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The purpose of this study is to distinguish between different epileptic states automatically in an EEG. The work focuses on distinguishing activity of a controlled patient from interictal and ictal activity and also from each other. Publically available Bonn database is used in this study. Seven such cases are considered. For this study three entropy features: approximate entropy, sample entropy and fuzzy approximate entropy are extracted from frequency subbands and are used with six classification algorithms which are Naive Bayes, LDA (Linear Discriminant Analysis), QDA(Quadratic Discriminant Analysis) from the generative group and RF(Random Forest), GB(Gradient Boosting) and Ada Boost from the ensemble group. The performance is evaluated on basis ofClassification accuracy, Sensitivity and Specificity.The results obtained direct that LDA as a classifier from the generative class and Ada boost from the ensemble group has outperformed other classifiers achieving the highest classification accuracies for three cases each respectively. Evaluating the results from subbands, we find out that D2 (21.743.4 Hz) subband clearly outperformed all the bands. Among the entropies used as features from sub bands, sample entropy outperforms the other entropies. From the results obtained it is established that frequency features from higher subband such as D2 (21.743.4 Hz) contain substantial information which can be used for identification of epileptic discharges which are however missed during visual analysis. This shows the impact automated methods can make in the field of identification of ictal and interictal activity.
EEG classification, approximate entropy, sample entropy, fuzzy approximate entropy, random forest, AdaBoost, gradient boosting, naïve Bayes, linear discriminant analysis, quadratic discriminant analysis
Epilepsy is a seizure disorder in which range of severity varies with the patient. 9.72% people of 7.2 billion people worldwide suffer from epilepsy; out of this 17.14% reside in India [1]. Approximately more than a quarter people with this disease fall into the category where medication has no effect. Epileptic patients are also prone to SUDEP, which is sudden unexpected death during epilepsy. The death can occur during or post a seizure without any anatomical cause. Thus, making timely diagnose of epilepsy is of utmost importance. The time a patient spends having a seizure is fringe and is known as the ictal interval. This period is usually marked by sensory disturbances, loss of consciousness, convulsions, associated with abnormal electrical activity in the brain [1]. Patients usually get examined in their interictal interval. Epileptiform activity present in patients EEG (Electroencephalography) post the seizures is referred to as interictal activity. It is the time period where there is no clinical sign of epilepsy. However, it is not important for the interictal activity to be always present and detailed study of patient history is always required for neurologist to make diagnosis. EEG is a safe technique used for diagnoses and monitoring for the presence of epileptiform discharges. The visual interpretation of EEG data for identification of epileptiform activity is a difficult task and needs a high level of expertise. With an enormous number of cases, the time for evaluation by neurologist/epileptologist also increases. To identify interictal and ictal activity in EEG of a patient through automation has been a topic of interest for more than a decade. The goal of current work is to automate the process of EEG interpretation and facilitate in labeling of interictal and ictal activity in EEG amid of various artifacts. The brain waves captured through EEG can be divided into five types’ Delta (04 Hz), Theta (48 Hz), and Alpha (813 Hz), Beta (1330Hz) and Gamma range (3060 Hz). The beta waves and gamma waves are difficult to interpret visually and hence are overlooked by neurologist during visual analysis. This works contributes by considering the frequency band of higher frequency range and analyzing their contribution. Figure 1 shows the dissimilarity between electrical activities of controlled, inter ictal and ictal states of patients taken from Bonn database.
To identify interictal and ictal activity different linear and nonlinear parameters have been used along with different classifiers [2]. Entropy based parameters are popular among researchers as a feature and have been used for this problem over time such as in the researches [39]. Discriminative classifiers too have been the popular choice of researchers among which SVM (Support Vector Machine), ANN (Artificial Neural network) and ELM (Extreme Learning Machine) have been used most commonly with linear as well as nonlinear methods such as in the researches [1013]. Chandaka et al. [10] used correlation a nonlinear technique as a feature with MLPNN (Multilayer perceptron neural network)
Figure 1. EEG of all groups
and SVM as classifier. They reported classification accuracy of 93.2% and 95.96% of for case AE respectively. Rivero et al. [11] used relative wavelet energy from the five subbands decomposed using DWT (Discrete Wavelet Transform), and using ANN as a classifier. The classification accuracy of 95.52% was achieved for case AE. Song et al. [12] explored Sample entropy as a feature changing the value of parameter ‘m’ (embedding dimension) from one to three; and value of ‘r’ (tolerance window) from 10% 50% of standard deviation of data with increase of 10% at each step which is vector comparison distance. The value of N (Data Points) were also varied for which the chosen were 256, 512, 1024, 2048 and 4097. Extreme learning machines and BPNN were used as classifiers. Average learning accuracy of 95.67% with average learning time of only 0.25seconds was achieved using ELM (Extreme Learning Machines) with parameters m=3, r=0.1 times standard deviation and N=1024. The paper compared between the sets A, D and E (ADE).
