Automated Diagnosis of Epilepsy Employing Multifractal Detrended Fluctuation Analysis Based Features

Automated Diagnosis of Epilepsy Employing Multifractal Detrended Fluctuation Analysis Based Features S. Pratiher 1 , S.Chatterjee 2 and R.Bose 3 1 Department o f Electrical Engineering , Indian Institute o f Technology, Ka npur, India 2 Electrical Engineering Depart ment, Jadavp ur University, Kolkata, I ndia 3 Electrical Engineering Depart ment, Calcutta Instit ute of Engineerin g and Management, K olkata, India { sawon1234 , chap eshwar , rohitbose94 } @gmail.com Abstract: This contribution reports an application of Multi Fractal Detrended Fluctuation Anal ysis (MFDFA) based novel feature extraction tec hnique for automated detection of epilepsy . In fractal geometr y, Multi-fractal Detre nded Fluctuation Analysis (M FDFA) is a po pular technique to examine the self-similarity of a non linear, chaotic and nois y time series. In the present research work, EEG signals re presenting healthy, interictal (seizure free) and ictal activities (seizure) are acquired fro m an existing available database. The acquired EE G signals of diff erent states are at fi rst anal y zed using MFD FA. To requisi te the time series singularity quantification at local and global scales, a novel set of fourteen different features. Suitable feature ranking employing student’s t -test has been done to select the most statistically significant features which are hen ceforth being used as inputs to a support vector machines (SVM) classifier for the classification of different EEG signals. Ei ght different classification problems have been presented in this paper and it has be en observed that the overall classification accuracy using MFDFA based features are reasonabl y satisfactory for all classification problems. The performance of the proposed method are also found to be quite commensurable and in some cases even better when compared with the results published in existing literatures studied on the similar data set. 1. Introduction Epilepsy is a ver y serious neurological disorder w hich affects about 1% -2% of human population on earth. Epilepsy is generally characterized by recurrent seizures which occur due to malfunctioning of neur ons located inside the human brain [1] . During s eizure activit y, the electrical signals transmitted by neurons become highly abnormal in nature. Symptoms like severe jerking movements of leg s, arms, loss of consciousness and awareness etc. are ve ry common among the patients suffering from epileps y. Earl y and accura te detection of epileps y is, therefore ex igent to prevent these unusual and undesirable physiological abnormalities. In pathology labs a nd clinics, epilepsy is detected usuall y b y expert neurologists through electroencephalogram ( EEG) screening, owing to the fa ct that EEG based dia gnosis is inexpensive and has better time re solution compared to fMRI-based treatment [2]. But the detection of epilepsy through visual inspection of EEG recordings, are often incorrect and inevitably lengthy. Hence, an automated computer a ided fast and accur ate disease detection scheme to detect e pilepsy s eizures correctl y and a t a much lesser time have become an utmost necessity. Considering the above-said fact, autom atic detection of epilepsy using suitable signal processing and machine learning algorithms have therefore been a major focal point of r esearch over the last couple of years. Analysis of epileptic seiz ure and h ealthy EEG signals in time domain using cross -correlation and Least Square Support Vector machines was reported b y Chandaka et a l. in [ 3]. I n Frequenc y domain, spectral analysis based on Fast Fourier Transform and Decision Tree classifier w as employed fo r automatic de tection and classification of epileptic seizures [4]. Artificial neural network ba sed combined time and freque ncy domain fe atures ha ve also be en succ essfully implemented to detect epileptic seizures in EEG signals in [5]. Anal ysis of EEG signa ls in joint time fr equency domain, based on wavelet transform and mixture of expert model have been reported in many existing literatures [6]. Epileptic seizure detection based on multiwave let transform and app roximate entrop y employing Ar tificial Neural N etworks have been reported in [7]. Analy sis of seiz ure and seizure free EEG signals b ased on empirical mode decomposition have been repo rted in many available literatures. Several feature parameters includin g, instantaneous a rea, second order difference plot, bandwidth features, phas e space re construction etc. derive d from resp ective intrinsic mode functions (I MF’s) have been used as inpu ts to a Least square Support Vector Machines (LS-SVM) classifie r for classification of EEG signals [8 - 11]. Fe ature parameters base d on local binary patterns, key point local