Entropy based features in FAWT framework for automated detection of

Entropy based features in FAWT framework for automated detection of epileptic seizure EEG signals M. Tanveer

R. B. Pachori

N. V. Angami

Discipline of Mathematics Indian Institute of Technology Indore Indore, 453552, India email: [email protected]

Discipline of Electrical Engineering Indian Institute of Technology Indore Indore, 453552, India email: [email protected]

Discipline of Mathematics Indian Institute of Technology Indore Indore, 453552, India email: [email protected]

Abstract—Flexible analytic wavelet transform (FAWT) is suitable for the study of oscillatory signals like electroencephalogram (EEG) signals with versatile features such as shift in-variance, tunable oscillatory properties and flexible time-frequency domain. In this paper, we propose an automated method for the classification of seizure and non-seizure EEG signals using FAWT and entropy-based features such as Stein’s unbiased risk estimator (SURE) entropy, log energy entropy, and Shannon entropy. The obtained features are given as input to robust energybased least squares twin support vector machines (RELS-TSVM) for classification. The proposed method has been implemented on publicly available epilepsy database (Bonn University EEG database) and is comparable with the existing methods with a maximum accuracy of 100% for the classification of seizure and non-seizure EEG signals. Index Terms—Electroencephalogram (EEG); Seizure and nonseizure; Flexible analytic wavelet transform (FAWT); Robust energy-based least squares twin support vector machines (RELSTSVM).

I. I NTRODUCTION Epilepsy is a neurological disorder affecting almost 1% of the world population and can occur in any age group [1]. It happens when the brain neurons undergo uncontrolled electrical impulses in the brain resulting in uncontrolled seizures in the person affected [2]. Electroencephalogram (EEG) is a non-invasive device used to measure the electrical activity of the human brain [3]. EEG is cost efficient and is widely used for the diagnosis of epilepsy. Detection and interpretation of EEG signals perform manually is prone to error and requires experts for interpretation. Hence, automated methods are being developed for reliable and accurate detection of epileptic activity in the EEG signals. For automated detection, the process consists of denoising the raw data, transform the signals to the different domain under study, extraction of features from the transformed signal for discrimination, then fed into classifiers for classification. Initially, EEG signals were studied by Fourier transformation assuming that they were stationary. However, studies show that EEG signals are non-stationary [4] and highly nonlinear [5]. Hence, various time-frequency domain methods have been

proposed for the detection of epileptic seizure in EEG signals. Recent works are focusing on wavelet transforms (WT) for signal processing. Since signals are ephemeral and non stationary, the properties of wavelets make it easier to analyze the signals. WT has good time-frequency concentration and multiresolution analysis capacity makes it a powerful mathematical tool for signal processing. The main advantage of flexible analytical wavelet transform (FAWT) is easy control over parameters like dilation, redundancy and Q-factor unlike in the case of discrete wavelet transform (DWT) [6]. Flexible analytic wavelet transform (FAWT) is also used for studying various bio-medical problems other than EEG signals [7–9] which yielded good results. The crucial task is now to extract features to discriminate the signals. Entropy based features has the ability to identify the complexities present in EEG signals which makes it easier to detect abnormal activities. Hence, the chaotic nature of the EEG signals can be evaluated efficiently using entropy features [10]. Applications of machine learning for classification has been widely used in literature. Least squares support vector machine (LS-SVM) is being used as a classifier for the higher rate of accuracy that has been achieved for the classification of EEG signals [11–13]. Several researchers have proposed methods for the study of EEG signals and the automated detection. Several methods are discussed briefly. Empirical mode decomposition (EMD) is applied for the analysis of EEG signals based on Hilbert transformation [14]. Classification of the epileptic seizure in EEG signals using second-order difference plot of intrinsic mode function (IMF) by artificial neural network (ANN) has been performed [15]. The method of classifying EEG signals based on fractional-order calculus and support vector machine (SVM) with different kernel function has been proposed in [16]. Features from phase space representations (PSRs) of IMFs of EEG signals and employed LS-SVM for classification[17]. A method based on one-dimensional local binary pattern (1D-LBP) features for the classification of seizure and seizure-free EEG signals by nearest neighbour classifier has

