A least square-support vector machine (LS-SVM) algorithm was also used to classify the extracted features into focal from non-focal EEG signals. Gupta et al. [4] applied a slightly different approach employing a flexible analytic wavelet transform (FAWT) to decompose EEG signals into fifteen different levels. A differencing method was also used to pre-process the EEG signals before applying the FAWT algorithm. A set of entropy features namely, the log entropy, cross correntropy and SURE entropy, were extracted and investigated to identify focal from non-focal EEG signals. The EMD approach has also received a great attention in analysing focal EEG signals. For example, a study by Das et al. [13] used EMD coupled with WT to discriminate between focal and non-focal EEG signals. A set of entropies was extracted including Shannon entropy, log-energy entropy, and Renyi entropy and forwarded to a k-nearest neighbour. Sharma et al. [14] adopted entropy features extracted from wavelet coefficients to classify EEG signals. In this study, the EEG signal was passed through the Butterworth filter followed by a time-frequency localised orthogonal wavelet filter and subsequently a wavelet transform was adopted for EEG signals decomposition where a LS-SVM was utilized to differentiate between focal and non-focal signals. Arunkumar et al. [15] employed entropy features, approximate entropy, sample entropy and Reyni’s entropy, to identify focal and non-focal features from EEG signals. A complex network of electroencephalogram was studied during emotional stimulation by Ahirwal et al. [16]. Correlation strength and degree of each node was investigated. Their result showed that male and female brain responded differently for same type of audio-visual stimulation. Ahirwal et al. [17] designed an emotion recognition system based on EEG signals. Three types of features: time domain, frequency domain and entropy features were investigated and studied in that study to classify EEG signals. More recently, the study of Raghu et al. [18] utilized a multidomains features process to classify focal and non-focal EEG signals, with a neighbourhood component analysis approach used to extract the most significant features. Sriraam et al. [19] designed a classification-based model with multi-features extracting from different domains. Utilising an SVM model to classify the extracted features, a total of 26 features were extracted and then reduced to only 21 features benchmarked by applying the Wilcoxon test criterion. In other study, Bhattacharyya et al. [8], adopted an empirical wavelet transform to analyse the EEG signals where a reconstructed phase plot was considered to extract the desired features from the

signals rhythm. In that study, a LS-SVM was finally employed to classify the extracted features. Graph theory, the focus of this research paper, has also inspired new research work in biomedical signal analysis including brain muddling, and identifying brain disorders [21–27]. These research efforts have suggested that neurons in the human brain are likely to exhibit nonlinear behaviours. As a result, much of the research based on graph theory has been developed to explore the relationship between complex network behaviours and the nature of EEG signals [7,25–27]. Our previously published method [20–23] revealed that EEG signals have nonlinear behaviours and the use of largely linear models to analyse the EEG signal provides promising results compared to their nonlinear counterparts. Consequently, these studies aver that more accurate approach would be to develop a nonlinear model to help in the discovery and analysis of focal and non-focal EEG signals. To provide a new fractal dimension model (FD-NG) employing an undirected correlations graph approach for identifying focal and non-focal EE signals, the novel element of this research paper is the development of a nonlinear model using fractal dimension based on undirected correlation graphs (FD-NG) coupled with a cine cosine support vector machine (SCA-SVM). A primary contribution is that the utility of the fractal dimensions of undirected correlation graphs for this purpose, which are constructed from different types of features, are carefully screened in the modelling process and then finally used to classify the EEG signals into their focal and non-focal signals. To reduce the dimensionality of the EEG signals, particularly for improved computational efficiency, each EEG signal is first segmented into its respective cluster using the same scenario used in our previous study [22], where a sliding window technique was used in the segmentation phase of the model. Following this, different sets of inputs features such as the time domain (TDF), statistical features (SF), and nonlinear features (NLF), are extracted and passed to the developed FD-NG model based on the SCA-SVM algorithm. The obtained results of the proposed methodology are benchmarked with the state of the art models to fully investigate the feasibility of the new approach. The results showed the superiority of the proposed methodology both in terms of the classification FC and the NFC EEG signals. The remainder of the paper is organised as follows: in Section 2, the experimental based EEG data are presented, Section 3 illustrates the proposed methodology, Section 4 presents the simulation results, and in Section 5, the significant findings and limitations of the proposed methodology are argued.