binary patterns using L S - SVM classifier for a utomated detection of epilepsy have b een reported in [12-13]. Since, EEG signals are representatives of complex bra in d ynamics, the y manifest highl y non linea r and chaotic behaviour. The refore, anal ysis of EE G signals based on sev eral non linear techniques like Approximate Entrop y, Fractal Dimension, Lyapnov exponent etc . for the purpos e of detection and classification of epileptic seizures in EEG signa ls have been reporte d in [14-16]. Detection of epileps y based on weighted visibility graph based features and fra ctal dimension of Flexible Anal ytic Wavelet Transform have been ver y reported ver y recentl y in [17 -18]. Hence, it is evident from the existing literature surve y, that EEG signals are typically manifest non stationary and non linear behavior. Therefore, non linear signal processing techniques can be effectively applied fo r anal y sis and classification of different categories of EEG signals. Considering th e above f act, in thi s contribution, feature parameters based on non linear anal y sis of EEG signals employing Multi Fractal Detren ded Fluctuation Analysis (MFDFA) have bee n reported for discrimination of different types of EEG signals. Detrended Fluctuation Analysis (DFA) was first proposed b y P eng et.al. to detec t th e lon g range correlation of DNA sequences [19]. Since then, D FA has bee n used widel y for the determination of monofractal scalin g properties in noisy, n on stationary time series [ 20-21]. However, man y real life signals do not ex hibit simple monofrac tal behaviour i.e. they cannot be characterized by a sin gle scaling exponent, rather different scaling exponents are required to manifest the ch aracteristic of different p arts of a non li near time series. This led to the development of Multi Fractal Detrended Fluctuation Ana lysis (MFDF A). MFDFA was first conceived b y Kantelhardt et al. [22] as a generaliz ation of the standard De trended Fluctuation Analysis (DFA). MFDFA overcame the limitation of a single scaling exponent of conventional DFA method using different order fluctuation functions. Using fluctuation functions of different order, the scaling b ehaviour of a nonlinear time series ca n be analy sed in different segments. Another distinct advantage o f using MFDFA technique is that it has low computational burden compared to existing techniques li ke Wavelet transform maximum modulus (WTMM) for determining the lon g ra nge correlation o f a multifractal time series [22 ]. MFDFA has been applied succ essfully to stud y the non linear and chaotic nature o f various tim e serie s li ke partial discharge si gnals [23] , be aring fault signals [24] and also for anal ysis of several ph ysiolo gical signals including EEG [25]. This work not onl y deals with the ana lysis of EEG signals based on MFDFA, but a lso classification of EEG signals based on seve ral new fe atures extracted from multi-fractal spec trum (MFS) of EEG signals have also been presented, which has not been reported so far in any literature s. In this contribution, fourteen different feature para meters obtained from the respective MFS of different EEG signals are being used for effective discrimination of different EEG signals. After feature rankin g using student’s t -test, four highly discriminative features are selected which are henceforth used as inpu ts to SVM a nd kN N classifiers for the purpose of classification of EEG signals. The paper is divided int o following sections. Section II explains the EEG data set used in thi s work following by the brief steps of MFDFA in section III. Section IV deals with the extracted features and their physical si gnificance. Section V provides a brief theory of SVM classifier . Finally, results and discussion are given in sec tion VI, followed b y conclusion in section VII. 2. EE G Signal Data set In the present wor k, EEG signa ls are take n from online available benchmark database of University of Bonn, Germany [26] . The dataset comprises of fiv e sets of single channel EEG recordings denoted by A, B, C, D, and E. Length of each signal is 23.6 sec. The data is sampled at a sampling frequency of 173.61 Hz. Recording of EEG signals are d one using similar 128- channel ampli fier system, using an average c ommon re ference After the signals are recorded, band- pass filtering was perf ormed with filter settings between 0.53 – 40 Hz. Each data set contains 100 single channel EEG segments. EEG signa ls of sets A and B are acquired from surface electrode placement using the standard 10 -20 electrode system from five health y volunteers in eyes open and eyes closed conditions respectively. EEG signals of sets C are recorded from the hippocampal formation in the opposite hemisphere and that of set D are recorded from the epileptogenic zone, respectively. Both sets C and