Epilepsy and Seizure Detection Using JLTM Based ICFFA and Multiclass SVM Classifier

Epilepsy is a disorder that affects the absence of neural stimulation in patients [1]. More recent evidence [2] shows that approximately 40 million across the globe are affected by epilepsy problems in the United States. Earlier detection of this risk of uncontrolled seizures and curing epileptic seizures in the patient at the right time can save the patient’s life. For the past ten years, there has been a rapid rise in using clinical research trials based on epilepsy circumvention techniques are in progress. These are very useful for epilepsy patients and can enable them to take tentative action to care for them from damage or follow precautionary treatment. Current solutions to seizure prediction are inconsistent, even the best approaches suffer from an inconsistency between sensitivity (able to predict seizures) and accuracy (circumvention of false alarms). Similarly, various approaches have been proposed by Ji et al, and Xia and Leung [3, 4] towards the multi-channel EEG signals for epileptic seizure detection. Most studies have focused on machine learning (ML) and optimization algorithms to improve epilepsy detection accuracy and make the process automatic. However, there is still a need for improvement of estimation of epilepsy detection and for classification problems; the optimization methods of feature selection (FS) can achieve high classifying accuracy. By combining other non-linear features, they can further improve accuracy. To optimize the feature selection, it uses an optimization algorithm and several other methods for the selection of sub-sets with multiple search strategies and evaluation functions have been developed and used. Standard optimization algorithms recently developed to find global solutions for combinatorial optimization problems. Some feature selection optimization has recently proposed, which includes Grey Wolf Optimizer (GWO) [5]. However, it should be noted that it generates the initial population of unique GWO randomly that lacks the diversity for the wolf swarms during the search space which makes it computationally time-consuming. Whale optimization algorithm (WOA) [6] is a new heuristic random intelligent algorithm based on population. However, whale optimization algorithm has the disadvantage of slow convergence speed because of its incapability of exploring the search space.

The Butterfly Optimization Algorithm (BOA) [7] introducing the migrate operator, the created monarch butterfly will be adopted in the next generation as a new monarch butterfly, no matter if it is good or even worse. Since the search, strategy of BOA easily falls into local optima, results in the reduced performance and early convergence on several complex optimization problems. In addition, classical particle swarm optimization (PSO) is suggested by Adamczyk [8] for the problem of continuous optimization, does not fit for issues of binary solution space feature selection. The principle of ant colony optimization (ACO) is to imitate the way actual ants find the best solution vector between their nest and a food supply. The ACO algorithm [9] and its iterations have long been considered resolving issues of combinatorial optimization. However, ACO’s performance is undesirable as each ant has to look for a valid solution, and the duration is large.

By constructing a relatively minimal number of feature subsets for assessment, the above-discussed methods find an optimal solution. Using some pre-determined assessment measure, it then tests the candidate subsets. In addition, the algorithm’s output depends upon the proper tuning factor and iterations involved. The FFA population-based [10] that replicates the flashing properties of fireflies to search for potential search space features. Initial population selection plays a significant role both quantitatively and qualitatively in the speed of global convergence and the efficiency of swarm-based optimization methods.

This encourages our efforts to put forward an improved version of FFA to deal with the feature selection problems. This concept has therefore inspired us to create a diversified initial population of the problem using logistic map it uses based CFFA for optimal collection of subset features from the diversification population. Therefore, there is need of improving the traditional firefly optimization algorithm further that can solve the feature selection problem with minimal efforts. Since chaotic map alone cannot achieve wide range, we use CFFA with Joint logistic-tent map (JLTM) is suggested in this work by combining the discovery and exploitation to cope with further feature selection problems.