2. The EEG data In this paper, reliable data were sought where the focal and non-focal EEG signals used to evaluate the proposed method were obtained from the Bern-Barcelona database, generated at the University of Bern, within the Department of Neurology [7].The studied dataset (which were of approximately 20 s per record) contained a relatively large volume of intracranial EEG signals and comprised of 3750 pairs of focal signals (FC) and non-focal signals (NFC). Five subjects with pharmaco-resistant temporal lobe epilepsy were involved in the recording of these EEG signals, labelled as X and Y for the FC and NFC datasets respectively. Fig. 1 shows an example of FC and NFC EEG signals. The FC recordings were captured from all of the five subjects using the respective channels, and identified visually by two high qualified neurologists. They were then used to detect the first ictal EEG changes. The NFC, however, were recorded from the channels within neighbourhood of the FC channels while all the other channels were labelled as the FC EEG channels. All EEG recordings

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Fig. 1. Shows an example of FC and NFC EEG signals.

were sampled at a frequency of 512 Hz and each one contained a total of 10,240 samples. In this paper, we have assessed the proposed method using all the 3740 FC signals and 3750 of NFC signals collected. Fig.1 shows an example for the focal and non-focal EEG signals. 3. Methodology Next, a fractal dimension-based undirected graph (FD-NG) model utilising a sine cosine support vector machine SCA-SVR algorithm was designed to identify and discriminate the FC and NFC EEG signals. In the first stage, each EEG signal was divided into segments using a sliding window technique [22]. To reduce the dimensionality of each data segment, each EEG segment was partitioned into various clusters following different sets of input features extracted from each designated cluster. We tested three types of input features: TDF and SF linear and NLF. Each EEG signal, represented by a set of segments, was fed into the proposed FD-ND model coupled with the SCA-SVM algorithm. Based on the proposed methodology, the FD-ND based SCA-SVM model, each EEG signal was mapped into an undirected graph for further analysis of the features. The fractal dimension (FD) of these graphs was then investigated using a box covering method. The fractal graphs’ attributes were utilized as inputs to the SCA-SVM model. The results confirmed that the FD-WD model based SCA-SVM identified FC and NFC EEG signals accurately compared with the previous studies of FC and NFC EEG signal classification. Fig. 2 shows the general framework of FD-ND model based on the SCA-SVM algorithm. The proposed model is executed in accordance with the following steps: 1 Dimensionality reduction: this is a dimensionality reduction stage where each EEG signal is divided into different segments, and each segment is partitioned into its respective clusters after which different sets of input features are extracted from each designated cluster Undirected graph construction (NG): this step intends to transfer each EEG signal represented by a set of segments, into an undirected graph (NG). Each segment is considered as a node in a graph and the similarities among graph nodes are calculated. To determine the connection between the graph nodes, the primary proposition