In the study [13], Multilayer perceptron neural network based classification model was used to classify between five different cases. The cases considered were ABCDE, AE, ABCDE, ABCDE and ADE. Discrete Wavelet Transform (DWT) was used to decompose the signal into five respective sub bands. By implementation of k means wavelet coefficients were clustered for each frequency subband and probability distributions were computed. The classification accuracies of 99.6%, 100%, 98.8%, 95.6% and 96.67% respectively were achieved for the cases specified above in order.
Chen et al. [14] compared ELM and SVM using three nonlinear features approximate entropy, Sample Entropy and RQA. These were extracted from the wavelet decomposed subbands. The preeminent performance was achieved using Sample entropy and ELM achieving utmost accuracy of 92.6%. The study by Kumar et al. [15] depicts the potential of subbands extracted using wavelet transform, (A1A5) and (D1D5). The study used approximate entropy with values of parameters r and m being 0.2 times standard deviation and 0.2 respectively. Performance of Artificial neural network and support vector machine was compared when fed with each sub band as a feature. A total of six cases were considered in this work; which were case 1(AE), case 2(BE), case 3(CE), case 4(DE), case 5 (ACDE) and case 6 (BCDE). The highest classification accuracy of 100% was achieved using approximate entropy as a feature from sub band D1 (43.486.8 Hz) and FBNN for the case (AE) and case(CE) respectively. Kaya et al. (2014) [16] implemented different classifiers such as SVM, ANN, Naive Bayes and others were used with the 1DLBP approach for six cases. For case (AE) and case (AD) it achieved highest accuracy of 99.50% with FT and Naïve Bayes respectively. For all other cases which were DE, ECD, ABCDE and ADE it achieved top classification accuracy of 95.5%, 97%, 93% and 95.67% respectively with Bayes Classifier. The results showed that Bayes classifier had the potential for classifying between different groups.
The proposed method by Xiang et al. [17] used fuzzy approximate entropy with dimension of phase space as two, i.e. (m=2) and similarity tolerance (r=0.25 times standard deviation). This is calculated from subbands using discrete wavelet transform and classified using SVMRBF has shown 100% accuracy. Tawfik et al. [18] used weighted Per mutation Entropy (WPE) from different sub bands of EEG signal extracted using DWT were fed into SVM for classification. For the two cases considered, ABCDE and ADE the author reported highest accuracies of 97.5% and 93.75% respectively. Supriya et al. [19] edge weight method using visibility graph in the complex network was implemented. Features including the average weighted degree of the complex network were inspected and fed into support vector machine (SVM). For the considered case (AE), 100% of classification accuracy was achieved.
The aim of the work is to find the combination of entropy based feature and classifier which has the potential to distinguish between various considerations of inter ictal and ictal activity as well as interictal and controlled activity. The group division and cases considered for this work are described in Table 2. For this work firstly, three entropies (approximate entropy, sample entropy and fuzzy approximate entropy) used in this work, which are explained in section 2.2 are extracted from five subbands specified in discussed in section 2.2. The work consists of two scenarios, for the first we take each entropy feature extracted from all five subbands considered as a feature set and feed into all six classifiers. For second scenario we used all three entropies extracted from five subbands; but each subband was used individually as a feature set for all six classifiers. This was done to find out if entropy extracted feature extracted from a single subband has potential to distinguish between different groups. The results obtained by first scenario are shown in Table 37 and for second scenario are shown in Table 810. Also, this work focuses to find if it is possible to successfully classify between different cases using a single sub band; considering this each entropy based feature which is extracted out of five subbands is used as only feature for all six classifiers. With the proposed method the D2 subband achieved highest classification accuracy of 100% for case 4(CE). Also this sub band showed potential as important frequency range for feature extraction. The results obtained by using entropy extracted from each subband as only feature are discussed in Table 810. Comparison with existing methods is also established in Table 12.
2.1 EEG database and group division
Table 1. Details of data used
Total Data Folders 
5 
Controlled Group 
2(A,B) 
InterIctal 
2(C,D) 
Ictal 
1(E) 
Time period of Signals 
23.6 seconds 
Sampling Frequency of Signal 
173.6 Hz 
Total no. of Data Points in each Signal 
4097 
Table 2. Division of groups for classification
Group 1: Healthy Ictal 

