Epilepsy and seizure characterisation by multifractal analysis of EEG subbands

Biomedical Signal Processing and Control 41 (2018) 264–270

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Epilepsy and seizure characterisation by multifractal analysis of EEG subbands Debdeep Sikdar a , Rinku Roy b , Manjunatha Mahadevappa a,∗ a b

School of Medical Science and Technology, Indian Institute of Technology Kharagpur, India Advanced Technology Development Centre, Indian Institute of Technology Kharagpur, India

a r t i c l e

i n f o

Article history: Received 3 August 2017 Received in revised form 19 December 2017 Accepted 21 December 2017 Keywords: EEG Epilepsy MFDFA EEG analysis Epilepsy detection Multifractal

a b s t r a c t Electroencephalography (EEG) is often used for detection of epilepsy and seizure. To capture chaotic nature and abrupt changes, considering the nonlinear as well as nonstationary behaviour of EEG, a novel nonlinear approach of MultiFractal Detrended Fluctuation Analysis (MFDFA) has been proposed in this paper to address the multifractal behaviour of healthy (Group B), interictal (Group D) and ictal (Group E) patterns. Following wavelet based decomposition of EEG into its frequency subbands, multifracatal formalism has been applied to extract four features, namely, spectrum width (˛), spectrum peak (˛0 ), spectrum skewness (B) and Hurst’s exponent (H). The effectiveness of the parameters has been also tested through statistical significance across the subbands. It has been found that no parameters in alpha subband exhibit significant differences across all the Groups, whereas, all the parameters for band-limited EEG significantly distinguish the Groups. However, at least one Group was found to be significantly isolated from the parameters across all the subbands. Furthermore, support vector machine (SVM) has been trained to classify the Groups with the multifractal features for different EEG subbands. An accuracy of 99.6% has been observed for the band limited EEG. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction Epilepsy is a short electrical spikes generated in the brain resulting in convulsions, muscle spasms, emotional and behavioural discrepancies and loss of consciousness [1]. It affects people of all ages spreading through 1% of children and 0.5% of adults [2], making it as fourth most common neurological disorder. Since childhood, it hampers education, employment and socialism by diminishing sense of self-worth. Primary diagnosis of epilepsy bases on the experiences from an eyewitness. For faster and accurate diagnosis of the types of epilepsy, EEG is one of the most useful analysis method [2]. Usually, by visual inspection of EEG recording, epilepsy can be detected. But it is a very time consuming and tedious work and moreover, chances of misreading are very high. So, an automated detection method is very essential for accurate and faster detection of epilepsy. In spite of several researches, there still exist several difficulties in the detection of epilepsy. Low accuracy, considerable false alarms and missed detections are inherent with most of the established methods [3]. Reliable epileptic data are also scarcely available to be utilised to test a developed algorithm.

∗ Corresponding author. E-mail address: [email protected] (M. Mahadevappa). https://doi.org/10.1016/j.bspc.2017.12.006 1746-8094/© 2017 Elsevier Ltd. All rights reserved.

For the detection of epilepsy as well as seizure, several approaches have been evaluated by the researchers. Spatiotemporal-spectral analysis is most sought after for analysis of any EEG. However, inherent nonlinearity in the synaptic interactions across frequency bands in brain and central nervous system [4], encompassed the requirement of nonlinear methodologies to address them [5]. Various nonlinear methodologies were implemented to extract information from EEG signals in different studies [6–8]. Nonlinear dynamics based on chaos has been extensively used in identification of disorders from neuronal activities [9,10]. In detection of epilepsy also, fractal dimension (FD) [11,12], approximate entropy (ApEn) [13,14], largest Lyapunov exponent (LLE) [15,16], correlation dimension (CD) [15,16] and intrinsic mode functions (IMFs) [11] have been explored for their suitability. Adeli et al. [15] have concluded that LLE is low in band limited EEG and alpha subband of epileptic EEG. Similarly, CD is also reduced for beta and gamma subbands of epileptic EEG. In case of ApEn, Bai et al. [17] also observed reduction in value for epilepsy. However, first four IMFs were found to be higher for epilepsy as reported by [11]. Study done by Accardo et al. [12] on usefulness of FD in epilepsy detection, has ambiguity due to strong noise contaminations. EEG is nonstationary in nature and it has large and small fluctuations. In this paper we have explored multifractal behaviour of EEG via multifractal formalisms. Detrended Fluctuation Analy-