is that each pair of nodes are linked if the degree of correlation between them satisfies a predefined condition 2 Fractal dimension calculation (FD): After graph construction, the fractal dimension (FD) of the graph is analysed using the box counting method. The fractal dimension features of each graph are calculated and fed into the SCA-SVM algorithm to classify the EEG signals into FC and NFC components. 3.1. EEG signals dimensionality reduction To reduce dimensionality of the EEG signals and eliminate any possible unwanted information passing into the final classification, each EEG signal was partitioned, and different input features were extracted. In this step, we applied the same scenario as that presented in our earlier study [22], segmenting each single EEG signal into respective clusters. The length of the window employed to partition the EEG signals was determined empirically. We then found that a window length of 1 s with an overlapping of 0.5 s presents the optimum modelling strategy outlined as follows: Suppose a given signal X = {x1 , x2 , x3 , x4 , . . ..., xn } had n data points. We firstly, divided the signal X into k segments using the sliding window approach. Each segment was partitioned into m clusters. Three types of features were investigated, extracted from each cluster. The signal X was represented by a series of segments X = {S1 , S2 , S3 , S4 , . . ..., Sn } where each segment was disintegrated into m cluster. The dimensionality of each cluster was reduced by extracting a set of input features. As a result, each segment was represented by a vector of (t ∗ m) features where t was the number of features extracted from each cluster, and m was the number of clusters. Finally, the influence of using different window lengths on the classification results was also investigated. More discussions in regards to this issue are presented in the experimental results. Fig. 3 shows a typical EEG signal being partitioned using the proposed signal segmentation technique. 3.2. Features extraction As EEG signals are nonstationary and have no-specific patterns, we have investigated three sets of input features to identify the most powerful pertinent one to be blended with the FD-WD

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Fig. 2. The methodology schema of the proposed model to identify FC and NFC EEG signals.

Fig. 3. EEG signal segmentation based on the proposed sliding window technique.

coupled SCA-SVM model to identify the FC and NFC EEG signals correctly. To deduce the most influential features representing the EEG signals, a thorough investigation in accordance with the literature was made. Three types of input features, namely time domain, nonlinear, and statistical features, were extracted. The extracted sets were fed into the proposed FD-WD coupled SCA-SVM model. Six input features were adopted from each type and used in this research. The three features sets were the time domain features

(Zero crossing, Shannon entropy, Renyi entropy, Hjorth parameters, Tsallis entropy, integrated EEG), Nonlinear features (Engery operator, Hurst exponent, Lyapunov exponent, phase space, correlation dimension, autoregressive), and Statistical features (median, maximum, minimum, mean, mode, standard deviation) [28–35]. As mentioned previously, each EEG signal was partitioned into a series of segments, with each segment represented as a vector with (t ∗ m) features. The three features sets were used to represent the EEG sig-

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Fig. 4. Correlation graph construction from EEG signals.

nal, and then employed as input into the proposed FD-WD coupled SCA-SVM model.

Fig. 5. An example of how to calculate the fractal dimension of a complex network using the box covering algorithm.

3.3. FD-WD coupled SCA-SVM model

Song et al. [40] to calculate the fractal dimension of a network. To analyse the dimension of a complex network in this study, we were required to deduce the minimum number of boxes, denoted by NB , required by covering the entire network. Each box covered a set of nodes in the complex network where the distances between any pair of nodes i, j in this box were smaller than the box size lB . However, if the distance between two nodes in a network was greater than the box size lB , these two nodes were not included in the same box. Finally, the fractal dimension of the network was defined by the following formula:

3.3.1. Graph construction This study has introduced a simple yet a robust versatile approach to analyse the FC and NFC of EEG signals by adopting the correlation graph analysis [36,37]. Each EEG signal was divided into its respective segments. The dimensionality of each segment was then reduced. A correlation coefficient matrix was calculated for all segments considered, and the correlation coefficient matrix was normalised. An undirected graph was constructed by considering each segment as a node and an edge built between the most similar ones according to the normalised correlation coefficient matrix. As a result, an undirected graph was constructed, and a structural graph was analysed using one of the most powerful fractal algorithms. Suppose a signal X = {x1 , x2 , x3 , x4 , . . ..., xn } contained n data points. Based on the segmentation technique in Section 3.1, the signal X was transformed into segments K =  S1 , S2 , S3 , S4 , . . ..., Sn . For each pair of segments, correlation was calculated as follows:

n

Ci,j =



i=1

n i [S1

[S1 (i) − (S1 )] . [S2 (i) − (S2 )] (i) − (S1 )]