Case 1 
AE 
Case 2 
BE 
Case 3 
ABE 
Group 2: Inter Ictal and Ictal 

Case 4 
CE 
Case 5 
DE 
Case 6 
CD E 
Group 3: Healthy and Inter Ictal 

Case 7 
ABCD 
Figure 2. Methodology
Data is taken from the online source, University of Bonn [20]. The data available is already divided into five folders and three basic groups i.e. Controlled, Epileptic in ictal period and Epileptic in interictal period. Each folder has 100 files, taken from 5 healthy and 5 epileptic subjects. Folder A and B contain data from healthy patients collected using surface electrodes. C and D have interictal data and folder E has ictal data collected using the intracranial method. Table 1 hold detail about the data.
Figure 2 depicts the work flow for the current work.
The first step is to divide the data into groups as per the aim of the work. Table 2 holds the summary of the division.
2.2 Feature extraction
The brain waves are divided into five waves which are Delta (04 Hz), Theta (48 Hz), and Alpha (813 Hz), Beta (1330Hz) and Gamma range (3060 Hz). Different features linear and nonlinear are extracted from these waves and are most generally used for seizure classification [21, 22]. In this work to understand the contribution of different frequency subbands and apprehend the role of higher frequency subbands in differentiating epileptiform discharges discrete wavelet transform was applied to the signal. The sampling frequency of the data is 173.6 Hz. DWT divides the complete frequency into different levels where each level of discrete wavelet transform corresponds to a specific subband. For this work level five decomposition is implemented using db4 wavelet. The level 5 was chosen as this decomposition allows to divide the subbands in frequency ranges closest to the required ranges of delta, theta, alpha, beta and gamma. Moreover, after the selected frequency range there is more possible of occurrence of the artefacts such as 50Hz (power line artefact).
The decomposition divides the data into following frequency: A5 (02.7125), D5 (2.715.4), D4 (5.410.8), D3 (10.8521.7) and D2 (21.743.4). Figure 3 diagrammatically shows the process.
Figure 3. Level 5 decomposition using DWT
From these subbands three nonlinear entropy based features approximate entropy [23], sample entropy [24] and fuzzy approximate entropy [25] were extracted. Since the data is of 23.6seconds, we extract the features using complete data length. The entropy based features are Here N is the number of data points which is 4097 for all the three entropy parameters. In this work for all entropy features the value of m (embedding dimensions) is taken as 2 is and r (vector comparison distance) is 0.3 times the standard deviation of the signal.
DWT formula:
$f(x)=\frac{1}{\sqrt{M}} \sum_{k} W_{\phi}\left(j_{0}, k\right) \phi_{j_{0}, k}(x)$
$+\frac{1}{\sqrt{M}} \sum_{j=j_{0}}^{\infty} \sum_{k} W_{\varphi}(j, k) \varphi_{j, k}(x)$ (1)
where, j_{0} is an arbitrary starting scale
$W_{\phi}\left(j_{0}, k\right)=\frac{1}{\sqrt{M}} \sum_{x=0}^{M1} f(x) \ddot{\phi}_{j_{0, k}}(x)$ (2)
$W_{\phi}\left(j_{0}, k\right)$ is called the approximation or scaling coefficients
$W_{\psi}=\frac{1}{\sqrt{M}} \sum_{x=0}^{M1} f(x) \breve{\psi_{J, k}}(x)$ (3)
$W_{\psi}$ is called the detail or wavelet coefficients
2.2.1 Approximate entropy
It is the likelihood that runs of patterns that are close remain close on next incremental comparisons. It is a measure of complexity that is applicable to noisy, mediumsized datasets. A high value of Approximate Entropy indicates random and unpredictable variation, whereas a low value of Approximate Entropy indicates regularity and predictability in a time series.
$A_{E}(m, r, N)=\frac{1}{Nm} \sum_{i=1}^{Nm} \ln \frac{n_{i}^{m}}{n_{i}^{m+1}}$ (4)
2.2.2 Sample entropy
Sample Entropy does not amount a selfmatch, thus eradicating the prejudice in the direction of regularity. Sample Entropy has been suggested to be independent of data length and demonstrates relative consistency. It is less sensitive to noise.
$S_{E}(m, r, N)=\ln \frac{\sum_{i=1}^{Nm} n_{i}^{m}}{\sum_{i=1}^{Nm} n_{i}^{m+1}}$ (5)