D comprises of activity in the seizure free intervals whereas, Set E consists of seizure activities onl y. In the present study, eight different classification problems are presented by combining five dif ferent sets (A,B, C, D and E) of EEG signals. The different CP along with brief descriptions are presented in Table- I. Table-1: Types of classification problem Classification Problem (CP) Class Description I A, E Healthy with eyes open vs Seizure II B, E Healthy with eyes closed vs Seizure III C, E Hippocampal Interictal vs Seizure IV D, E Epileptogenic Interictal vs Seizure V AB,E Healthy vs Seizure VI CD,E Interictal vs seizure VII AB,CD Healthy vs Interictal VIII ABCD,E Seizure free vs seizure 3. Multi-Fractal Detrended Fluctuation A nalysis After a cquisition of EEG signa ls of different sets, they are at first anal ysed using MFDFA. The basic steps of MFDFA as are described briefly as follows: Let us consider a non stationary and non-linear time series x(n ) for n=1,……. N of length N. Step 1: First step is to compute the mean of the time series given by    N n n y N y 1 ) ( 1 (1) Step 2: After computation of mean value, in the next step, y is subtracted from the signal to compute the integrated time series g iven b y ] ) ( [ ) ( 1     i n y n y i Y for i=1,…..,N (2) Step 3: The integrated time series is divided into N s number of non overlapping segments (where Ns = int(N/s) and s is the time scale or length of each s egment). When N is not a multiple of s, some data remains at the end of the series Y(i). In order to include th e remaining part of the series, the entire process is repeated again from t he opposite end, thus giving a total number of 2Ns seg ments. The local RMS va riation/trend of each segment out o f t otal 2Ns segments is obtained by usin g a l east square pol ynomial fit o f the time series and then the variance for each segment is determined by      , 2 s       2 1 ) 1 ( 1      s i i y i s Y s   for ν=1,……..,N s (3)      , 2 s       2 1 ) ( 1       s i s i y i s N N Y s   for ν= Ns + 1, . . . , 2Ns (4) Here y ν (i) is the least square fitted value in the segment ν. Step 4 : The q th order fluctuation function   s q  is obtained after computi ng average procedure of 2Ns segments, where q is an index which can take all possible values except q=0.For q=0, a logarithmic averaging procedure is followed, instead of normal averaging procedure.   s q  = q Ns q v s Ns / 1 2 1 5 . 0 2 )] , ( [ 2 1           (5) From Equation (5), it is e vident that the fluctuation function F q (s) depe nds on the time scale s for di fferent values of q. The steps 2-4 are therefore repeated by varying the time scales s. For q=2, the method reduces to standard DFA. Step 5 : Va riation of   s q  ve rsus s for each value of q is a nalysed using a log -log plot. When the anal ysed time series y(n) is long-range power-law co rrelated, va riation of   s q  versus s, shows a power-law behaviour,with h(q) as the slope, where h(q) is known as the generalized Hurst exponent, which depends on the value of q.   s q     q h s (6) For a monofractal time series, scaling b ehaviour of    , 2 s  is a lmost identical in all segments ν, for all values of q. Hence, h(q) is independent of q. However, for a multi fractal time series, h(q) is a function of q, and for q = 2, i.e. h(2)gives the value of simple Hurst ex ponent. The average value of   s q  in equation (5) will be mainly influenced by larger and smaller variance of    , 2 s  within segment ν, corresponding to q > 0 and q < 0,respectivel y. Therefore, h(q) describes the scaling behaviou r of the s egments with large an d small fluctuations, respectively fo r positive and negative values of q. Further, the la rge fluctuations are generally characterized by a smaller scaling e xponent h(q) for multifractal series and vice-versa [24-26] . 3.1 Determination of Multi-Fractal Spectrum The relationship between the generalized Hurst exponent h(q) of MFDFA and multi fractal scaling exponent τ(q) is given by     1   q qh q  (7) A monofr actal time seri es with long range corre lation is chara cterized by a single Hurst Exponent, where the multifractal sc aling exponent τ(q) shows a linear dependency on q. On the contrary, multi fractal time series have multiple Hurst exponents and τ(q) depends nonlinearl y on q [50]. Using a Legendre transform, the relationship between the singularity spectrum f (α) and scaling exponent τ(q) is obtained, which are given by [23 -25] dq d    (8) and     q q f      (9) where α is known as singularit y exponent and f(α) is the fractal dimension of s ubset of the series characterized by α. Now , Using Eq. (6) α and f (α) can be expressed in terms of h(q) as follows     q h q q h     (10)       1    q h q f   (11) In general, the singularity spectrum f (α) quantifies the long ran ge correlation property of a time series [24 -26]. The