In this sub-section the proposed Epilepsy proposed epilepsy framework comprises of five phases such as dataset collection, signal pre-processing, feature extraction (FE), feature selection (FS) (i.e., optimization), and classification (see Figure 1). The first & second phases are the EEG dataset followed by the pre-processing phase with precise filtering strategies to remove artifacts. The third phase is a feature extraction of statistical features (SF1-SF9), entropy features (EF1-EF2) with the assistance of Power Spectral Density (PSD), Common spatial pattern (CSP), and Autoregressive (AR) model. The fourth phase CFFA performs the feature selection process that results in reduced feature subset (RFS1, RFS2, ..., RFSn) which can be used to build and test the multi-class SVM classifier (M-SVM) in the final phase.

3.1 EEG data selection

In this paper, we used the publicly available data set [16] that comprises of 5 sets, namely (A, B, C, D, and E), each with 23.6 seconds of EEG blocks with 100 individual channels. EEG recordings with severe artifacts like activity in eye muscles, and noise variations can be removed using Principal component analysis (PCA) with automatic target generation process (ATGP), and other artifact removal methods [17]. In this work, we are concerned with a three-class case that accompanies with the PSD, which provides us an energy distribution across frequency bins, whose frequency ranges differ and which can be very useful for extraction. The CSP procedure helps to separate the relevant and non-relevant channels from EEG signals (i.e. channel selection). Finally, the use of a prediction filter AR pattern improves EEG signal accuracy [18].

The first phase is the EEG dataset followed by the pre-processing phase with precise filtering strategies to remove artifacts. The third phase is a feature extraction of statistical features (SF1-SF9), entropy features (EF1-EF2) with the assistance of PSD, CSP, and AR model. The fourth phase CFFA performs the feature selection process that results in reduced feature subset (RFS1, RFS2, ..., RFSn) which can be used to build and test the multi-class SVM classifier in the final phase.

3.2 Preprocessing

The preprocessing phase is customized to suit all requirements of artifacts and noise removal to preserve the EEG rhythms. All the specifications are provided in the proposed diagram.

3.3 Feature extraction

It is the process of decreasing the amount of data (i.e., dimension) for obtaining less computation time for further process. The epileptic EEG varies considerably with the frequency, duration, intensity of the regular EEG signal, etc.

Feature vectors Extraction using DWT: Each EEG signal is decomposed by discrete wavelet transformation (DWT) into 5 constituent EEG sub-bands. We analysed the EEG epochs into different frequency bands using 4th-order wavelet feature Daubechies (db4) up to 4^th level of decomposition as shown in Figure 2. The EEG signals were then decomposed into D1-D4 information and one final approximation of A4. For each EEG segment, the first, second, third, and fourth-level detail-wavelet coefficients (d^k, k = 1, 2, 3, 4) in the order of (129 + 66 + 34 + 18 coefficients) and fourth-level approximation wavelet coefficients (a4) (18 coefficients) were determined. Thereafter, 265 wavelet coefficients for each EEG section were obtained. The wavelet coefficients of the EEG signals formed the first diverse feature vector representing the EEG signals.

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Figure 1. Overview of proposed 5-phase framework

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Figure 2. Arrangement of discrete wavelet transform (DWT)

In this paper, we have extracted the statistical values like Standard deviation (SD), Entropy, Variance, Median, Kurtosis, Skewness, Co-variance, Energy of wavelet coefficients from each sub-band that were chosen to classify EEG signals. By removing the data redundancy that has been stored in continuous wavelet transformation, DWT enables computation simpler and more efficient. To evaluate both frequency components, DWT of a signal s[n] is considered as it passes through a series of low pass filter (LPF) and high-pass filter (HPF).

$Ylow[n]=s[n]*g[n]=\sum\limits_{k=-\infty }^{\infty }{s[k]}.g[n-k]$     (1)

$Yhigh[n]=s[n]*h[n]=\sum\limits_{k=-\infty }^{\infty }{s[k]}.h[n-k]$      (2)

In Eqns. (1) and (2) the terms g[n] and h[n] indicate the impulse response of both filters (i.e. LPF and HPF). Although it undergoes down sampling the filter does not loss any information.