2

 n i

[S2 (i) − (S2 )]

(1) 2

In Eq. (1), the values of Ci,j were restricted between −1 ≤ Ci,j ≤ 1, where, 1 refers to perfect correlation, -1 perfect anti-correlation and 0 no correlation. Then, the values of Ci,j matrix were normalised using the following formula. Di,j =

   1 Ci,j  ≤ ˇ 0 |Ci,j | ≥ ˇ

(2)

As a result, the matrix Di,j was obtained and used to construct an undirected graph G=(N,V), where N=(1,2,. . ., n) was the number of nodes that represented the total number of segments in X, V=(1,2,. . .m) was the total number of links connecting graph nodes between each other based on the Di,j conditions. Fig. 4 shows an example of an EEG signal being mapped into an undirected graph. 3.3.2. Analysis fractal dimension of graph based on box-covering algorithm We adopted previous approaches including those of Bunde et al. [38], and Newman et al. [39] who have defined the box-covering method of a complex network. This approach was later used by

Nd (B) =

lnNB lnlB

(3)

The primary steps of the box-covering algorithm of a complex network [39], can be written as follows: • For any graph G with a box size lB , a new a graph is obtained in which the distance between any pair of nodes is less than lB . • Greedy algorithm is chosen to deduce the minimum number of colours to colour graph nodes, marking each node with different colour. The colour of each node must be different from its nearest neighbour’s colour • Assign one colour for each box in graph G, and then the value of NB is equal to the different colours. Several box covering algorithms were studied and their results were investigated. We noticed that complex networks based on greedy algorithm generate different fractal dimensions for FC and NFC EEG signals. This makes identifying these EEG signals more accurate than using other graphs attributes. Fig. 5 illustrates an example of calculating the fractal dimension of a network. First,  graph G was constructed from graph G using a box size lB = 3 by which any two nodes in the graph were connected if the distance between them was satisfied the condition in Eq.(4). The greedy algorithm was used to determine the box covering in G dist i,j < lB

(4)

3.4. SVM and parameters optimization using SCA In this work, a SVM classifier was used to classify EEG data into focal and non-focal signals. The SVM classifier is a binary classifier that aims to categorise data belonging to two groups into two different classes by finding the best separation hyper-plane between those two groups.

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Suppose there was a learning dataset X = (xi , yi ) where xi ∈ R represents the input dataset and yi ∈ [1, −1] refers to the corresponding outputs classes for xi = 1, 2, 3, . . .., N . This indicates that if the input value xi belonged to a specific class, it is assigned value −1 otherwise 1. To separate the input data X into two classes, a functional relationship f (x) must be found between the input data xi and the ouput value yi . The functional relationship is defined as f (x) =< w, x > +b

(5)

where w and b are the weight and constant coefficients. As the input learning data X can be nonlinear, a nonlinear function was defined to simplify a nonlinear problem into a linear problem with Eq. (1) is updated as follows: f (x) =< w, ˚(x) > +b

(6)

The values of w were minimized to avoid the over-fitting problem and to make the function f (x) as flat as possible to fit the training data. In some cases, the optimization problem was not satisfied because of an overlapping between the training data belonging to two classes. To solve this problem, two slack variables i and i∗ were defined. Then, the convex optimization problem was formulated as minimize 0.5 ∗ abslot(w)2 + C

m 

i + i∗

(7)

i=1

subject to yi (w. ˚ (x) + b) ≥ 1 − i

(8) ∗

Where C is a regularisation parameter, and i ,  i refer to the differences between the estimated value and targeted value. Choosing C value plays an important role in the classification results. A SVM minimises | |w| | to maximise the margin. To solve the minimization problem, a lagrange multiplier method was employed. Let K = {k1 , k2 , k3 . . ..kn } be a set of lagrange multipliers, the optimisation problem is formulated as R (K) =

i=K

Subjectto

i=1

i=k

kn − 0.5

i=k i=1

i=1

kn kj yi yj (x, xi )

kn kj = 0

(9) (10)