been performed in [18]. Empirical wavelet transform (EWT) has been explored for the analysis of multivariate signals with six classifiers namely: random forest (RF), functional tree (FT), C4.5, Bayes-net, Naive-Bayes, and K-nearest neighbours (K-NN) in [19]. EEG signal classification using universum support vector machine [20]. The methods in [6] and [12] proposes study of EEG signals by FAWT with fractal dimension [6] and entropy-based features [12] with LS-SVM classifier. In this paper, our contribution is to use the entropy based features with FAWT to measure the information in the subbands after decomposition. The chosen entropies are log energy entropy, Shannon entropy and Stein’s unbiased risk estimator (SURE) entropy. We use various combination of the entropies viz., Shannon-log energy entropy, log energy- SURE entropy, SURE-Shannon entropy and all the three entropies combined. Another contribution is the application of twin support vector machine (TSVM) [21], least squares twin support vector machine (LSTSVM) [22] and robust energy least squares twin support vector machines (RELS-TSVM) [23] as classifiers for EEG signals. In the recent years, some variants have emerged based on the idea of constructing non-parallel hyperplanes [21–30]. TSVM is one of the powerful classification methods. TSVM seeks two non-parallel proximal hyperplanes such that each hyperplane is closer to one of the two classes and as far as possible from the other one [21]. Experimental results have shown the promising performance over SVM and LS-SVM with lesser training time due to its strong generalization ability. Recently, few studies [22–26], [26–30] have proposed variants of TSVM. LS-TSVM has been proposed by replacing the convex quadratic programming problem (QPP) with convex linear system leading to very fast computational speed [22]. Different energy for each class has been considered in energy LS-TSVM (ELS-TSVM) [25] proposed by Nasiri et al., and can be also applied to unbalanced datasets. To overcome the problems in TSVM, LSTSVM and ELS-TSVM like satisfying only empirical risk-minimization principle and the matrices used in the formulation to be always positive semi-definite, robust ELS-TSVM (RELS-TSVM) algorithm has been proposed by Tanveer et al. [23] in which the margin is maximized with a positive definite matrix formulation. Furthermore, the algorithm for RELS-TSVM does not need any specific optimizer and applies energy parameters to minimize the effect of the noise and outliers which makes the classification not only robust to noise and outliers but also more stable [23]. Hence, this motivated us to explore the performance of FAWT with entropy based features using TSVM, LSTSVM and RELS-TSVM for classification. The results has been compared to some existing methods as well. This paper is divided into four sections: Section I covers the introduction, section II describes the data and methodology briefly, section III contains the results and discussion and section IV concludes the paper.

Fig. 1. Methodology for automated seizure detection with different classifiers.

II. M ETHODOLOGY A. Dataset The EEG database has been taken from Bonn University which is publicly available compiled by Andrzejak et al.[31], [32]. The sets Z, O, N, F, S contain 100 EEG segments with each segment having duration of 23.6 s with 4097 samples, sampled at a sampling rate of 173.61 Hz. The sets Z and O contain EEG recordings of five normal volunteers in a relaxed and awake state with eyes open and eyes closed respectively. The sets N and F are recorded from five patients during seizure free intervals. The EEG signals in dataset N were recorded from the epileptogenic zone while the signals in F were recorded from the opposite hemisphere of the brain. The set S comprises EEG recordings during seizure activity. In this paper, we have combined (Z, O, N, F) as non-seizure group and S as seizure group.

Fig. 2. EEG signals for various subsets [31].

B. FAWT The iterated filter banks of FAWT is constructed by one lowpass channel and two highpass channels, where one of the highpass channel analyzes ‘positive frequencies’ and the other ‘negative frequencies’. In separating the positive and the negative frequencies we obtain Hilbert transform pairs of wavelet bases. The coefficients in all the channels can be set to 0 except one channel of interest, then the wavelet subband signal can be reconstructed individually. Let f (θ) be a polynomial [6], p 1 f (θ) = (1 + cos(θ)) 2 − cos(θ), (1) 2

P  X S = P − # i : |yi | ≤ ε + min(yi2 , ε2 ),

which satisfies the perfect construction condition [33]: |f (θ)|2 + |f (θ − π)|2 = 1, θ ∈ [0, π].