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265

Fig. 1. Schematic representation of multifractal spectral parameters.

sis (DFA) [18] has been established as an important tool to obtain monofractal scaling properties of a time series [19]. But, DFA may not provide local extreme large magnitude within time periods of large fluctuations. Due to the presence of multifractality in EEG, FD may not be useful in EEG analysis as used by Accardo et al. An alternative approach of Multifractal Detrended Fluctuation Analysis (MFDFA) has been developed to estimate multifractality [20]. A large dataset has been used consisting three different Groups of EEG signals namely Group B (healthy), Group D (interictal) and Group E (ictal) to explore multifractal features through MFDFA. The EEGs were first decomposed into the five subbands, namely, delta (0–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), beta (12–30 Hz) and gamma (30–60 Hz). Four multifractal parameters spectrum width (˛), spectrum peak (˛0 ), spectrum skewness (B) and Hurst’s exponent (H) were extracted from each subbands of EEG of each Groups and tested for their effectiveness in separability between the Groups through analysis of variance (ANOVA). Furthermore, the significant parameters were tested with Tukey’s honest significant difference (HSD). Finally, fivefold cross validated multiclass oneagainst-one cubic polynomial kernel based SVM was trained for each subbands and band-limited EEG to classify the Groups based on the multifractal features.

band-limited EEG at 0–60 Hz band. For further decomposition into individual EEG subbands, a DWT, based on fourth order daubechies (db4), was used. Major advantages of using wavelet transform include its excellent multiresolution representation encompassing time-frequency localisation and scale-space analysis [22,23]. Moreover, employment of variable window size further enhances feature-extraction from non-stationary signals (e.g. EEG) by frequency based stretching or compressing of the wavelet [15,23]. For faster and efficient computation, dyadic (powers of 2) scales and positions were followed in this study. First level decomposition of band-limited EEG (0–60 Hz) yielded detail coefficients as Gamma (30–60 Hz) and approximate coefficients (0–30 Hz). These approximate coefficients were further decomposed to get higher resolution components as Beta (15–30 Hz) and lower resolution components (0–15 Hz). After similar decomposition of these lower resolution components, Alpha (8–15 Hz) subbands were extracted along with the approximate coefficients (0–8 Hz). These approximate coefficients were decomposed further for high resolution Theta (4–8 Hz) and low resolution Delta (0–4 Hz). So, altogether 4 level decomposition was done.

2. Materials and methods

Wavelet transform analyses a signal at different frequency subbands, with different resolutions by decomposing the signal into a coarse approximation (approximation coefficients, CA) and detail information (detailed coefficient, CD). Repeated filtering of the signal with a pair of low pass and high pass filter divides the signal in frequency domain into two halves. CA can be subdivided again iteratively to get different levels of decomposition.

2.1. Data EEG data for both healthy and epileptic subjects by Dr. Ralph Andrzejak of the Epilepsy Center at the University of Bonn, Germany are used in this study [19]. From the database, three different groups of EEG data were analysed: Group B (healthy subjects), Group D (interictal), and Group E (ictal). In this dataset, Group B data were taken from the five healthy subjects with international 1020 electrode placement system. Group D and Group E data were obtained from interictal and ictal segments of epilepsy patients. The interictal segments were recorded during seizure free intervals from the depth electrodes that were implanted into the hippocampal formations. The ictal segments were recorded from all sites exhibiting ictal activity using depth electrodes and also from strip electrodes that were implanted into the lateral and basal regions of the neocortex [21]. 100 single channel EEG segments of 23.6 s duration were recorded using a 128-channel amplifier system, digitised with a sampling rate of 173.61 Hz and 12-bit A/D resolution, and filtered using a 0.53–40 Hz (12 dB/octave) band pass filter. Fig. 1 shows the sample EEG signal one from each group. There are five broad spectral subbands of EEG signal of clinical interest: delta (0–4 Hz), theta (4–8 Hz), alpha (8–15 Hz), beta (15–30 Hz) and gamma waves (30–60 Hz). A traditional low pass finite impulse response (FIR) filter was employed on EEG to get