Several kernel functions were used with a SVM including Gaussian radial basis function, linear and polynomial functions. Based on the literature, Gaussian radial basis function (RBF) is superior to other functions due to its ability to solve different problems in data classification. The Gaussian radial basis function is represented by the following formula. k (x, y) = exp

2

||x − y|| 2 2

(11)

Where  is a parameter which controls the complexity of the model, x is the input features vector, and y is the parameter of the kernel function. In this paper, to select the parameters of a SVM carefully, we used Sine cosine algorithm (SCA). Further SCA details are presented in the next section 3.5. Selecting optimal SVM parameters The literature offers several approaches to choosing the optimal parameters of SVM. These methods are divided into trial and error methods using prior knowledge. In this paper, we used the SCA to select the optimal values for each , C and RBF to train a SVM. Based on the SCA algorithm, the optimisation problem begins by proposing a set of initial solutions for these values. The SCA seeks the best solutions and then uses them as a destination point to modify other solutions. The optimisation process is terminated once the number of iterations becomes higher than the default number of

Table 1 Short explanation of the metrics used to evaluate the proposed method. No.

Metric

Formula

No.

Metric

Formula

1 2 3 4

Sen ACC FPR FSCOR

TP TP+FN TP+TN TP+FP+TN+FN

7 8 9 10

Spec PPV FNR MCC

TN TN+FP TP TP+FP

5 6

INFO NLR

11 12

PLR DOR

1 − SP

2TP 2TP+FP+FN

Sen + Spec − 1 FNR Spec

1 − Sen TTP∗TN−FP∗FN √

(TP+FP)(TP+FN)(TN+FP)(TN+FN) Sen FPR PLR+ NLR−

iterations set by the user. To update the solutions positions in the search space, the positions of the current solutions are randomly selected by SCA and then it adjusts them to the old positions as shown in Eq. (7) [42].

    n+1 ⎣   lj =   ljn + r1 cos (r2 ) r3 pnj − ljn  , r4 < 0.5 ⎡

ljn + r1 sin (r2 ) r3 pnj − ljn  , r4 < 0.5

(12)

Where lin is the current solution’s position at nth iterations, and pi is the iteration destination point’s position in the jth The value of r1 in Eq. (8) is used to dictate the next position region and is defined as r1 = b − h

a H

(13)

Where h is the current iteration, H is the maximum number of iterations defined by a user, and b is a constant value. The steps to train a SVM to obtain the best performance are based on the SCA 1 The C-C method is adopted to choose the best embedding dimension 2 The EEG data is divided into the training set and the testing set 3 The values of , C and RBF initially set the iteration variable h to 0 however, the optimisation process is started from step 4 to 6 4 The random solution of search agent and the object function and the best objective value is initialised 5 Update the sin and cosine functions, the destination point position and the objective value 6 Go to step 6 if the number of iterations is reached, otherwise go to step 4 7 Train the SVM model with the obtained values of the , C and RBF parameters. 3.6. Performance evaluation metrics The performance of the proposed model was tested using several metrics: sensitivity (Sen), specificity (Spec), accuracy (ACC), negative predictive value (PPV ), positive predictive value (PPV ), false negative rate (FNR), false positive rate (FPR), f-score (FSCOR), informedness (INFO), negative likelihood ratio (NLR), positive likelihood ratio (PLR), diagnostic odds ratio (DOR), and Mathews correlation coefficients (MCC) [20]. The terminologies of true positive (TP), false negative (FN), true negative (TN), and false positive (FP), derived from the confusion matrix, were used to calculate these metrics. Table 1 presents a short description of the metric’s formulas used in this paper. 4. Experiment results and parameters setup In this study, the FD-NG model based SCA-SVR was designed to classify FC and NFC EEG signals. The proposed model was evaluated and tested with a publicly available dataset. The dimensionality of EEG signals was reduced and three features sets were extracted and were then passed to the FD-NG model based SCA-SVR. The results