Let H(ω) and G(ω) be the frequency response of the lowpass filter and highpass filters respectively for the underlying perfect reconstruction filter banks. The attributes of the filters can be controlled by the parameters p, q, r and s. The positive constants β and ε and the parameters p, q, r and s should satisfy the below constraints [34]: 1−

r p p − q + βq
π. ≤β≤ , ε≤ q s p+q

where wp =

1−β p π

+ pε , ws =

1−β ε r π+ r,

w1 =

|w| < wp , wp ≤ w ≤ ws ,

(4)

−ws ≤ w ≤ −wp , |w| > ws ,

π q.

p qr π,

w2 =

π r

− rε , w3 =

π r

+ rε .

The parameters p, q, r, s and β with desired Q-factor Q, dilation factor d and redundancy factor R give flexibility to design wavelets where the accurate extraction of the impulse intervals can be extracted. The factors Q, d and R are related as given [34], Q≈

P X

yi2 log2 yi2 ,

(9)

i=1

where yi is the ith sample of the signal, ε > 0 and P represents the length of the signal. Entropies are calculated for each of the sub-bands using the MATLAB command wentropy. D. Classification

√   0)  , w0 ≤ w ≤ w1 , rsf (π−w+w  (w −w ) 1 0   √rs, w1 < w < w 2 , G(ω) = √ (5)  (w+w2 )  rsf , w ≤ w ≤ w ,  2 3 (w −w )  3 2   0, w ∈ [−π, w0 ] ∪ [w3 , π], where w0 =

H=−

(3)

H(ω) and G(ω) can be mathematically defined as[33]: √   pq,    √pqf (w−wp ) , (ws −wp ) H(ω) = √  (π−w+w  p)  pqf ,  (w −w )  s p   0,

2−β r/s β , d ≈ p/q, β ≤ 1, R ≈ , R> . (6) β 1−d 1−d
p−q+βq

1 For the parameter selection we selected ε = 32 π, p+q p = 3, q = 4, r = 1 and s = 2 with decomposition up to J = 15th level [12], entropies for each of the sub-bands were obtained.

We use TSVM [21], LSTSVM [22] and RELS-TSVM [23] for the classification of seizure and non-seizure signals. The mathematical formulation of RELS-TSVM [23] has been discussed below. For binary classification, let matrix X ∈ Rm1 ×n denote the data points containing class +1, and Y ∈ Rm2 ×n denote the matrix containing the data points of class -1. 1) Linear RELS-TSVM: The linear RELS-TSVM involves the following pair of minimization problems [23]:

  2

a1 t a3 1 2

µ+ kXµ+ + eb+ k + ξ1 ξ1 + min

µ+ ,b+ ,ξ1 2 2 2 b+ s.t. − (Y µ+ + eb+ ) + ξ1 = E1 (10) and min

µ− ,b− ,ξ2

  2

a2 a4 1 2

µ− kY µ− + eb− k + ξ2t ξ2 +

2 2 2 b−

s.t. (Xµ− + eb− ) + ξ2 = E2 , (11) where e is a vector of ones of appropriate dimensions. a1 , a2 , a3 , and a4 are positive parameters, E1 and E2 are energy parameters of the hyperplanes. µ+ ∈ Rn , µ− ∈ Rn , b+ ∈ R and b− ∈ R. The solution of the QPP (10) is obtained as follows: −1

z1 = −(a1 B t B + At A + a3 I) a1 B t E1 , (12)   µ where z1 = + , A = [X e] and B = [Y e]. b+ Similarly, the solution of QPP (11) is obtained as follows: −1

C. Entropy based features extraction Log energy entropy evaluates the degree of complexities in EEG signals [35–37]. Stein’s unbiased risk estimate (SURE) is a measuring tool for quantifying properties related to information for an accurate representation of the signal [36– 38]. Shannon entropy measures uncertain information in EEG signal [39]. The mathematical formula for above mentioned entropies are given respectively as follows: L=

P X i=1

z2 = (a2 At A + B t B + a4 I) a2 At E2 , (13)   µ− where z2 = , A = [X e] and B = [Y e]. The label b− of an unknown data point xi ∈ Rn is assigned to the class i = {+1, −1}, depending on the following decision function:  xi µ+ +eb+  +1 if | xi µ− +eb− | ≤ 1  f (xi ) =   −1 if | xi µ+ +eb+ | > 1 xi µ− +eb−

log(yi2 ),

(8)

i=1

(2)

(7)

where |.| is the absolute value.