2.2. Wavelet based decomposition

2.3. Multifractal Detrended Fluctuation Analysis (MF-DFA) MFDFA algorithm for a signal time series xk of length N is divided into following five steps. Step 1. Cumulative deviation of xk for the ‘profile’ Y(i) is determined Y (i) =

i 

[xk − x],

i = 1, . . ., N

(1)

k=1

where 1 xk N N

x =

(2)

k=1

This signal xk is converted into random walk like time series Y(i) to highlight its self similar fractal characteristics for further DFA. Step 2. Profile Y(i) is divided into Ns non overlapping segments of length s (Ns ≡ int(N/s)). This is repeated from reverse order too to

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Fig. 2. Schematic representation of multifractal spectral parameters.

Fig. 3. Actual data points and fitted curve plot for multifractal spectrum.

accommodate all the sections of the data. So, 2Ns intervals of same length are obtained. Step 3. Local trend of each interval v (v = 1, 2, . . ., Ns ) of length s is calculated by least square fit for m-th order polynomial series.

2 1  Y [( − 1)s + i] − y (i) s s

F 2 (s, ) =

(3)

i=1

for each segment v, v = 1, . . ., Ns and

2 1  Y [N − ( − Ns )s + i] − y (i) s

Fig. 4. Flowchart for estimating multifractal parameters.

s

F 2 (s, ) =

(4)

i=1

The trends of m-th order (MF-) DFAm in the profile are eliminated. Through this step, the impacts of interference from noise and nonstationary trend can be excluded to get the multifractal feature. Step 4. For each scale s, qth order fluctuation function is calculated from qth order RMS.

 Fq (s) ≡

q/2 1  2 F (s, ) 2Ns 2Ns

1/q

2.4. Multifractal spectral parameters Generalised Hurst exponent h(q) is further related to mass exponent (q). (q) = qh(q) − 1

(5)

=1

/ 0. where q = Step 5. Scaling exponents are calculated from the log–log plots of Fq (s) versus s for each q. For scale invariant structure with selfsimilar characteristic, the series Fq (s) are long range power-law correlated with analysis scale s. So, Fq (s) ≈ sh(q)

exponent, H and it is independent of q. Thus as EEG has multifractal structure, the change of h(q) with q can be a feature of it.

(6)

The slope of this curve h(q) may depend on q. h(q) is termed as generalised Hurst exponent. For q = 2, h(q) is equal to the Hurst

(7)

First order Legrende transformation derives another multifractal parameter, multifractality spectrum f(˛) from Hölder exponent (singularity exponent) ˛. ˛=

∂(q)  = h(q) + qh (q) ∂q

f (˛) = q˛ − (q) = q[˛ − h(q)] + 1

(8) (9)

The singularity exponent ˛ is a measure of local roughness of the series. Whereas f(˛) represents the strength of multi-fractality or fractal dimension of points having same singularity exponent ˛. For multifractal data, the singularity spectrum has a shape like wide

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267

Table 1 Performance measures for multiclass classification for classes Ci and l represents number of classes. Measures

Formula

Interpretation

l

tp +tn i i i=1 tpi +tni +fpi +fni

l l tp l i=1 i (tp +fp ) i i i=1 l tp i=1 i l (tp +fn ) i i i=1 l tn i=1 i l

Average accuracy Precision

Recall

Specificity

i=1

(1 + ˇ

F-Score

Overall effectiveness of the classifier. Relevancy of the classified instances.

Efficiency of the classifier to detect relevant instances.

Measure of the classifier to appropriately exclude irrelevant instances.

(fp +tn ) i

2

i

) 2Precision · Recall ˇ · Precision+Recall

Efficacy of the classifier’s accuracy.