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Table 2 Performance evaluation of the FD-WG model based SCA-SVR using different features sets to classify FC and NFC EEG signals. The model whose metrics are boldfaced is the best. Method

Sen

Spec

ACC

PPV

NPV

FNR

FPR

FSCOR

INFO

NLR

PLR

DOR

MCC

FD-WG model based SCA-SVR with TDF FD-WG model based SCA-SVR with SF FD-WG model based SCA-SVR with NLF

0.8902 0.8902 0.9632

0.8604 0.8604 0.9754

0.89 0.94 0.96

0.8521 0.8521 0.932

0.8832 0.8832 0.9421

0.0921 0.0921 0.644

0.1466 0.1466 0.1011

0.8802 0.8802 0.961

0.7863 0.8363 0.9076

0.123 0.123 0.0757

5.771 5.9801 6.8542

51.54 80.54 89.65

0.763 0.812 0.912

Table 3 Classification accuracy of FC and NFC EEG signals based on SCA-SVM. 

C

Accuracy

MSE

0.01 1 5 6 10

0.01 10 20 100 1000

89% 94% 93% 91% 96%

0.1231 0.0345 0.0032 0.0101 0.0001

Table 4 Comparisons among SCA-SVM vs other algorithms.

Fig. 6. Performance evaluation of the proposed method based on The ROC.

obtained from the proposed model were compared with several state of the art techniques. Our experiments and simulations were carried out using Matlab 2017b, on a computer with the following specifications: Intel Core i7, 1.750 GHz CPU and 16 RAM.

Methods

Accuracy

Sensitivity

GA-SVM PSO-SVM ABC-SVM SSo-SVM SCA-SVM

92 91 89 90 96

91 89 84 82 97

The obtained results showed that the ANOVA attained higher F values (classification F = 221.87, p-value<0.05, classification F = 254.12, p-value<0.05, classification F = 295.23, p-value<0.05) for the FD-NG model based SCA-SVR with NLF than other sets. 4.2. SVM optimisation using SCA

4.1. Features selection using FD-NG model based SCA-SVR This experiment investigated the best features set to be transferred into an undirected graph (NG). The extracted sets of features were used to represent EEG data. The behaviours of graphs were analysed using the FD. The FD of graphs were investigated and used to classify and discriminate FC and NFC EEG signals. The FD of graphs were fed to the SCA-SVM. Different metrics were used and calculated, including sensitivity (Sen), specificity (Spec), accuracy (ACC), negative predictive value (NPV ), positive predictive value (PPV ), false negative rate (FNR), false positive rate (FPR), f-score (FSCOR), informedness (INFO), negative likelihood ratio (NLR), positive likelihood ratio (PLR), diagnostic odds ratio (DOR), and Mathews correlation coefficients (MCC), to evaluate the performance of the proposed method with each features set. As mentioned above, three sets of features, time domain (TDF), nonlinear (NLF), and statistical features (SF), were extracted and forwarded to the FD-NG model based SCA-SVR. As shown in Table 2, the proposed model FD-NG model based SCA-SVR achieved higher classification results with the NLF than the other SF and TDF. Furthermore, our findings showed that the FD of graphs exhibited a high discrimination ability between FC and NFC EEG signals when the NLF were used to construct graphs. Receive operating characteristic (ROC) curves and their areas were plotted and used to assess the performance of the proposed model with each set of features. Fig. 6 shows ROC curves of the FD-NG model based SCA-SVR with TDF, SF, NLF. The results demonstrate that, when the NFL is used with the proposed model, it gives a higher classification rate than other sets. Finally, one-way AVOVA was performed to identify the best features test to be used with the proposed model. The classification, specificity, and sensitivity rates of each features set were compared.