shape of the mul tifractal spectrum looks like an inverted parabola, where th e width of the parabola is a measu re of the mul tifractality of th e spectrum. A larger spectral width is an indicator of high degree of multifractality . For a monofractal time series, since h(q) is independent of q, the width will be zero. 4. Fea ture extraction using MFDFA 4.1 Extracted Features: In the present work, EEG signals of five different sets re presenting differe nt states of human brain are at first characterized by multifractal parameters. From the multifractal spectrums i.e. f (α) and α curves for five EEG si gnals, four teen distinct new f eatures are obtained for discrimination of different EEG signals. The prop osed set of features which are used in this work are as follows: F 1 : Generalized Hurst Exponent F 2 : Singularity exponent (α) corresponding to peak of singularity spectrum=α peak F 3 : Right extremity of the sing ularity exponent= α max F 4 : Left extremity of the singularity exponent=α min F 5 : Mean singularity exponent=α mean= (α max + α min )/2 F 6 : Singularity spectrum width=∆α=(α max - α min ) F 7 :Horizontal distance between the peak and the minimum value of singularity exponent = (α peak - α min ) F 8 : Horizontal distance between th e peak and t he maximum value of singularity exponent = (α peak - α max ) F 9 : Singularity spectrum corresponding to α max =f(α max ) F 10 : Singularity spec trum corresponding to α min =f(α min ) F 11 : Mean singularity spectrum=f(α 0 )= {f(α max )+f(α min )}/2 F 12 : Vertical distance be tween f(α max ) and f(α min ) =∆f(α)= f(α max )- f(α min ) F 13 : Vertical distance be tween the peak value of singularity spectrum and f(α min )=f(α peak )- f(α min ) F 14 :Vertical distance be tween the peak value of singularity spectru m and f( α max )= f(α peak )- f(α min ) 4.2 Physical significance of the extracted features: The significance of these features are explained briefly. F 1 is the generalized hurst exponent i.e. h(2) which indicates the long range a utocorrelation behaviour pe rsisti ng in a non stationary time series. A higher valu e of h(2) indi cates a lon g range autocorrelation persisting in a non linear and non stationary time series where as the lower value of hu rst exponent indicates that the persistence property decreases and the time series tends towards random b rownian motion behaviour. As stated earlier in section- 3, the multifra ctal spectrum i.e. variation of f(α) versus α, resembles a wide inverted parabola, the feature F 2 indicates the value of value of the singularity ex po nent corresponding to maximum fluctuation of a time series. α peak is the value of singularity exponent for which the singularity spectrum f(α) has a maxim a. α peak indicates the degree of correlation of a time serie s. A hig her value of α peak indicates that the data point s are highly correlated. To elucidate further, if a past EEG si gnal emitted from human brain reveal spike, the probabilit y of occurrence of the spike in the next EEG signal is greater than 0.5. The process is repetitive in nature and indicates a high degree of correlation between two pulses. On the other hand, if the subsequent EEG signals are not affected by spikes, and be come independent of the previ ous state, then it indicates a lower degree of cor relation and a lmost a regular pattern. F 3 and F 4 are the two extreme va lues of singularity exponent α, which indicates the maximum and minimum fluctuations, respectively. Feature F 5 represents the mean of two extreme values of α, which c orresponds to average fluctuations. Feature F 6 is the width of the singularity spectrum. A ti me series showing high degree of fluctuations are characterized b y a large value of spectral width. F 7 and F 8 denotes the horizontal dist ances between the pe ak and the minimum and maximum values of singularity exponents, respe ctively. This horizontal distance is the measure of the difference between average f luctuations with the min imum and maximum fluctuations of a ti me series. Features F 9 and F 10 are the ordinates i.e. singularity spectrum values f(α), corresponding to two extreme values of singularit y exponents and F 11 represents the m ean of the two. Feature F 12 is the vertical difference between F 9 and F 10. F 9 and F 10 indicate the unit number max imum and minimum probability su bset in EEG signals and F 12 is the measure the proportion of large and small peaks in EEG si gnals [24]. F or F 12 < 0, the propo rtion of lar ger peaks in EE G si gnals are less compared to smaller peaks, he nce amplit ude distortion is lower. For F 12 > 0, the proportion of large peaks are higher than small peaks, wh ich indicates a higher amplitude distortion. Features F 13 and F 14 indicates the difference in height between the mean and the extreme values minimum and maximum) of the singularity spectrums, respectively. 