Effectiveness of Multi Input Data and a Novel CNN Model for Epilepsy Classification

4.1 Pre-processing

In biomedical signal processing, there are different methods applied for pre-processing and filtering of non-stationary signals, that are contaminated by artifacts during acquisition such as EEG that it can reduce the quality of these signals. Most of these methods are widely used encompass Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT) and Discret Wavelet Transform (DWT) in time and frequency domains.

4.1.1 Short Time Fourier Transform (STFT)

Short Time Fourier Transform (STFT) convert the signal from the time domain to the time-frequency domain. It uses a sliding window function that is multiplied with the signal x(t), and Fast Fourier Transform (FFT) is applied to find the spectrogram which contain characteristics in both time and frequency. It can be defined mathematically by Eq. (1):

${STFT}(v, u)=\int_{-\infty}^{\infty} x(t) w(t-u) e^{-j v t} d t$            (1)

where, x is the signal, w: is the window function, and t is the time period. By using STFT, the spectrogram (S) of signal is the energy around the time-frequency ($v$, u), and can be obtained by Eq. (2) [17, 23, 31].

$S=|{STFT}(v, u)|^2$              (2)

4.1.2 Continuous Wavelet Transform (CWT)

The most popular method for signal processing is the wavelet transform (WT) contains large amount of information, that characterizes the EEG signals. The continuous wavelet transform (CWT) is defined by using mother wavelet which provides a list of scales of signal that can be analyzed [31]. It can surmount the problem of redundancy of STFT, and it has high temporal resolution than Fourier Transform. Other advantages of CWT are detailed by Mao et al. [17]. The results of the CWT are presented with scalograms and the mother wavelet (φ) can form a basis set of CWT denoted by Eq. (3) [23].

$\left.\left\{\varphi_{s, u}(t)=\frac{1}{\sqrt{s}} \varphi\left(\frac{t-u}{s}\right)\right\}\right|_{u \in R, s \in R^{+}}$         (3)

where, s is the scale parameter, u is the translation parameter that represents the position of the wavelet along the time axis. The CWT of signal x(t) described by Eq. (4) [17, 28, 32, 33].

${CWT}(s, u)=\int_{-\infty}^{\infty} x(t) \frac{1}{\sqrt{s}} \varphi^*\left(\frac{t-u)}{s}\right) d t$                  (4)

4.1.3 Discret Wavelet Transform (DWT)

CWT has some limitations related to the problem of redundancy, because it uses continues implementation of coefficients that the reconstruction of the original signal is expensive [34]. However, the Discret Wavelet Transform (DWT) characterized by non-redundancy that it uses two successive filters high and low pass filters. DWT decomposes the signal x(t) into sub-bands called approximation coefficients A_i(k) and detail coefficients D_i(k) at i^th level of decomposition (Figure 3), they are calculated mathematically by Eq. (5) and Eq. (6), respectively [22, 24].

$A_i(k)=\left\{\frac{1}{\sqrt{N}} \sum_x f(x) \cdot \varphi_{j, k}(x)\right\}$           (5)

$D_i(k)=\left\{\frac{1}{\sqrt{N}} \sum_x f(x) \cdot \psi_{j, k}(x)\right\}$         (6)

where, A_i(k): approximation coefficients; D_i(k): details coefficients; N: length of signal x; φ: mother wavelet function; ψ: scaling function. The high-pass filter (g) used the wavelet function j_j,k(x), and the low-pass filter (h) used scaling function y_j,k(x) denoted by Eq. (7) and Eq. (8), respectively [24].

$\varphi_{j, k}(x)=2^{j / 2} g\left(\left(2^j x-k\right)\right.$            (7)

$\psi_{j, k}(x)=2^{j / 2} h\left(\left(2^j x-k\right)\right.$           (8)

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Figure 3. DWT decomposition at three levels

4.2 Feature extraction

This step is crucial for features extraction from different sub-bands after decomposition with DWT in time, frequency and time-frequency domains [35], and nonlinear analysis [36, 37], for using in the classification approach [38]. These statistical features including mean, variance, coefficient of variation [39], standard deviation, Skewness, Kurtosis [40], max and min [36], root mean square and Renyi entropy [41, 42]. They are determined by equations from Eq. (9) to Eq. (18). where, N is the length of signal x(t).