To select the most appropriate parameters for the SCA-SVM, extensive experiments were performed. The number of iterations tested varied between 10 and 100, and the number of search agents studied ranged from 10 to 100. The SVM was observed to offer the best classification results when the number of agents and the number of iterations was set to 20 and 10 respectively. Different experiments were designed to test the parameters of the SCA-SVM through which the value of  was set to 0.1, 5, 6 and 10, and C was set to 0.011 10, 20, 100 and 1000. However, the searching range used to identify the best values for C, and  were bounded between 2−10 to 210 . Our findings showed that the SVM offered high classification accuracy and mean square error (MSE) when the RBF kernel parameters  was set to 10 and C was set to 100. Table 3 illustrates the obtained results based on different parameters’ values of the SCA-SVM. The terms’ accuracy and MSE were used for comparisons. To analyse the performance of the SCA in the selection the SVM parameters were compared with other optimisation techniques such as genetic algorithm (GA-SVM), particle swarm optimisation (PSO-SVM), artificial bee colony (ABC- SVM) and social spider optimisation (SSo-SVM). These techniques were tested with the same training and testing datasets. The parameters of these methods were also selected carefully. In this experiment, nonlinear features were extracted and used in the training phase. The extracted features were fed to the FD-NG model based SCA-SVR. At each experiment, a different optimisation technique was used and combined with the SVM to identify the best optimisation algorithm. Table 4 shows the obtained results based on different optimisation methods. The results showed that the SCA-SVM outperformed other techniques in terms of accuracy and sensitivity. As a result, we adopted the SCA to optimise the SVM to obtain the best outcomes from the proposed model.

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Fig. 7. Classification accuracy based on different window lengths.

5. Discussion and limitations In this study, we have investigated the possibility of using the FD of graphs which were constructed from nonlinear features, to classify FC and NFC EEG signals. For this purpose, the dimensionality of EEG signals was reduced using the sliding window method. We also adopted the window length of 1 s with an overlapping of 0.5 s. Three types of features were extracted from EEG signals and then mapped into undirected graphs. The SCA-SVM was used to classify the FD attributes of graphs into FC and NFC EEG signals. To choose the best window length, a thorough investigation was made in which different window length were tested. Fig. 7 shows classification accuracy of FC and NFC EEG signals based on different window lengths. In this experiment, the nonlinear features were adopted and the SCA-SVM was used for the classification purpose. Window lengths of 0.5, 1, 1.5 2, 2.5 and 3 s were tested to determine the best length window. From the obtained results, it can be noticed that the window length of 1 s with an overlapping 0.5 s achieved a higher discrimination and accuracy rate compared with other window lengths. As mentioned in Section 3.2, the box counting method was used to calculate the FD of graphs. Our best findings indicate the best classification results were obtained when the nonlinear features were used in graph construction. It found that the FD of graphs exhibited different values for FC and NFC signals indicating that the proposed model was able to accurately reflect the difference between the FC and NFC EEG signals. Fig. 8 shows the FD vales of graphs for FC and NFC EEG signals. From Fig. 8 it can be seen that the graphs generated vary in term of their FD values. One of noteworthy findings is that the generated values of the FD were very different between FC and NFC EEG signals. Different fractal dimension algorithms were investigated, and their results were compared with those from the greedy algorithm. The Compact-Box-Burning (CBB) algorithm, Maximum-ExcludedMass-Burning (MEMB) algorithm and Random Bunning Algorithm (RBA) were investigated and used to study the FD of graphs. The extracted FD of each algorithm was fed to the SCA-SVM. It was noticed that graphs’ structural behaviours with the greedy algorithm reflected a higher discrimination ability to separate FC from NFC EEG signals than the other algorithms. However, the preference of the proposed model showed slightly similar results to the CBB and MEMB algorithms, while with the RBA, performance was degraded. Fig. 9 shows the accuracy of the FD-NG model based SCA-SVR for FC and NFC EEG signals classification using different fractal dimension algorithms.