2.2.3 Fuzzy approximate entropy
In a real world scenario it is difficult to categorize an input to a specific class. Fuzzy approximate entropy works on this concept. With the concept of Lotfi, Zahed theory membership degree is introduced by fuzzy function u_z (x) having a real value between the range [0, 1].
For N data points u (i) =u (1), u (2), u (3)…..u (N) for finding the fuzzy approximate entropy
$X_{i}^{m}=\left\{u(i), u(i+1), \ldots \ldots u(i+m1\}u_{0}(i)\right.$
for i=1,2,3…Nm+1 (6)
$u_{0}(i)$ is baseline value:
$u_{0}(i)=\frac{1}{m} \sum_{j=0}^{m1} u(i+j)$ (7)
Distance $d_{i j}^{m}$ between two vectors $X_{i}^{m}$ and $X_{j}^{m}$ is defined as:
$d_{i j}^{m}=d\left[X_{i}^{m}, X_{j}^{m}\right]=m a x_{k €(0, m1)}  \mathrm{u}(\mathrm{i}+\mathrm{k})u_{0}(i)$
$\left(u(j+k)u_{0}(j) , \mathrm{j} \neq \mathrm{I}\right.$ (8)
For a given r, the similarity degree $D_{i j}^{m}$ between $X_{i}^{m}$ and $X_{j}^{m}$ is determined by a fuzzy membership function u ($d_{i j}^{m}, r$).
$D_{i j}^{m}=u\left(d_{i j}^{m}, r\right)$ (9)
$\mathrm{u}\left(d_{i j}^{m}, r\right)=\exp \left(^{d_{i j}^{2}} / r\right)$ (10)
$C_{r}^{m}(i)=\frac{1}{Nm+1} \sum_{j=1, j \neq i}^{Nm+1} D_{i j}^{m}$ (11)
$\varphi^{m}(r)=\frac{1}{Nm+1} \sum_{i=1}^{Nm+1} \ln \left[C_{r}^{m}(i)\right]$ (12)
$\mathrm{FAE}(\mathrm{m}, \mathrm{r}, \mathrm{N})=_{\varphi}^{m}(r)_{\varphi}^{m+1}(\mathrm{r})$ (13)
2.3 Classification
Two different categories of classifiers have been used in this work, generative class and ensemble class. The models are LDA, QDA, Naive byes, Random Forest, Ada boost and Gradient Boosting. For random forest, Ada boost and gradient boosting; 10 trees are used for this work. For gradient boosting algorithm the value of alpha which is the regularization coefficient is set to 1.
2.4 Data division
The data is divided into training (70%) and testing (30%). Performance parameters of the testing data are used for the comparison and evaluation.
2.5 Performance evaluation
Parameters which will evaluate the performance such as Accuracy, Sensitivity, Specificity, and Recall are calculated.
2.5.1 Accuracy
Proportion of people correctly identified into their actual groups i.e. in case1 (AE) the accuracy will be high if all samples are allocated to their actual group.
2.5.2 Specificity
It is the measures the percentage of genuine positive cases that are suitably recognized as such. For example in case1 AE, specificity will be high if number of signals correctly identified as ictal; i.e. correctly classified in group E will be high.
2.5.3 Sensitivity
Specificity events the percentage of actual negatives that are fittingly recognized as such for example in the case of B E; the sensitivity will be high if the proportion of people identified as a controlled group i.e. with no epileptic discharge will be high.
EEG signals from different sets were decomposed into subbands A5 (02.71 Hz), D5 (2.715.4 Hz), D4 (5.410.8 Hz), D3 (10.8521.7 Hz) and D2 (21.743.4 Hz). From these decomposed subbands approximate entropy, Sample entropy and fuzzy approximate entropy were computed. Six different classifiers LDA, QDA, Naive Bayes, Random Forest, Ada Boost, and Gradient Boosting are used in this study. The following table summarizes the results obtained when each type of entropy was extracted from five specified sub bands and used as set of features for a classifier; Table 37 hold the results for this scenario.
For Case 1 (AE) the highest classification accuracy of 96.67% has been achieved by using a combination of Fuzzy Approximate Entropy and Naive Bayes as well as with Sample Entropy and Random Forest. In Case 2 the highest accuracy of 96.67% is achieved by using LDA as classifier and sample entropy or approximate Entropy as a feature. Also, for case 2 the ensemble models achieved the same result with respect to classification accuracy; when Random forest and Adaboost are used as classifiers with the combination of approximate entropy or sample Entropy as feature from all subbands.
Table 3. Results by generative models on case 1, case2, case 4 and case 5