(1) Mean (µ)

$\mu=\frac{1}{N} \sum_{i=1}^N x_i$            (9)

(2) Variance (σ²)

$\sigma^2=\frac{1}{N} \sum_{i=1}^N\left(x_i-\mu\right)^2$            (10)

(3) Coefficient of variation

$\mathrm{CV}=\frac{\sigma^2}{\mu^2}$             (11)

(4) Standard deviation (σ)

$\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^N\left(x_i-\mu\right)^2}$           (12)

(5) Skewness (sk)

$s k=\frac{1}{N} \sum_{i=1}^N\left(\frac{x_i-\mu}{\sigma}\right)^3$             (13)

(6) Kurtosis (kr)

$k r=\frac{1}{N} \sum_{i=1}^N\left(\frac{x_i-\mu}{\sigma}\right)^4$             (14)

(7) Max and min

$\max =\max \left[x_N\right]$              (15)

$\min =\min \left[x_N\right]$             (16)

(8) Root mean square (RMS)

$R M S=\sqrt{\frac{1}{N} \sum_{i=1}^N\left(x_i\right)^2}$             (17)

(9) Renyi entropy (REn)

$R E n=\frac{1}{1-q} \ln \left(\sum_{i=1}^N p_i^q\right)$              (18)

where,

$\left\{\begin{array}{c}0<q<\infty \\ q \neq 1\end{array}\right.$

4.3 Classification approach

4.3.1 Support Vector Machine (SVM)

Support Vector Machine (SVM) is a supervised ML classifier used for classification and regression tasks [43, 44]. It based on learning of data then classified them into different classes [45, 46]. Initially, it was introduced by Vapnik and Cortes in 1995 for binary classification, that it consists to separate data into two classes by planes or called support vectors which can be described by Eq. (19) and Eq. (20)

$W^T x+b=1$             (19)

$W^T x+b=-1$          (20)

where, W: positions of the hyperplane, x: data points and b take value of +1, -1 [47, 48].

The hyperplane is separated with the same distance between support vectors, that it requires to increase the margin width to obtain the optimal hyperplane [44] (Figure 4), for minimizing errors of misclassification. The optimal hyperplane can be described by Eq. (21) [46, 49, 50].

$W^T x+b=0$             (21)

The margin is the minimum distance from support vectors separating each class to the hyperplane presented in Eq. (22) [51].

$M=\frac{2}{\|w\|}$              (22)

2.4.png

Figure 4. Linear SVM [45]

After that, the SVM was developed for multiclass and nonlinear data [35, 42]. Nonlinear SVM tricks to transform data into higher dimensional feature space based on mapping function (Φ) using kernel functions (Kf) [48, 49] defined in Eq. (23). Kernel functions are radial basis kernel function [43, 52], linear kernel function, polynomial and sigmoid kernel function [53], that used to find the hyperplane to separate data [54].

$K f\left(x_i, x_j\right)=\Phi\left(x_i\right)^T \Phi\left(x_j\right)$              (23)

4.3.2 Convolutional neural network (CNN)

Convolutional neural network (CNN) is very used in signal and image analysis which is constructed of multiple and successive layers [1, 14]. Its structure consists of several convolution layers with Rectified Linear Unit (ReLU) to extract features, pooling layers which is widely used for dimensionality reduction and avoid the problem of redundancy in feature extraction [31, 55], thus fully connected layer, Softmax and output layer [56, 57].

·Input layer

In this paper, the input layer corresponds to the input images that used after selection of MID which are spectrograms and scalograms images.

·Convolutional layer

The convolution layer is used to extract features from the input images, it convolves the input data or from the previous layer by shifting a filter to produce the feature map. The feature map h^k is determined by convolving input image (I) with weight filter W^k and adding the bias b^k as described by Eq. (24):

$h_{i j}^k=f\left(\left(W^k * I\right)_{i j}+b_k\right)$            (24)

where, h: is the output of the convolution layer, f is the activation function, W is the weights, and b is the bias. The size of the feature map depends on three parameters: depth, stride, and padding [56, 58].

·Batch normalization

Batch normalization is applied to each layer to make the mean zero and normalize the variance [57].

·Rectified Linear Unit (ReLU) Layer

Rectified Linear Unit (ReLU) is a non-linear function that defined by Eq. (25) that it substitutes all negative pixel values in the feature map by zero with the purpose of introducing non-linearity in the network [57].

$f(x)=\max (0, x)$             (25)

·Pooling layer

The pooling layer is used to reduce data dimensionality and controls the overfitting. Different types of pooling operation are widely used including max-pooling and average-pooling [1]. In this work, the maxpooling layer is applied where the maximum value in each window is determined [57, 58].

·Flatten layer

The Flatten layer is used before fully connected layer to convert a multidimensional tensor into a one-dimensional tensor to facilitate its processing [58].