2) Nonlinear RELS-TSVM: The following kernel-generated surfaces are considered for the nonlinear case [23]: K(xt , C t )µ+ + b+ = 0 and K(xt , C t )µ− + b− = 0, where C = [X; Y ] and K is a suitably chosen kernel. Like in the linear case, the above two kernel-generated surfaces are obtained through the following two QPPs: min

µ+ ,b+ ,ξ1

1 a1 2 kK(X, C t )µ+ + eb+ k + ξ1t ξ1 2 2

  2 a3 µ+

+ 2 b+

(14)

s.t. − (K(Y, C t )µ+ + eb− ) + ξ1 = E1 and min

µ− ,b− ,ξ2

1 a2 2 kK(Y, C t )µ− + eb− k + ξ2t ξ2 2 2

  2

a4 µ−

+ 2 b−

where m1 ×m and m2 ×m are the sizes of the kernel matrices K(X, C t ) and K(Y, C t ) respectively and m = m1 + m2 . The solution of the QPP (14) is obtained as follows: −1

a1 V t E1 .

(16)

Similarly, the solution of QPP (15) is obtained as follows: −1

z2 = (a2 U t U + V t V + a4 I) a2 U t E2 , (17)     µ µ where z1 = + , z2 = − , V = [K(Y, C t ) e] and U = b+ b− [K(X, C t ) e]. The matrices (a1 V t V + U t U + a3 I) and (a2 U t U + V t V + a4 I) are positive definite, which makes the nonlinear RELSTSVM more robust and stable than that of LSTSVM and ELSTSVM. The following decision function labels an unknown data point xi ∈ Rn to the class i = {+1, −1} accordingly.  K(xi ,C t )µ+ +eb+   +1 if | K(xi ,C t )µ− +eb− | ≤ 1 f (xi ) =

  −1

Sub-band 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

Log energy entropy 10−39

4.98 × 7.78 × 10−06 1.43 × 10−98 1.82 × 10−110 3.91 × 10−122 4.51 × 10−121 43.35 × 10−116 4.20 × 10−120 8.81 × 10−129 5.49 × 10−129 2.44 × 10−113 4.94 × 10−107 1.53 × 10−95 5.68 × 10−70 1.48 × 10−52 1.39 × 10−17 3.38 × 10−126

Shannon entropy 10−80

1.07 × 7.43 × 10−45 6.07 × 10−110 2.51 × 10−120 2.67 × 10−126 4.03 × 10−122 1.43 × 10−117 3.16 × 10−120 3.86 × 10−128 1.41 × 10−128 3.25 × 10−115 4.82 × 10−109 1.71 × 10−99 1.16 × 10−74 1.33 × 10−57 2.04 × 10−32 2.63 × 10−128

SURE entropy 8.91 × 10−27 0.034845084 2.46 × 10−88 5.36 × 10−99 1.17 × 10−114 4.56 × 10−116 2.12 × 10−113 5.15 × 10−118 3.22 × 10−129 3.04 × 10−127 2.65 × 10−109 1.57 × 10−104 4.88 × 10−89 1.51 × 10−62 2.01 × 10−47 5.11 × 10−10 4.03 × 10−110

(15)

s.t. (K(X, C t )µ− + eb− ) + ξ2 = E2 ,

z1 = −(a1 V t V + U t U + a3 I)