AE 


LDA 
QDA 
Naive Bayes 


SE 
AE 
FAE 
SE 
AE 
FAE 
SE 
AE 
FAE 
AC (%) 
90 
90 
85 
95 
91.66 
95 
93.33 
93.33 
96.67 
SP (%) 
96.15 
92.05 
95.65 
96.55 
96.29 
100 
96.42 
100 
100 
SN (%) 
85.29 
87.5 
78.37 
93.54 
87.87 
90.90 
90.62 
88.23 
93.75 

BE 


LDA 
QDA 
Naïve Bayes 


SE 
AE 
FAE 
SE 
AE 
FAE 
SE 
AE 
FAE 
AC (%) 
96.66 
96.67 
91.66 
88.33 
93.33 
91.66 
90 
91.67 
81.66 
SP (%) 
100 
100 
93.10 
87.09 
100 
93.10 
96.15 
100 
73.17 
SN (%) 
93.75 
93.75 
90.32 
89.65 
88.23 
90.32 
85.29 
85.71 
100 

CE 


LDA 
QDA 
Naïve Bayes 


SE 
AE 
FAE 
SE 
AE 
FAE 
SE 
AE 
FAE 
AC (%) 
96.66 
96.67 
88.33 
98.33 
100 
91.67 
98.33 
95 
91.67 
SP (%) 
100 
100 
100 
96.77 
100 
100 
96.77 
100 
100 
SN (%) 
93.75 
93.75 
81.05 
100 
100 
85.71 
100 
90.90 
85.71 

DE 


LDA 
QDA 
Naïve Bayes 


SE 
AE 
FAE 
SE 
AE 
FAE 
SE 
AE 
FAE 
AC (%) 
80 
83.33 
73.3 
86.66 
81.66 
86.67 
73.33 
71.66 
68.33 
SP (%) 
84.61 
85.71 
93.75 
92.30 
85.18 
92.30 
81.81 
84.21 
64.86 
SN (%) 
76.47 
81.25 
65.90 
82.35 
78.78 
82.35 
68.42 
65.85 
73.91 

AE 


Random Forest 
Gradient Boosting 
Ada Boost 


SE 
AE 
FAE 
SE 
AE 
FAE 
SE 
AE 
FAE 
AC (%) 
96.6 
95 
95 
95 
95 
95 
91.679 
95 
93.33 
SP (%) 
93.75 
93.54 
93.54 
96.55 
93.54 
96.55 
87.87 
96.5 
96.42 
SN (%) 
100 
93.54 
96.52 
93.54 
96.55 
93.54 
96.29 
93.54 
90.62 

BE 


Random Forest 
Gradient Boosting 
Ada Boost 


SE 
AE 
FAE 
SE 
AE 
FAE 
SE 
AE 
FAE 
AC (%) 
96.67 
91.66 
88.33 
86.66 
93.33 
83.33 
95 
96.66 
95 
SP (%) 
100 
100 
87.09 
95.83 
100 
88.46 
96.55 
100 
93.54 
SN (%) 
93.75 
85.71 
89.65 
80.55 
88.23 
79.41 
93.54 
93.75 
96.55 

CE 


Random Forest 
Gradient Boosting 
Ada Boost 


SE 
AE 
FAE 
SE 
AE 
FAE 
SE 
AE 
FAE 
AC (%) 
98.33 
95 
88.33 
96.66 
100 
85 
100 
98.33 
90 
SP (%) 
100 
100 
96 
100 
100 
88.88 
100 
100 
96.154 
SN (%) 
96.77 
90.90 
82.57 
93.75 
100 
81.81 
100 
96.77 
85.29 

DE 


Random Forest 
Gradient Boosting 
Ada Boost 


SE 
AE 
FAE 
SE 
AE 
FAE 
SE 
AE 
FAE 
AC (%) 
86.66 
83.33 
81.66 
86.66 
76.66 
83.33 
86.66 
85 
81.66 
SP (%) 
86.66 
83.33 
77.30 
95.83 
80.76 
85.71 
82.35 
83.87 
85.18 
SN (%) 
86.66 
83.33 
75.67 
80.55 
73.52 
81.25 
92.30 
86.20 
78.75 
Cases 4 and 5 achieved similar accuracy in all subbands. In Case 4, 100% accuracy, specificity and sensitivity were achieved with RF+SE or RF+AE for D2; 85% accuracy was achieved with SE+LDA, SE+QDA, and SE+ Naïve Bayes for D3. In Case 5, 86.67% accuracy was achieved with AdaBoost+SE and with AdaBoost+AE for D2.
Table 5. Results by all models on case 3
Case 3 (ABE) 