Fig. 5. Level 4 decomposition of the EEG into five subbands using fourth-order Daubechies wavelet.

inverted parabola with its maxima at ˛0 [˛(q = 0)]. For an underlying correlated process, ˛0 has small value. For monofractal series, h(q) is constant resulting (q) having linear relationship with q and f(˛) reduces to a single point. Spectrum width ␣ represents the dynamic nature of the series. A wider ␣ depicts rich in dynamics with high degree of multifractality. ˛ = ˛max − ˛min

(10)

where ˛max and ˛min are the two extremities of ˛. Fig. 2 shows a schematic of the above parameters. To characterise the multifractal spectrum, a quadratic fitting function with maxima at ˛0 has been proposed as f (˛) = A(˛ − ˛0 )2 + B(˛ − ˛0 ) + C

(11)

here, C = f(˛0 ) = 1. By least-square method, values of A and B are obtained. Parameter B is called asymmetry parameter. For symmetric spectrum, B is zero and for asymmetric shape, its value can be positive for left skewed and negative for right skewed spectrum. A left skewed spectrum has relatively weaker weighted low fractal exponents resulting dominance of extreme events, whereas, a right spectrum has relatively strongly weighted low fractal exponents resulting fine structure. Fig. 3 shows a sample plot of actual data points and plot of fitting polynomial. Here we can see f(˛0 ) = 1.

To identify the internal nonlinear dynamics of EEG, MFDFA was performed in this study. The parameters extracted as features from EEG are ␣, ˛0 , B, and H. The overall flowchart of the process is shown in Fig. 4. 2.5. Statistical analysis Mean and standard deviations were calculated from the MFDFA parameters extracted for each of the EEG subbands as well as band limited EEG from EEG dataset. Besides, the differences between the group means were explored by one-way analysis of variance (ANOVA) at 99% confidence level. ANOVA quantifies the interaction between dependent and independent variable(s) through linear regression and models [24]. Following ANOVA, to explore further for differences in the Group means, post hoc test was performed. Tukey’s pairwise honestly significant difference (HSD) test was chosen for post hoc comparisons due to its inherent ability to adjust confidence level inflation [25]. 2.6. Classification method In order to classify the Groups based on the multifractal parameters, SVM was employed instead of other conventional classifiers because of its potential for high accuracy with few training sets [26]. “One-against-one” SVM classifier was used with cubic polynomial

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Table 2 Mean values and standard deviations of the parameters for band-limited EEG and EEG subbands of all groups. Parameters

Group (N = 100)

˛

˛0

B

H

Delta (0–4 Hz)

B D E

0.256 ± 0.113 0.369 ± 0.183 0.660 ± 0.305

0.023 ± 0.007 0.056 ± 0.066 0.097 ± 0.081

0.111 ± 0.170 −0.060 ± 0.271 0.242 ± 0.149

0.002 ± 0.001 0.002 ± 0.001 0.002 ± 0.001

Theta (4–8 Hz)

B D E

0.445 ± 0.076 0.558 ± 0.20 0.786 ± 0.332

0.046 ± 0.009 0.089 ± 0.080 0.115 ± 0.084

0.229 ± 0.103 −0.020 ± 0.301 0.264 ± 0.145

0.001 ± 0.001 0.002 ± 0.001 0.001 ± 0.002

Alpha (8–12 Hz)

B D E

0.608 ± 0.093 0.720 ± 0.194 0.776 ± 0.282

0.091 ± 0.016 0.124 ± 0.081 0.117 ± 0.063

0.268 ± 0.102 0.125 ± 0.270 0.315 ± 0.077

0.025 ± 0.006 0.021 ± 0.002 0.021 ± 0.004

Beta (12–30 Hz)

B D E

0.911 ± 0.095 0.911 ± 0.161 0.834 ± 0.218

0.144 ± 0.013 0.197 ± 0.068 0.168 ± 0.034

0.358 ± 0.065 0.261 ± 0.175 0.340 ± 0.061

0.031 ± 0.012 0.069 ± 0.013 0.069 ± 0.019

Gamma (30–60 Hz)

B D E

1.077 ± 0.110 1.146 ± 0.178 1.011 ± 0.179

0.519 ± 0.040 0.560 ± 0.110 0.399 ± 0.124

0.345 ± 0.068 0.319 ± 0.133 0.350 ± 0.054

0.377 ± 0.041 0.399 ± 0.070 0.274 ± 0.109

EEG (0–60 Hz)

B D E

0.431 ± 0.082 0.609 ± 0.205 0.715 ± 0.292

0.111 ± 0.025 0.327 ± 0.125 0.207 ± 0.108

0.193 ± 0.115 −0.012 ± 0.233 0.288 ± 0.109

0.065 ± 0.024 0.232 ± 0.062 0.113 ± 0.055

Table 3 Statistical significance of the parameters for each subbands for their efficacy of separability between the Groups. Signals