TABLE I p- VALUES FOR SUB - BANDS

t

K(xi ,C )µ+ +eb+ if | K(x |>1 t i ,C )µ− +eb−

where |.| is the absolute value. III. R ESULTS AND D ISCUSSION After obtaining the sub-bands, Kruskal-Wallis (K-W) test [40] is applied to test the significance of each of the subbands, testing non-seizure sub-bands against seizure sub-bands with p-value ≤ 0.05. Table I shows that the p-values of the entropies are less than p = 0.05 which is the level of significance. Hence, all the sub-bands of the entropies are considered for feeding into the classifier. The choices of kernel function and the value of its parameter play a crucial role in order to get a better classification performance. We optimized

the values of parameters by the grid search method [41]. The Gaussian kernel parameter ρ is selected from the sets {2j |j = −10, −9, ..., 10}. The values of the parameters (a1 , a2 , a3 , a4 ) and (E1 , E2 ) for both the linear and as well as nonlinear kernel were selected from the sets {2j | = −5, −3, −1, 0, 1, 3, 5} and {0.6, 0.7, 0.8, 0.9, 1} respectively. The computational cost of the parameter selection is reduced by setting a1 = a2 and a3 = a4 [23]. The ten-fold cross-validation methodology has been used for classification accuracy of each features [42]. We choose 70% of the data for training and rest 30% for testing. Several works are done in this area for different subsets of EEG signals. Table II contains some of the works done on seizure versus non-seizure classification of EEG signals. In [4], the ability of time-frequency domain has been explored on EEG signals containing epileptic seizures classified by artificial neural network (ANN) provided an accuracy of 97.73%. In [43], line length features were extracted by discrete wavelet transform (DWT) and classified by multi-layer perceptron neural network (MLPNN) given an accuracy of 97.77%. Orhan et al. [44] used a MLPNN-based classification model to classify EEG signals by DWT and clustering approach with classification accuracy of 99.60%. In [45], discrimination of the EEG signals were done both by SVM and probabilistic neural network (PNN), signals decomposed by DWT with energy standard and entropy features which gave an accuracy of 95.44%. In [46], permutation entropy with SVM gave an accuracy of 88.10%. In [47], decomposition of EEG signals were done by DWT with fuzzy approximate entropy and classified by SVM with accuracy 97.38%. In [48], MLPNN is fed by the coefficients of rational discrete short-time Fourier transform (DSTFT) giving an accuracy of 98.10%. In [49], dual tree complex wavelet transform (DTCWT) was used with complex-valued neural network (CVANN) classifier with an accuracy 99.15%. In [39], DTCWT with features energy, standard deviation (std), root-mean-square (rms), Shannon

TABLE II C OMPARISON OF EXISTING METHODS FOR CLASSIFICATION OF SEIZURE AND NON - SEIZURE EEG SIGNALS Works

Year

Method

Classifier

Accuracy (%)

Tzallas et al.[4] Guo et al.[43] Orhan et al.[44]

2007 2010 2011

ANN MLPNN MLPNN

97.73 97.77 99.60

Gandhi et al.[45]

2011

SVM and PNN

95.44

Nicolaou et al.[46] Bajaj and Pachori [13] Kumar et al.[47]

2012 2012 2014

SVM LS-SVM SVM

86.10 99.50-100 97.38

Samiee et al.[48] Peker et al. [49] Swami et al.[39]

2015 2016 2016

MLPNN CVANN GRNN

98.10 99.15 100

Bhattacharyya et al.[50]

2017

SVM

99

Sharma et al.[6] Tiwari et. al [51] Our work

2017 2017 2018

Time-frequency analysis Line length EEG classification-K means clustering DWT and energy- and entropy features Permutation entropy EMD DWT-fuzzy approximate entropy Rational DSTFT DTCWT DTCWT and energy, std, rms Shannon entropy features TQWT-based multi-scale K-NN entropy ATFFWT and FD features LBP and histogram feature FAWT with log energy entropy

LS-SVM SVM RELS-TSVM

99.20 99.31 100

IV. C ONCLUSION entropy are applied through general regression neural network (GRNN) yielding an accuracy of 100%. In [50], signal decomposition based on tunable-Q wavelet transform (TQWT) and using multi-scale K-NN entropy features over conventional K-NN entropy features yielded 99% accuracy for classifying seizure and non-seizure EEG signals by SVM with radial basis function (RBF) kernel. Recent work [6], analytic timefrequency flexible wavelet transform (ATFFWT) with fractal dimension (FD) features with least squares support vector machine (LSSVM) gave an accuracy of 99.20%. In [51], local binary pattern (LBP) with histogram features fed to SVM gave an accuracy of 99.31%. In our present work, EEG signals decomposed by FAWT with combined entropies (Log energy entropy, Shannon entropy and SURE entropy) fed into TSVM, LSTSVM, RELS-TSVM gave an maximum accuracy of 100%. Table III shows the accuracy of the entropies and their combination by TSVM, LSTSVM and RELS-TSVM classifier. TABLE III ACCURACY OBTAINED FROM DIFFERENT CLASSIFIERS