Approximate Entropy 
Sample Entropy 
Fuzzy Approximate Entropy 


AC (%) 
SN (%) 
SP (%) 
AC (%) 
SN (%) 
SP (%) 
AC (%) 
SN (%) 
SP (%) 
LDA 
93.33 
90.91 
100 
92.22 
89.55 
100 
88.89 
85.71 
100 
QDA 
93.33 
93.55 
92.86 
93.33 
93.55 
92.86 
93.33 
93.55 
92.86 
Naive Bayes 
90 
91.80 
86.21 
90 
91.80 
86.21 
96.67 
96.72 
96.55 
Adaboost 
91.11 
91.94 
89.29 
92.22 
94.92 
87.10 
90 
89.23 
92 
RF 
82.22 
69.44 
90.74 
93.33 
92.86 
93.55 
76.67 
59.57 
95.35 
Gradient Boosting 
83.33 
92.45 
70.27 
93.33 
93.55 
92.86 
77.78 
93.48 
61.36 
Table 6. Results by all models on case 6
Case 6 (CDE) 


Approximate Entropy 
Sample Entropy 
Fuzzy Approximate Entropy 


AC (%) 
SN (%) 
SP (%) 
AC (%) 
SN (%) 
SP (%) 
AC (%) 
SN (%) 
SP (%) 
LDA 
83.33 
86.89 
75.86 
83.33 
86.89 
75.86 
75.56 
77.941 
68.18 
QDA 
81.11 
89.09 
68.57 
81.11 
89.09 
68.57 
81.11 
89.091 
68.57 
Naive Bayes 
75.56 
82.76 
62.5 
75.56 
82.76 
62.5 
70 
77.966 
54.84 
Adaboost 
78.89 
100 
61.22 
78.89 
81.54 
72 
78.89 
81.538 
72 
RF 
78.89 
61.70 
97.67 
80 
63.04 
97.73 
80 
66.667 
88.89 
Gradient Boosting 
82.22 
89.29 
70.59 
82.22 
89.29 
70.59 
78.89 
85.97 
66.67 
Table 7. Results by all models on case 7
Case 7 (ABCD) 


Apen 
Sample Entropy 
Fuzzy Approximate Entropy 


AC (%) 
SN (%) 
SP (%) 
AC (%) 
SN (%) 
SP (%) 
AC (%) 
SN (%) 
SP (%) 
LDA 
55 
54.69 
55.36 
60 
58.82 
61.54 
80 
92.86 
73.08 
QDA 
69.17 
64.94 
76.74 
73.33 
70.59 
76.92 
64.17 
70.73 
60.76 
Naive Bayes 
55 
53.26 
60.71 
55.83 
54.12 
60 
70.83 
73.59 
68.66 
Adaboost 
69.17 
69.49 
68.85 
70.83 
70.49 
71.19 
60.83 
65.85 
58.23 
RF 
79.17 
73.97 
87.23 
75 
72.06 
78.85 
66.67 
61.91 
77.78 
Gradient 
67.5 
69.09 
66.15 
76.67 
79.63 
74.24 
64.17 
68.09 
61.64 
Table 8. Results of generative models with sub bands by sample entropy and approximate entropy or case 1, 2, 4 and 5

AE 


LDA 
QDA 
Naive Bayes 


Sample Entropy 
Approximate Entropy 
Sample Entropy 
Approximate Entropy 
Sample Entropy 
Approximate Entropy 


CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 

D3 
85 
76.92 
100 
83.3 
75 
100 
83.33 
76.32 
95.46 
83.33 
76.32 
95.46 
83.33 
76.32 
95.46 
83.33 
76.32 
95.46 

D4 
80 
75 
87.5 
73.3 
69.4 
79.1 
80 
76.5 
84.6 
70 
66.7 
75 
80 
76.5 
84.6 
70 
66.7 
75 


CE 


LDA 
QDA 
Naive Bayes 


Sample Entropy 
Approximate Entropy 
Sample Entropy 
Approximate Entropy 
Sample Entropy 
Approximate Entropy 


CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 

D3 
85 
76.9 
100 
81.7 
73.2 
100 
85 
76.9 
100 
83.3 
75 
100 
85 
76.9 
100 
83.3 
75 
100 

A5 
81.7 
77.1 
88 
66.7 
66.7 
66.7 
76.7 
71.1 
86.4 
66.7 
61.9 
77.8 
76.7 
71.1 
86.4 
66.7 
61.9 
77.8 
Table 9. Results of ensemble models with sub bands by sample entropy and approximate entropy or case 1, 2, 4 and 5

Random Forest 


AE 


Approximate 
Sample 
Fuzzy 


CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 
D2 
85 
78.38 
95.65 
85 
76.92 
100 
91.66 
93.10 
90.32 

Adaboost 

D2 
85 
100 
76.92 
86.67 
95.83 
80.56 
85 
76.92 
100 
D3 
85 
76.92 
100 
85 
76.92 
100 
61.67 
56.60 
100 

BE 


Random Forest 

D2 
93.33 
88.23 
100 
86.66 
82.35 
92.30 
81.66 
75.67 
91.30 
Adaboost 

D2 
93.33 
88.24 
100 
93.33 
88.24 
100 
86.67 
78.95 
100 
A5 
73.33 
70.59 
76.92 
66.67 
63.16 
72.73 
68.33 
64.10 
76.19 

CE 


Random Forest 

D2 
100 
100 
100 
100 
100 
100 
85 
83.87 
86.20 
Adaboost 

DE 

D2 
86.67 
100 
78.95 
86.67 
100 
78.95 
73.33 
93.75 
65.91 
Table 10. Results of ensemble models with sub bands by fuzzy approximate entropy or case 1, 2, 4 and 5

Fuzzy Approximate Entropy 


DE 


LDA 
QDA 
Naive Bayes 


CA 
SN 
SP 
CA 
SN 
SP 
CA 
SN 
SP 
A5 
73.33 
69.44 
79.17 
61.67 
57.78 
73.33 
61.67 
57.78 
73.33 
EEG sub bands, A5 (02.7 Hz), D5 (2.715.4 Hz), D4 (5.410.8 Hz), D3 (10.8521.7 Hz) and D2 (21.743.4 Hz) were considered for this work. The data was divided into three groups and seven cases. Three entropy features which are approximate entropy, sample entropy and Fuzzy approximate entropy were calculated for all five subbands for each set for each sample. From analysis it has been observed that subband D2 plays important part in identification of interictal and ictal discharges. Each set had a total of a hundred samples. The below given line plots with depict how approximate entropy and sample entropy for various samples of set C and set D vary for sub band D2.
In Figure 4, Figure 5, Figure 6 and Figure 7 the xaxis denotes the sample number and yaxis denotes the value of corresponding approximate entropy or sample entropy of the sub band D2 of specified set. From Figure 4 and Figure 5 it is evident that for subband D2 of set C has an evidently higher approximate entropy and sample entropy of subband E. Both the entropy features show a very similar trend when compared for set C and set D. In Figure 6 comparison of approximate entropy of subband D2 for set D and Set E is done while Figure 7 compares both the sets on sample entropy of samples obtained from sub band D2 .From these it is evaluated that both parameters i.e. approximate entropy and sample entropy of sub band set D lie in the lower spectrum compared from set E.
Figure 4. Line plots of Approximate entropy for case 4
Figure 5. Line plots of Sample Entropy for case 4
Figure 6. Line plots of Approximate Entropy for case 5
Figure 7. Line plots of sample entropy for case 5
The results obtained established that D2 subband has outperformed other bands as a singular feature with different classifiers. Table 11 summarizes the result obtained by D2 subband.
Table 11. Performance analysis of D2 sub band
D2 sub band 