˛

˛0

B

H

Delta (0–4 Hz) Theta (4–8 Hz) Alpha (8–12 Hz) Beta (12–30 Hz) Gamma (30–60 Hz) Band-limited EEG (0–60 Hz)

B,D,E (p < 0.001) E (from B, D) (p < 0.001) B (from D, E) (p < 0.001) B,D,E (p < 0.001) B,D,E (p < 0.001) B,D,E (p < 0.001)

B,D,E (p < 0.001) B,D,E (p < 0.001) B (from D, E) (p < 0.001) B (from D, E) (p < 0.001) B,D,E (p < 0.001) B,D,E (p < 0.001)

– D (from B, E) (p < 0.001) D (from B, E) (p < 0.001) D (from B, E) (p < 0.001) B,D,E (p < 0.001) B,D,E (p < 0.001)

E (from B, D) (p < 0.001) B (from D, E) (p < 0.001) B (from D, E) (p < 0.001) – – B,D,E (p < 0.001)

Table 4 Boxplot representation of the significant parameters.

Table 5 The value of statistical parameters of classification. Groups

Accuracy (%)

Precision (%)

Recall (%)

Specificity (%)

F-Score (%)

Group B Group D Group E Average

99.7 99.3 99.7 99.6

99.0 99.0 100.0 99.3

100.0 99.0 99.0 99.3

99.5 99.5 100.0 99.7

99.5 99.0 99.5 99.3

Table 6 Summary of the previous works done utilising the same dataset for classifying normal, ictal and interictal EEGs. Reference

Feature

Classifier

Accuracy (%)

[29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]

Entropy Higher order statistics based features Frequency domain parameters, Burg’s method Wavelet coefficient Nonlinear features Empirical mode Discrete wavelet transform Mixed-band feature space Lyapunov exponent Nonlinear pre-processing filter Entropies

Adaptive neuro-fuzzy interference system (ANFIS) Gaussian mixture model SVM Mix of expert neural networks Gaussian mixture model C4.5 Artificial neural network Back propagation neural network Recurrent neural network Artificial neural network Fuzzy

92.22 93.1 93.3 94.5 95.0 95.3 96.7 96.7 96.8 97.2 98.1

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kernel. “One-against-one” method has already been established with high accuracy for multiclass classification [27]. 5-Fold cross validation was also employed to ensure the integrity of the classification. The performance measures of the network were further evaluated using the number of correctly detected relevant class instances (true positive, tp ), the number of correctly identified instances irrelevant to the class (true negatives, tn ), the number of incorrectly assigned instances to the class (false positives, fp ) and the number of undetected relevant class instances (false negatives, fn ). Table 1 shows the formulae for the multiclass performance parameters. 3. Results and discussion 3.1. Filtering and wavelet analysis Fig. 5 shows the sample result of one EEG set. These five separate EEG subbands were analysed further with MFDFA to extract the multifractal parameters. ‘db4’ was used based on its similarity with EEG signals. Computational complexity was also reduced due to its orthogonal property and optimum number of filter coefficients. Moreover, time-frequency localisation properties of ‘db4’ are also near optimum to extract the subbands efficiently [28]. 3.2. Statistical analysis Multifractal parameters were extracted from band limited EEG as well as for five subbands of each of 300 EEGs (100 from each group B, D, E). The average values and standard deviations of the parameters are summarised in Table 2. It can be observed that Group B has the least values for ˛, in all the subbands and bandlimited EEG. For low frequency subbands delta and theta have the widest singularity spectrum ˛, making it more dynamic in nature. On the other hand in all cases, Group E has the highest ˛, inferring it as more developed multifractal than Group B and Group D. In beta subband, ˛ has similar mean values for both Group B and D. It signifies that epileptic EEGs are more prone to sudden fluctuations over normal ones. Group B is found to have most correlated underlying process among the groups as ˛0 of Group B have the least values in all the subbands including band-limited EEG. Higher frequency beta and gamma subbands have highest values for ˛0 for Group E, whereas lower frequency subbands have highest values for Group D depicting more uncorrelated and Group E in higher frequency subbands and more uncorrelated Group D in lower frequency subbands including band-limited EEG. B parameter shows another trend exhibiting left skewness in all cases excepting high frequency beta and gamma subbands along with band-limited EEG for Group D only. Moreover, Group D has the least values for parameter B indicating that it has relatively strong weighted low fractal exponents than in other groups. High frequency beta and gamma subbands have considerably low in parameter H. However, other subbands also do not exhibit any significant trend in this parameter across the groups. One-way analysis of variance (ANOVA) was performed on all the feature values. Furthermore, Tukey’s HSD was also evaluated for analyzing the group differences for the significant ones. The results are shown in Table 3. ANOVA and Tukey HSD exhibit similar results at 99% confidence interval. It is evident from the results that all the parameters have different contribution in differentiating among the Groups in different subband levels. Boxplot representation of the parameters is also plotted in Table 3 to highlight the contrasts between the parameters across the subbands. Table 4 represents the boxplots of the statistical characteristics of the significant features of each bands.