The experimental results presented in this paper demonstrates that FAWT is a useful tool to decompose EEG signals and RELS-TSVM as classification model with Gaussian kernel gives a maximum accuracy of 100%. The accuracy may differ when applied to restricted subsets of the EEG signals. The proposed method has been studied on relatively smaller size of EEG dataset. In future, the suggested method should be studied on large EEG dataset before applying it for clinical purpose. The future direction of this paper may involve the application of the proposed method with other features and other classifiers. An optimization problem can be formulated to find the optimal values of the parameters of the filter bank of FAWT and the level of decomposition. The results achieved in this work motivates to investigate the proposed method in this paper for study and classification of other bio-medical signals. ACKNOWLEDGMENT This work was supported by Council of Scientific & Industrial Research (CSIR) under Extra Mural Research (EMR) Scheme grant no. 22(0751)/17/EMR-II. R EFERENCES

Entropy based features

TSVM

LS-TSVM

RELS-TSVM

Log energy entropy Shannon entropy SURE entropy Combined Shannon-log energy entropy Log energy-SURE entropy SURE-Shannon entropy

100 98.75 96.25 99.58 99.58 97.5 98.33

100 98.75 98.33 96.25 95.83 99.58 99.58

100 97.92 98.75 100 99.17 99.58 99.17

[1] Epilepsy. World Health Organization. [Online]. Available: http://www.who.int/mental health/neurology/epilepsy/en/index.html [2] Epilepsy 2017. World Health Organization. [Online]. Available: www.who.int/mediacentre/factsheets/fs999/en/ [3] A. Ulate-Campos, F. Coughlin, M. Ga´ınza-Lein, I. S. Fern´andez, P. L. Pearl, and T. Loddenkemper, “Automated seizure detection systems and their effectiveness for each type of seizure,” Seizure, vol. 40, pp. 88–101, 2016. [4] A. T. Tzallas, M. G. Tsipouras, and D. I. Fotiadis, “Automatic seizure detection based on time-frequency analysis and artificial neural networks,” Computal. Intell. Neurosci., vol. 2007, 2007.