Fig. 8. FD values for FC and NFC EEG signals.

To assess the proposed model, we have compared the model with some of the other well-known methods that have been developed to identify FC and NCF EEG signals. Table 4 presents comparisons between the proposed model with other existing approaches which were implemented with the same dataset used in this paper. The methods in Table 5 were sorted in ascending order based on accuracy achieved. Three factors were considered in the comparison: number of signal pairs, accuracy and features used to represent EEG signals. Sharma et al. [43] classified FC and NFC EEG signals based on Empirical mode decomposition. They achieved an average accuracy of 87% using 50 pairs of EEG signals. The accuracy of the proposed method is 9.5% higher than Sharma et al. [41] although our proposed method was implemented with the entire dataset consisting of 750 pairs of EEG signals. Recently, Bhattacharyya et al. [8] applied an empirical wavelet transform technique with a reconstructed phase space to analyse FC and NFC EEG signals. It can be noticed that the proposed model achieved a higher classification rate than Bhattacharyya et al. [8]. Sharma et al. [42], classified FC and NFC EEG signals using a time frequency localized orthogonal. Our proposed method surpassed their method by 1.25%. It was evidenced that, among all existing methods, the proposed model achieved the highest accuracy rate. We archived an average accuracy of 96.5% which is considered a significant improvement for the medical field. A 10-cross validation was conducted to validate the performance of the proposed model.

M. Diykh, S. Abdulla, K. Saleh et al. / Biomedical Signal Processing and Control 54 (2019) 101611

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Fig. 9. Performance evaluation of the proposed model based on different FD algorithms. Table 5 Comparisons among the proposed model vs previous studies for automatic classification of FC and NFC EEG signals. Author

Technique

Features

ACC (%)

No. of EEG pairs

Sharma et al. [43] Sharma et al. [12]

Empirical mode decomposition (EMD) EMD

87 85

50 50

Bhattacharyya et al. [8]

Empirical wavelet transform technique with reconstructed phase space Time frequency localized orthogonal Fractal graphs blending with nonlinear features

Entropy Average sample entropy, average variance of instantaneous frequencies Reconstructed phase space plot

82

750

Entropies Fractal dimension of undirected graph

94.25 95.6

750 750

Sharma et al. [44] The proposed model FD-NG model based SCA-SVR

Fig. 10. Performance evaluation using 10-cross validations.

Fig. 10 shows performance evaluation based on 10 cross validation. From the obtained results, we can notice that the performance of the proposed model is stable and there are no high fluctuations in the obtained results among the 10 crosses. Despite the good accuracy obtained, the proposed method has some limitations that provide opportunity for further studies. First, this method was implemented with a relatively small dataset and could therefore be a limitation in terms of being a benchmark to fully validate the proposed method. In addition, the proposed method could be explored further with other EEG signals. As a result, we will attempt to validate the proposed model using a large dataset with the other types of EEG signals. In the Future, we will improve the performance of the proposed model using an ensemble classifier and reduce the number of features used in this paper.

Declaration of Competing Interest Authors declare that there is no conflict of interest in this paper. References [1] D. Cho, B. Min, J. Kim, B. Lee, EEG-based prediction of epileptic seizures using phase synchronization elicited from noise-assisted multivariate empirical mode decomposition, IEEE Trans. Neural Syst. Rehabil. Eng. 25 (2017) 1309–1318. [2] S. Chatterjee, N.R. Choudhury, R. Bose, Detection of epileptic seizure and seizure-free EEG signals employing generalised S-transform, Iet Sci. Meas. Technol. 11 (2017) 847–855. [3] A. Gupta, P. Singh, M. Karlekar, A novel signal modeling approach for classification of seizure and seizure-free EEG signals, IEEE Trans. Neural Syst. Rehabil. Eng. 26 (2018) 925–935.

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