5.Support vector machines SVM is a supervised machine learning algorithm developed primaril y to solve a binary classification problem. Detailed description of the SVM algorithm can be f ound out in [ 3,26]. An SVM performs classification by finding an optimum hyper plane havin g a maximum margin (i.e. the distance between the boundary and the nearest points) betwee n the two classes using the principle of Structural R isk Minimization (SR M) [3]. In the present stud y since, all classification problems are binary in nature, therefore SVM classifier is used. In the present study since, all classification proble ms are binar y in nature, therefore SVM classifier is used. I n ca se of non linear SVMs, the training data are mapp ed into a high dimensional feature space usin g different kernel functions, which perf orms thi s mappin g operation satisf ying M ercer’s theorem. There can be several kernel functions in an SVM like Linear, Polynomial, Radial Basis Function etc . I n the initial part of the present work different kernel fun ctions of SVM have b een emplo yed to test the performance of the classifier, and it has been o bserved that the perf ormance of R adial Basis Function kernel has been found to be s atisfactory for all ca ses. M athematically, for a linearl y separable training data (c, d) the RBF kernel function   d c ,  can be expressed as Radial basis function:   ) ( 2 , d c e d c      (12) where  is known as kernel parameter and 2 2 1    , with ‘ω’ as the width. 6. Res ults and Discussion 6. 1 Analysis of EEG signals using MFDFA: As highlighted in this paper, the EEG signals representing h ealthy, interictal and s eizure activities are atfirst ch aracterized b y mutifractal para meters. Figure (a) shows the variation of generalized Hurst exponent against q for five different sets A- E. In the present work, ‘q’ is varied from - 5 to + 5 in steps of 0.1and the value of ‘s’(scale) is chosen be tween 16– 1024, having a total number of 19 equal logarithmic intervals in betwee n. Figure1.Variation of h(q) vs. q for EEG signals of different sets It c an be observed from Figure 1, that the Hurst exponent curve s shows a non linear relationship with ‘q’ for all sets indicating a multifractal nature of EEG signals. Moreover, since EEG signals of different sets represe nt different states of human brain, a wide variation in shape, size and position of Hurst exponent curves are observed in Figure 1. Further, since the smaller values of generalized Hurst exponent indicate large fluctuations for positive values of ‘q’, it i s therefore evident from Figure 1, that epileptic seiz ure EEG signals correspondin g to set-E, the gene ralized Hurst ex ponent shows minimum value for ‘q’ > 0 compared to inter -i ctal and healthy EEG signals, which indicat es high de gree of flu ctuations. Therefore, the Hurst ex ponent curves obtained for different EEG sig nals clearly bears the evidence of chaotic and non linear beha vior representing complex dynamics of human brain. Figure 2 shows the variation of multifractal scaling exponent τ(q) versus q for d ifferent sets of EEG signals, which also shows a t ypical non linear behavior. Figure 2.Variation of τ (q) vs. q for EEG signals of different sets The shape of the curves are ty pically convex in nature, which clearly manifests a multifractal nature of EEG signals of differe nt sets. The most int eresting observa tion is the degree of non linearity, which is found to be hi ghest for seizure signals corresponding to set -E, compared to healthy and inter-ictal EEG signals, respective ly. which again indicates that during seizure activity, the EEG signals show a greater amount of fluctuations. Figure 3 shows the multifractal spectrum obtained for different EEG signals. It can be pointed out from Figure 3, that the MFS of diff erent EEG signals reveal a wide inverte d parabolic nature, with different values of singularity spec trum widths ∆ α . The greatest width of the MFS is obtained for seiz ure signals followed b y interictal and healthy si gnals. Sinc e, the width of MFS indicate a higher de gree of multifractality, it is evident that during epileptic seiz ures, the EEG signals manifest a high degree of multifractality followed by interictal and healthy states. Moreover, it can be observed that the seizure EEG si gnal have extended ‘right tail’ c haracteristic which are absent for either healthy and seizure si gnals. MFS having ex tended ‘right tail’ characteristic indicate that the MFS are insensitive to local fluctuations with larger magnitudes. Besides, it can be observed that the MFS Figure 3.Variation of f(α) vs. α for EEG signals of different sets of different EEG si gnals are not perfectl y s ymmetric, i.e. their singularit y spectrums f(α) do not attain peak for a fixed value of singularit y exponent α for all cases. Therefore different feature parameters can b e extracted from their respective MFS to distinguish between different t ypes of EEG signals. As mentioned earlier in Section-4 fourteen different fe atures have been e xtracted initially, among which a feature ranking t est is being done to select the most significant f eatures for performing the classification task. The details of the selected features and feature ranking are discussed in the following section. 