Case 
CA (%) 
Feature 
Classifier 
AE 
91.66 
FAE 
RF 
BE 
93.3 
AE 
RF 
BE 
93.3 
AE 
ADABOOST 
BE 
93.3 
SE 
ADABOOST 
CE 
100 
AE 
RF 
CE 
100 
SE 
RF 
DE 
86.67 
AE 
ADABOOST 
DE 
86.67 
SE 
ADABOOST 
To establish a fair comparison this work is compared with other works done on similar lines. Table 12 holds comparison of current work with the previous work done by researchers. Kumar et al. [15] used approximate Entropy with artificial neural network and support vector machine; both of which are discriminative classifiers. For the work case 1, case 2, case 4 and case 5 considered in this study, were also evaluated along with some others. Comparing the results, we find that for case 2 using approximate entropy with LDA and Ada boost algorithm we achieved highest accuracy of 96.67% which is an improvement from 92.5% by the previous research. Xiang et al. [17] fuzzy approximate entropy and sample entropy were used with support vector machine for case 4 and case 5 considered in this study. Though, with Fuzzy approximate entropy and SVM 100% classification accuracy was achieved in both the cases; but with Sample entropy the accuracy yielded were 88.6% and 88.5%. In this study improvement with use of sample entropy has been achieved by its combination with all the other classifiers, where with Ada boost it achieved 100% accuracy and with LDA and Gradient Boosting it achieved 96.6% and with QDA and NB it achieved 98.33%. The improvement was also seen in parameters of specificity and sensitivity where the highest of 100% for both parameters was reached by the combination of this parameter with Ada Boost. Conventional features such a mean absolute value, standard deviation and others [26] were extracted from sub bands D3D5 and A5 and classifiers SVM and Naïve Bayes was used in this work for classification. Case 4 used in this study was also considered by them; the researchers achieved 99.5% classification accuracy with 12 features; while, Kumar et al. [25] achieved highest accuracy of 99.6% for the same case with fuzzy entropy using all five sub bands. However, this study achieved 100% in all three statistical parameters with single sub band D2 with approximate entropy and random forest as well as with sample entropy and random forest.
Table 12. Comparison with existing work
Researcher and Year 
Signal Used 
Features Extracted 
Classification 
Data 
Cases Considered 
CA% 

Kannathal et al. 2005 [7] 
 
Entropy measures 
Neurofuzzy inference system 
Bonn Data 
AE 


92.25 


Umut Orhan et al. 2011 [13] 
DWT 
Clustered K means Coefficients of all sub bands 
MLPNN 
Bonn Data 


Yatindra Kumar et al. 10 August 2014 [15] 
Discrete wavelet transforms (DWT)

Approximate entropy (ApEn)· 
Artificial neural network (ANN)·Support vector machine (SVM) 
Bonn Data 


5fold scheme 

holdout method 

Yatindra Kumar et al. 20 January 2014 [25] 
Discrete wavelet transforms (DWT) 
Fuzzy approximate entropy 
Support vector machine (SVM) 
Bonn Data 


Jie Xiang et al. 10 January 2015 [17] 
Complete Signal 
Fuzzy approximate entropy Sample approximate entropy 
SVM 
Bonn Data
CHBMIT 


Current Work 
DWT 
Sample Entropy, Fuzzy Approximate Entropy, Sample Entropy 
Naïve Bayes, LDA, QDA, Ada Boost, Gradient Boost, Random Forest 
Bonn Data


Among the entropies used as features from sub bands, sample entropy outperforms the other entropies. It achieved highest accuracy with combination with Random forest for case 1. With LDA and Random forest for case 2. For case 4 and case 5 with Ada boost as well as Gradient Boosting; and only with LDA for case 6. LDA has outperformed all the classifiers achieving the highest accuracy for five out of seven cases which are case 2, case 3, case 4, case 6 and case 7. For case 2, case 3 and case 6 it provided the highest accuracy with approximate entropy while for case 4 and case 7 it was the combination of sample and fuzzy approximate entropy. Naive Bayes achieved the highest accuracy in consideration for case1 with fuzzy approximate entropy. Among the ensemble methods Ada boost has achieved the highest accuracy for case 2 with approximate entropy and case 4, case 5 with Sample Entropy. Gradient boosting achieved the highest accuracy for case 4 with Approximate Entropy. The D2 sub band has outperformed all the other sub band; it achieved accuracy as high as achieved using all the sub bands together for case 3 and case 4 which was 86.66% and 100% respectively. Ada boost has achieved the highest accuracy for case 2 and case 5 with sample and approximate entropy. While Random forest has achieved with case 4 and case 2 with sample and approximate entropy.
The authors would like to acknowledge Dr R.G.Andrzejak of University of Bonn, Germany, for providing permission to use the EEG data available in the public domain.
SE 
Sample Entropy 
AE 
Approximate Entropy 
FAE 
Fuzzy Approximate Entropy 
LDA 
Linear Discriminant Analysis 
RF 
Random forest 
QDA 
Quadratic Discriminant Analysis 
NB 
Naive Bayes 
SVM 
Support vector Machine 
ELM 
Extreme Learning Machine 
SP 
Specificity 
SN 
Sensitivity 
AC 
Accuracy 
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