·Fully connected layer

The fully connected layer is used after the convolutional layer and max-pooling layer. The purpose of the fully-connected layer is to use these features for classifying the input image into various classes based on the training dataset [56, 57].

·Output layer

The output layer used to show the classification results that it predicts different classes based on the features obtained from the fully-connected layer [8]. The two of the most widely used activation functions for classification are Softmax and sigmoid functions. In this study, Softmax which is used as an activation function [56], that the range values of Softmax is between (0,1). The mathematical equation of Softmax is defined by Eq. (26) [59].

${Softmax}\left(x_i\right) \frac{e^{x_i}}{\sum_{k=1}^K e^{x_k}}$             (26)

where, x input and i=1, …, k.

Softmax provides more effective results for binary and multiclass classification. Each class presented by probabilities as outputs and the highest probability value can be considered as the output that each class gives the best prediction [7].

4.4 Proposed framework

The objective of this work is to develop and build an accurate, robust and reliable framework for epileptic disease detection using deep learning in EEG signals. Thus, it will be compared with machine learning technique including two types of SVM classifiers.

4.4.1 Classification with SVM

In the first stage, DWT is applied to decompose EEG signals into different sub-bands. Then, statistical features are extracted in time-frequency domain from these subbands. After that, two models of SVM are applied for classification process including linear SVM (LSVM) and quadratic SVM (QSVM). The bloc the framework is illustrated in Figure 5.

4.4.2 Classification with MID-CNN model

In the second stage, a proposed MID-CNN model of deep learning is examined. Before that, the EEG signals are processed and converted to different spectrogram and scalogram images by using STFT and CWT, respectively defined by multi-input data (MID). After that, the selected images of MID with dimensions of 228x228x3 are input to the MID-CNN network for extraction features and classification. The bloc diagram of the proposed model is shown in Figure 6. The MID-CNN model composed of two layers C1 and C2 with one convolutional layer (Conv1 and Conv2) in each layer, followed by a batch normalization (BN), Rectified Linear Unit (ReLU), and max pooling (MP) layers. The first convolutional layer used 16 filters with kernel dimensions of 5×5, and the second employed 32 filters with kernel dimensions of 3×3. Batch normalization is applied to each layer to make the mean zero and normalize the variance. For the next layer, ReLU have been used as an activation function which it has a faster execution time when compared to the tanh and sigmoid activation function. Then, this is followed by max pooling layers with dimensions of 2 ×2, to mitigate overfitting of the dimension of each feature map and effectively reducing its spatial dimensions that the MP layers down sampling data with a pooling size of 2. Then, a flatten layer (FL), one fully connected (FC) layer, and a Softmax output layer are used. After the flattening process, the fully connected layer comprising 128 units that is used for dimensionality reduction. Different names and types of MID-CNN layers is presented in Table 2, and parameters of the configuration is detailed in Table 3. Subsequently, this model is simple which required only in their architecture two layers compared with other algorithms that they used more layers. Thus, the convolution layers used for this network used minimum number of filters. The CNN component effectively extracts spatial features from the images input data. Moreover, this approach based on MID-CNN network and augmentation of data collecting with MID input images ensures that this model reaches with an optimal performance level.

4.4.3 Training and validation

The most common measure of success in deep learning is the accuracy that the mean purpose is how many of the objects in the data set were correctly classified. The splitting of training and testing in this paper is used by 90% for training and 10% for testing. A more advanced set of validation techniques known as cross-validation is employed and known as k-fold cross-validation. To select a value of k, the advantage of higher values is obvious that retaining more data for training. In this work, 10-fold cross-validation is used. However, the common disadvantage is that higher values of k significantly increase the time required for training, and associated with higher variance of the accuracy estimated [28, 31].

Table 2. Architecture of the proposed MID-CNN

Table 3. Parameters of the configuration [22]

4.5 Performance evaluation

The performance evaluation provides the effectiveness of classification approach by computation of statistical parameters defined by accuracy (ACC), sensitivity or recall (SEN), specificity (SPE), precision (PRE) and F1-score (FSC) which are implemented and defined by Eq. (27), Eq. (28), Eq. (29), Eq. (30) and Eq. (31), respectively [23, 26, 41].

$A C C=\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}}(\%)$           (27)

$SEN (recall)=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}(\%)$              (28)

$S P E=\frac{T N}{T N+F P}(\%)$             (29)

$P R E=\frac{T P}{T P+F P} \times 100$            (30)

$F S C=\frac{2 * { precision } * { sensitivity }}{{ precision }+ { sensitivity }}$           (31)

where, TP: true positive, FN: False negative, TN: True negative, FP: False positive.

2.5.png