6.2 Feature Ranking using student’s t -test: In the present study, a student’s t -test is done to rank th e features e xtracted from MFS of different EEG signals. The purpose of using a student’s t -test is to reduc e the siz e of the feature vector to eliminate feature redundanc y and at the same time to im prove the computational cost. In a student’s t -test, the features are ranked on the basis of their t -values. A hig her value of t indicate a better rank of a feature. For eight classification problems, eight paired student’s t -test are conducted. For a two class problem like the present case, the outcome of the t - test y ields a ‘ p ’ value which is almost similar like a one way Analysis of Variance ( ANOVA) test [28-29] . A lower ‘ p ’ value indicat es ver y high discrimination ability of the selected features . After conducting student’s t -test, for ea ch classifi cation problem, sequential feature selection procedure ( S FS) is adopted to determine the most optimal feature set for each classification problem. In SFS techni que, a subset of features from the entire feature data set are selected sequentially according to the rank of the feature. The classification accuracy is tested each time with the selected feature, till no further improvement in accuracy is observed. The number of selected features for each CP is therefore the optimized feature set that can be used to train a classifier y ielding maximum classification accuracy. The optimiz ed features with their feature values and respective ‘ p ’ values for eight CP are shown in Tables 2-9. It can be pointed out from Tables-2-9, that the selected optimal fe ature p arameters for eight CP have a significant amount of class sep aration between them. Hence, the discriminative ability of the select ed features a re statistically significant u pon statistical h y pothesis testing. The performance parameters for each CP have been eva luated based on the selected optimal fe ature sets which are discussed in the following section. Table-2:Results of paired students t -test for classification problem-I with feature values No of selected features Selected Features Feature values (Mean  Standard deviation) ‘ p ’ values 3 A E F 1 0.78  0.08 0.41  0.17 2.84e-37 F 4 0.68  0.10 0.31  0.14 9.94e-40 F 12 0.23  0.14 0.62  0.21 2.50e-26 Table-3:Results of paired students t -test for classification problem-II with feature values No of selected features Selected Features Feature values (Mean  Standard deviation) ‘ p ’ values 5 B E F 1 0.62  0.10 0.41  0.17 4.03e-18 F 4 0.54  0.12 0.31  0.14 2.32e-22 F 6 0.37  0.11 0.66  0.27 1.19e-16 F 7 -0.26  0.07 -0.48  0.18 1.36e-19 Table-4:Results of paired students t -test for classification problem-III with feature values No of selected features Selected Features Feature values (Mean  Standard deviation) ‘ p ’ values 4 C E F 1 0.78  0.08 0.41  0.17 4.42e-36 F 4 0.87  0.08 0.49  0.20 2.48e-32 F 6 0.21  0.14 0.62  0.21 3.45e-24 F 7 0.53  0.13 0.27  0.15 1.95e-24 Table-5:Results of paired students t -test for classification problem-IV with feature values No of selected features Selected Features Feature values (Mean  Standard deviation) ‘ p ’ values 9 D E F 1 0.73  0.11 0.41  0.17 3.13e-29 F 2 0.84  0.16 0.49  0.20 2.29e-23 F 3 1.24  0.22 0.97  0.35 6.16e-09 F 4 0.53  0.10 0.31  0.14 3.45e-24 F 5 0.89  0.13 0.64  0.23 3.64e-15 F 8 0.30  0.15 0.18  0.10 2.09e-09 F 10 0.48  0.16 0.74  0.16 2.25e-19 F 12 0.29  0.17 0.62  0.21 1.95e-24 Table-6:Results of paired students t -test for classification problem-V with feature values No of selected features Selected Features Feature values (Mean  Standard deviation) ‘ p ’ values 8 AB E F 1 0.68  0.13 0.41  0.17 1.07e-24 F 2 0.72  0.13 0.49  0.20 1.72e-17 F 4 0.59  0.13 0.31  0.14 1.23e-27 F 6 0.37  0.11 0.66  0.27 7.50e-17 F 7 -0.24  0.08 -0.48  0.18 5.50e-22 F 9 0.43  0.16 0.12  0.24 4.47e-19 F 12 0. 29  0.1 9 0.62  0.21 3.13e-19 F 13 0.57  0.16 0.89  0.24 4.33e-19 Table-7:Results of paired students t -test for classification problem-VI with feature values No of selected features Selected Features Feature values (Mean  Standard deviation) ‘ p ’ values 7 CD E F 1 0.75  0.11 0.27  0.15 1.68e-31 F 2 0.86  0.15 0.41  0.17 3.94e-27 F 4 0.56  0.11 0.49  0.20 2.90e-25 F 5 0. 