[5] H. Ocak, “Automatic detection of epileptic seizures in EEG signals using discrete wavelet transform and approximate entropy,” Expert Syst. Appl., vol. 36, pp. 2027–2036, 2009. [6] M. Sharma, R. B. Pachori, and U. R. Acharya, “A new approach to characterize epileptic seizures using analytic time-frequency flexible wavelet transform and fractal dimension,” Pattern Recogn. Lett., vol. 94, pp. 172–179, 2017. [7] M. Kumar, R. B. Pachori, and U. R. Acharya, “An efficient automated technique for CAD diagnosis using flexible analytic wavelet transform and entropy features extracted from HRV signals,” Expert Syst. Appl., vol. 63, pp. 165–172, 2016. [8] M. Kumar and R. B. Pachori and U. R. Acharya, “Characterization of coronary artery disease using flexible analytic wavelet transform applied on ECG signals,” Biomed. Signal Process. and Control, vol. 31, pp. 301– 308, 2017. [9] M. Kumar, R. B. Pachori, and U. R. Acharya, “Use of accumulated entropies for automated detection of congestive heart failure in flexible analytic wavelet transform framework based on short-term HRV signals,” Entropy, vol. 19, no. 3 (92), 2017. [10] D. S. Lemons, A student’s guide to entropy. Cambridge University Press, 2013. [11] M. Sharma and R. B. Pachori, “A novel approach to detect epileptic seizures using a combination of tunable-Q wavelet transform and fractal dimension,” J. Mech. Med. Biol., vol. 17, no. 7, 1740003 (20 pages), 2017. [12] V. Gupta, T. Priya, A. K. Yadav, R. B. Pachori, and U. Acharya, “Automated detection of focal EEG signals using features extracted from flexible analytic wavelet transform,” Pattern Recogn. Lett., vol. 94, pp. 180–188, 2017. [13] V. Bajaj and R. B. Pachori, “Classification of seizure and non-seizure EEG signals using empirical mode decomposition,” IEEE Trans. Inf. Technol. Biomed., vol. 16, no. 6, p. 1135–1142, 2012. [14] R. B. Pachori and V. Bajaj, “Analysis of normal and epileptic seizure EEG signals using empirical mode decomposition,” Computer Methods and Programs in Biomed., vol. 104, no. 3, pp. 373–381, 2011. [15] R. B. Pachori and S. Patidar, “Epileptic seizure classification in EEG signals using second-order difference plot of intrinsic mode functions,” Computer Methods and Programs in Biomed., vol. 113, no. 2, pp. 494– 502, 2014. [16] V. Joshi, R. B. Pachori, and A. Vijesh, “Classification of ictal and seizure-free for EEG signals using fractional linear prediction,” Biomed. Signal Process. and Control, vol. 9, pp. 1–5, 2014. [17] R. Sharma and R. B. Pachori, “Classification of epileptic seizures in EEG signals based on phase space representation of intrinsic mode function,” Expert Syst. Appl., vol. 42, no. 3, pp. 1106–1117, 2015. [18] T. S. Kumar, V. Kanhangad, and R. B. Pachori, “Classification of seizure and seizure-free EEG signals using local binary patterns,” Biomed. Signal Process. and Control, vol. 15, pp. 33–40, 2015. [19] A. Bhattacharyya and R. B. Pachori, “A multivariate approach for patient-specific EEG seizure detection using empirical wavelet transform,” IEEE Trans. on Biomed. Eng., vol. 64, no. 9, pp. 2003–2015, 2017. [20] B. Richhariya and M. Tanveer, “EEG signal classification using universum support vector machine,” Expert Syst. Appl., vol. 106, pp. 169–182, 2018. [21] Jayadeva, R. Khemchandani, and S. Chandra, “Twin support vector machines for pattern classification,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 5, pp. 905–910, 2007. [22] M. A. Kumar and M. Gopal, “Least squares twin support vector machines for pattern classification,” Expert Syst. Appl., vol. 36, no. 4, pp. 7535–7543, 2009. [23] M. Tanveer, M. A. Khan, and S.-S. Ho, “Robust energy-based least squares twin support vector machines,” Appl. Intell., vol. 45, no. 1, pp. 174–186, 2016. [24] M. Tanveer, “Robust and sparse linear programming twin support vector machines,” Cogn. Comput., vol. 7, pp. 137–149, 2015. [25] J. A. Nasiri, N. M. Charkari, and K. Mozafari, “Energy-based model for least squares twin support machines for human action recognition,” Signal Process., vol. 104, pp. 248–257, 2014. [26] M. Tanveer, “Newton method for implicit lagrangian twin support vector machines,” International Journal of Machine Learning and Cybernetics, vol. 6, no. 6, pp. 1029–1040, 2015.