269

Band-limited EEG can be used in significantly isolating the Groups alone using all parameters. Gamma subbands also can be utilised to differentiate the Groups with all except H parameter. However, alpha subband is least useful in significantly distinguishing all of the three Groups. Table 4 shows the boxplots of the parameters which were able to distinguish three Groups significantly. We can observe that spectrum width ˛ shows highest in Group E and lowest in Group B in high frequency subbands beta and gamma and also in band-limited EEG. But in delta subband, this trend is different where Group D is highest. Again band-limited EEG, along with low frequency subbands delta and theta show a trend of high ˛0 in Group D but gamma subband has it high in Group E. B parameter has significance in gamma and band-limited EEG only and both are showing similar trend with lowest in Group D. Lastly, only band-limited EEG has significant trend in case of parameter H. 3.3. Classification 70 samples were randomly chosen out of 100 samples of each groups and used for training SVM, and the remaining 30 samples from each groups were used for testing phase. A 5-fold cross validation was also employed for the randomness of this training phase. Classification result including accuracy, precision, sensitivity, specificity, recall and F-score for each class is displayed in Table 5. According to the result, correct classification of Group B and Group E is same (99.7%), while Group D has slightly lower accuracy of 99.3%. Considerably high average accuracy of 99.6% in classification has been observed. Earlier, Kannathal et al. [29] have used entropies of EEG waveforms to classify epileptic EEGS through adaptive neuro-fuzzy interference system (ANFIS) classifier to achieve an accuracy of 92.2%. Chua et al. [30] have reported an accuracy of 93.1% using higher order spectra feature classified with Gaussian mixture model. In another work, Faust et al. [31] have found that spectrum estimation with Burg’s method in combination with SVM produced best accuracy rate of 93.3%. Subasi [32] utilised mix of experts neural networks to classify epileptic EEGs on the basis of wavelet coefficients with an accuracy of 94.5%. Different nonlinear features like correlation dimension, Hurst exponent, and approximate entropy can were used to characterise the epileptic EEG signal and thereby classified by GMM with 95% accuracy rate by Acarya et al. [33]. Another study by Martis et al. [34] showed EEG decomposition using EMD yielded 95.3% accuracy with C4.5 algorithm. Orhan et al. [35] have classified epileptic EEGs from discrete wavelet coefficients classified with artificial neural network at an accuracy rate of 96.7%. The works of Adeli et al. [15] with Lyapunov exponent and correlation dimension were further classified with Levenberg-Marquardt backpropagation neural networks at an accuracy of 96.7% by Dastidar et al. [36]. Guler et al. [37] have proposed recurrent neural networks (RNN) employing the Lyapunov exponents to achieve 96.8% accuracy while analysing long-term EEG signals for epilepsy detection. Nigam et al. [38] have observed 97.2% accuracy using nonlinear pre-processing filter along with artificial neural network. A high accuracy rate of 98.1% has been reported by Acarya et al. [39] using four entropy features namely Approximate Entropy, Sample Entropy, Phase Entropy 1, and Phase Entropy 2 with Fuzzy classifier to classify between epileptic and normal EEGs. Table 6 shows a summary of the previous studies explored on the same dataset. 4. Conclusion This study explored the significance of multifractal attributes of EEGs along with their subbands namely, delta, theta, alpha, beta and gamma for detection of epilepsy and seizure. This novel approach

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