90  0.12 0.64  0.23 1.20e-17 F 10 0.47  0.15 0.74  0.16 1.09e-21 F 12 0.25  0.16 0.62  0.21 5.30e-28 F 14 0.53  0.15 0.27  0.15 7.58e-22 Table-8:Results of paired students t -test for classification problem-VII with feature values No of selected features Selected Features Feature values (Mean  Standard deviation) ‘ p ’ values 6 AB CD F 3 0. 96  0.12 1.24  0.20 1.30e-24 F 6 0.37  0.11 0.68  0.20 3.95e-25 F 8 0.13  0.06 0.30  0.13 5.27e-22 F 10 0.72  0.13 0.47  0.15 6.39e-24 F 11 0.58  0.10 0.36  0.12 2.54e-24 F 14 0.28  0.12 0.53  0.15 4.63e-24 Table -9:Results of paired students t- test for classification problem-VIII with feature values No of selected features Selected Features Feature values (Mean  Standard deviation) ‘ p ’ values 7 ABCD E F 1 0.73  0.12 0.27  0.15 3.67e-27 F 2 0.7 9  0.14 0.41  0.17 5.81e-21 F 4 0.5 9  0.13 0.49  0.20 4.19e-25 F 7 -0.31  0.11 -0.48  0.18 1.65e-11 F 9 0.35  0.17 0.12  0.24 1.42e-10 F 12 0.28  0.15 0.62  0.21 3.89e-23 F 13 0.65  0.17 0.89  0.24 3.64e-11 6.3 Performance Analysis of SVM classifier : The performance metric of the proposed seizure detection scheme is being evaluated using different statistical parameters li ke Accurac y , S enstivit y , and Specificity. Mathematically, th ese parametes can be expressed as 100 ) (       FP TP FN TN TN TP A cc ur ac y (13) 100 ) (    FN TP TP y Sensit i vi t (14) 100 ) (    FP TN TN y Spec if i ci t (15) In the above equations, True Positive (TP), False Neg ative (FN), False P ositive (FP) and True Negative (TN) are evaluated from the respective confusion matrix for a ll eight classifica tion problems. True Positive and True Negative signifies the number of correctl y classified cases and on the other False posi tive and False n egative signifies the number o f mi sclassified cases. In the present stud y, seizure sig nal is considered as negative class, whereas healthy a nd interic tal ar e considered to be positive classes, respectively. Table-10 presents the performance pa rameters evaluated for ei ght CP s using S VM classifier. I n case of SVM, the kernel functions are varied and it ha s been observed that the hig hest classi fication accurac y is obtained for Radial Basis Function (RBF ) kernel compar ed to ot her kernel func tions. Hence, pe rformance pa rameters based on R BF kernel function have b een reported in this paper. To assess the reliable performance of the classifiers, a tenfold cross validation technique has been adopted in this work . and at the same time to increase the robustness o f the wo rk. The value of kernel parameter  of the RBF kernel fun ction in equation (13), should be opti mized meticulously , since it can affect the classifica tion accuracy significantly. The value of kernel parameter are g enerally selected using either a grid searc h a lgorithm or b y implementing any other optimization a lgorithm like PSO, GA etc. In the present work, a grid search algorithm has been emplo yed to find th e optimal value of  yielding highest classification accuracy. Table 10: Performance of the proposed method using SVM classifier CP Acc Sen Spe I (A,E) 100 100 100 II (B,E) 98.75 100 97.56 III (C,E) 100 100 100 IV (D,E) 100 100 100 V (AB,E) 100 100 100 VI (CD,E) 100 100 100 VII (AB,CD) 95.50 94.75 95.20 VIII (ABCD,E) 100 100 100 As it ca n be obse rved from Ta ble-10, that the maximum classifica tion a ccuracy of 100% is obtained for six cases out of eig ht CPs addressed in this paper. For CP-I, III , IV,V,VI and VIII, the proposed method y ielded maxim um a ccuracy of 100%. For CP-II a nd CP-VII, maximum accuracy of 98.75% and 95.50% have been achieved in this work. Besides, the maximum sensitivity and specificity of 100% has been obta ined for seven and six CPs , re spectively which is a significant improvement in comparison with t he existing results. Therefore it c an be s aid that the proposed method is highl y s ensitive and can also discriminate healthy, interical and seizure free EEG signals from seizure signals with utmost accuracy . 6.3 Performance analysis using different classifiers: In order to e nsure the robustness of the work, al ong with SVM, the performance of the proposed method is also being evaluated using different classifiers like k neare st Neighbour (kNN), D ecision Tree (DT) and Probablistic Neural N etwork (PNN). Table-11 report the classification accuracies obtained for eight CPs using SVM, kNN, DT and PNN classifiers. Table-11: Performance analysis using different classifiers CP SVM kNN DT PNN I 100 100 100 100 II 98.75 96.25 97.52 98.5 III 100 100 98.85 100 IV 100 98.45 100 98.72 V 100 100 99.15 100 VI 100 97.45 98.25 97.5 VII 95.50 92.75 93.50 94.25 VIII 100 98.25 97.75 100 It can be observed from Table-11, that 100% classification accuracy is obtained for six CPs using SVM classifie r, followed b y PNN whi ch r esults in 100% classification a ccuracy for four CPs. The performance of kNN and DT classifiers ar e al so reasonable satisfactory for all CPs, yielding 100% classification accuracy for three and two CPs