[27] Y. H. Shao, C. H. Zhang, X. B. Wang, and N. Y. Deng, “Improvements on twin support vector machine for classification,” IEEE Trans. Neural Netw., vol. 22, no. 6, pp. 962–968, 2011. [28] Y. Tian, Z. Qi, X. Ju, Y. Shi, and X. Liu, “Nonparallel support vector machines for pattern classification,” IEEE Trans. Cybern., vol. 44, no. 7, pp. 1067–1079, 2014. [29] M. Tanveer and K. Shubham, “Smooth twin support vector machines via unconstrained convex minimization,” Filomat, vol. 31, no. 8, pp. 2195–2210, 2017. [30] M. Tanveer, “Application of smoothing techniques for linear programming twin support vector machines,” Knowledge Info. Syst., vol. 45, no. 1, pp. 191–214, 2015. [31] R. G. Andrzejak, K. Lehnertz, C. Rieke, F. Mormann, P. David, and C. E. Elger, “Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: dependence on recording region and brain state,” Phys. Rev. E., vol. 64, no. 6 (Part 1) 061907, 2001. [32] EEG time series data. University of Bonn Germany. [Online]. Available: http://epileptologie-bonn.de/cmsfront content.php?idcat=193 [33] I. Bayram, “An analytic wavelet transform with flexible analytical timefrequency covering,” IEEE Trans. Signal Process., vol. 61, no. 5, pp. 1131–1142, 2013. [34] C. Zhang, B. Li, B. Chen, H. Cao, Y. Zi, and Z. He, “Weak fault signature extraction of rotating machinery using flexible analytic wavelet transform,” Mech. Syst. Signal Process., vol. 64, pp. 162–187, 2015. [35] A. Sharma, M. Amarnath, and P. K. Kankar, “Feature extraction and fault severity classification in ball bearings,” J. Vib. Control, vol. 22, no. 1, pp. 176–192, 2016. [36] D. W. Aha, D. Kibler, and M. K. Albert, “Instance-based learning algorithms,” Mach. Learn., vol. 6, no. 1, pp. 37–66, 1991. [37] R. G. Andrzejak, K. Schindler, and C. Rummel, “Nonrandomness, nonlinear dependence, and nonstationary of electroencephalographic recordings from epilepsy patients,” Phys. Rev. E., vol. 86 (046206), 2012. [38] D. Anci, “An expert system for speaker identification using adaptive wavelet SURE entropy,” Expert Syst. Appl., vol. 36, no. 3 (Part 2), pp. 6295–6300, 2009. [39] P. Swami, T. K. Gandhi, B. K. Panigrahi, M. Tripathi, and S. Anand, “A novel robust diagnostic model to detect seizures in electroencephalography,” Expert Syst. Appl., vol. 56, pp. 116–130, 2016. [40] P. McKight and J. Najab, Kruskal-Wallis test. Corsini Encycl. Psychol., 2010. [41] C. W. Hsu and C. J. Lin, “A comparison of methods of multi-class support vector machines,” IEEE Trans. Neural Netw., vol. 13, no. 2, pp. 415–425, 2002. [42] R. O. Duda, P. R. Hart, and D. G. Stork, Pattern classification, 2nd ed. New York: Wiley, 2012. [43] L. Guo, D. Rivero, J. Dorado, J. R. Rabunal, and A. Pazos, “Automatic epileptic seizure detection in EEGs based on line length feature and artificial neural networks,” J. Neurosci. Methods, vol. 191, no. 1, pp. 101–109, 2010. [44] U. Orhan, M. Hekim, and M. Ozer, “EEG signals classification using the K-means clustering and a multilayer perceptron neural network model,” Expert Syst. Appl., vol. 38, no. 10, pp. 13 475–13 481, 2011. [45] T. Gandhi, B. K. Panigrahi, and S. Anand, “A comparative study of wavelet families for EEG signal classification,” Neurocomputing, vol. 74, no. 17, pp. 3051–3057, 2011. [46] N. Nicolaou and J. Georgiou, “Detection of epileptic electroencephalogram based on permutation entropy and support vector machine,” Expert Syst. Appl., vol. 39, no. 1, pp. 209–219, 2012. [47] Y. Kumar, M. L. Dewal, and R. Anand, “Epileptic seizure detection using DWT based fuzzy approximate entropy and support vector machine,” Neurocomputing, vol. 133, pp. 271–279, 2014. [48] K. Samiee, P. Kov´acs, and M. Gabbouj, “Epileptic seizure classification of EEG time-series using rational discrete short-time fourier transform,” IEEE Trans. Biomed. Eng., vol. 62, no. 2, pp. 541–552, 2015. [49] M. Peker, B. Sen, and C. Delen, “A novel method for automated diagnosis of epilepsy using complex-valued classifiers,” IEEE J. Biomed. Health Inform., vol. 20, no. 1, pp. 108–118, 2016. [50] A. Bhattacharyya, R. B. Pachori, A. Upadhyay, and U. R. Acharya, “Tunable-Q wavelet transform based multiscale entropy measure for automated classification of epileptic EEG signals,” Appl. Sci., vol. 7, no. 4, 385 (18 pages), 2017. [51] A. K. Tiwari, R. B. Pachori, V. Kanhangad, and B. K. Panigrahi, “Automated diagnosis of epilepsy using key-point-based local binary

pattern of EEG signals,” IEEE J. Biomed. and Health Inform., vol. 21, no. 4, pp. 888–896, 2017.