respectively. However, the most important observation is that all classifiers ha ve d elivered c onsistent pe rformance i n c lassifying different EEG signals based on MFDFA based features for all ei ght CPs, which is an indica tor of the stable and reliable performance of the proposed work. 6.4 Comparative study with existing literatures: In this section, the performanc e of th e proposed method employing MF DFA base d feature extraction technique is compared with some state of the art techniques of seizure detection. Table-12 compare the cl assification accuracies obtained using the proposed method for CP-I- VIII, with the existing literatures studied on the same dataset, but usin g different methodolog y. It can be observed that the proposed method is c apable of delivering almost identical and for som e cases even better per formance in comparison with some existing results for all classification problems addre ssed in this paper. For CP-II, the results presented in [18] is highe r than the present work, but the method proposed in [18] used more number of feature sets as compared to the present work. For the rest of the CPs, the proposed method is found to outperform most of the recently publi shed results. Hence, the proposed metho d based on MFDFA based features has a reasonabl y high de gree of accurac y in detecting healthy, interictal and seiz ure free signals from epileptic seizure EEG signals and can be applied for clinical diagnosis of patients suffering from epilepsy. Table-12: Comparative study with state of the art methods CP Method Accuracy ( %) I ( A, E) Chandaka et al., [3] 95.96 Kaya et al., [12] 99.50 Sammie et al.,[31] 99.80 Supriya et al.,[17] 100 Swami et al., [30] 100 Sharma et al.,[18] 100 Proposed Work 100 II Nicoletta et al., [32] 82.9 ( B, E) Supriya et al., [17] 97.25 Sharma et al.; [18] 100 Proposed Method 98.75 III (C,E) Sammie et al., [31] 98.50 Supriya et al.,[17] 98.50 Swami et al., [30] 98.72 Sharma et al; [18] 99.00 Proposed Method 100 IV (D,E) Supriya et al.,[17] 93.25 Kaya et al., [12] 95.5 Swami et al., [30] 93.33 Sharma et al., [18] 98.50 Proposed Method 100 V (AB, E) Swami et al., [30] 99.18 Sharma et al., [18] 100 Proposed Method 100 VI (CD,E) Swami et al., [30] 95.15 Kaya et al. [12] 97.00 Sharma et al., [18] 98.67 Proposed Method 100 VII (AB,CD) Sharma et al., [18] 92.50 Proposed Method 95.50 VIII (ABCD,E) Sammie et al.,[31] 98.1 Swami et al., [30] 95.24 Sharma et al., [18] 100 Proposed Method 100 Conclusion In this paper, a novel feature extraction technique based on MFDFA is presented for automated detection and classifica tion of EEG signals. The EEG sig nals representing different states of human brain (healthy, inter -ictal and seizure) are at first analysed using MFDFA. It has been observed that the M FS of EEG signals during health y, inter -ictal and seizure states of brain behave diff erently indicating a wide variation in their nature of mul tifractality . From the MFS of five EEG signals, fourteen new features have been extracted to discrimi nate betw een diff erent types of EEG signals. After feature ranking employing student’s t -test, features with hi gh discriminative ability have been selected usin g SFS technique to serve as input feature sets for effective classification of EEG signals. SVM classifier have been imple mented in the pre sent work and its performa nce is also compared with several benchmark c lassifiers. Besides, eight different cl assification problems have been reported in this stud y and it has been observed that the proposed method is capable of yielding 100% classification accuracy in six cases indi cating the reliabilit y of the pr oposed work. The p erformance of the pr oposed MFDFA aided SVM classifier is also found to outperform the existing methods in terms of overall classification accuracy for man y classi fication problems. Hence, it can b e inferred th at the proposed method can be potentially implemented in practice for di agnosis of epilepsy. The present method has an added advantage of lower computational burden since MFD FA is computationally inexpensive compared to several other non linear analy sis techniques. However, the present anal ysis is based on a sin gle channel avail able EEG signal recording consisting of only 409 7 samples. It would be interesting to observe the efficacy of the proposed method when it is being applied to large EEG recordings and especiall y for multiple channels, which will be don e as a part of the future research work. The present work employing MFDFA based feature extraction technique will also be applied in future in the field of automated diagnosis of not onl y epilepsy but also several other neurological and neuromuscular disorders etc. REFERE NCES [1] U.R. Acharya, S.V.Sree, S. Chatto padhyay, W . Yu and P.C.A. 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