$Ydownsample[n]=\sum\limits_{k=-\infty }^{\infty }{s[k]}.g[2n-k]$     (3)

Shannon entropy method: This is the strongest lossless compression available, which provides low and high values of entropies that can be formulated asIn addition to boost the classifiers performance Shannon and Renyi entropies are used as parameters for classifier.

$E(S)=-q\sum\limits_{i=1}^{n}{pi\log 2pi,q=1}$     (4)

where, S signifies the EEG signal, p_i the average probability and n the total number of EEG signal vector count.

Renyi entropy method: Renyi is the generalized from of Shannon entropy with α=1 and quadratic entropy with α=2, so their respective equation can be written as

$Eq(S)=\frac{1}{1-q}\log \sum\limits_{i=1}^{n}{\mathop{pi}^{q}}$     (5)

where, q≥0 and q≠1. Here, q in the Eq. (5) signifies the entropy order and variable n stand for total values of EEG data.

3.4 Feature selection

The primary goal of this work is to reduce the number of selected features and improve classification accuracy that can be treated to be multi-objective optimization problem. To take these two goals into consideration, so it can be formulated as a linear weighting solution to the fitness function as

$\Psi FS=x.E+y\frac{R}{C}$      (6)

and

$E=\frac{\text{ No}\text{. of wrongly predicted instance}}{\text{ Total number of instances}}$                (7)

In Eq. (7) E denotes the classification error, R denotes selected features from the subset C denotes total number of features available in the dataset. The weights used in comparisons x and y meet two of these objectives.

Firefly optimization Algorithm: The primary intention of the sub-section is twofold. First, to exemplify the improving firefly through the development of chaotic maps for chaotic FFA and second, to use logistic-tent maps (LTM) for faster convergence, and robustness to solve feature selection problem. According to Marie-Sainte' study [19] the flash frequency reduces as distance (r) rises with that of the equation

$I\left( r \right)={{I}_{0}}{{e}^{-\gamma {{r}^{2}}}}$        (8)

Attractiveness (β) is described in the map with an absorption coefficient (γ) and distance (r) as

$\beta \left( r \right)={{\beta }_{0}}{{e}^{-\gamma {{r}^{2}}}}$        (9)

The Cartesian distance between and two i^th and j^th fireflies at x_i and x_j respectively, the Cartesian distance is determined by

${{r}_{ij}}=\sqrt{\sum\limits_{k=1}^{d}{{{\left( {{x}_{i,k}}-{{x}_{j,k}} \right)}^{2}}}}$      (10)

where, x^i,k is the k^th element of the x of i^th firefly d space coordinate, the number of dimensions is. The firefly movement happens if it is drawn to another (brighter) j^th firefly that is defined by the equation.

${{x}_{i}}={{x}_{i}}+{{\beta }_{0}}{{e}^{-\gamma r_{ij}^{2}}}\left( {{x}_{j}}-{{x}_{i}} \right)+\alpha \in$     (11)

${{\beta }_{0}}{{e}^{-\gamma r_{ij}^{2}}}\left( {{x}_{j}}-{{x}_{i}} \right)$ is due to attraction.

α ϵ is due to randomization.

α is the randomization parameter.

ϵ is a vector of random numbers drawn from Gaussian or uniform distribution.

According to Gupta' study [20], the algorithm involves in decreasing the randomness gradually and incorporating the social dimension for every firefly (i.e., global best). The distance function (r_i) put in the mathematical form as

${{r}_{i,best}}=\sqrt{{{\left( {{x}_{i}}-{{x}_{gbest}} \right)}^{2}}+{{\left( {{y}_{i}}-{{y}_{best}} \right)}^{2}}}$      (12)

The movement of i^th firefly is determined by the equation

$x_{i}=x_{i}+\left(\beta_{0} e^{-\gamma r_{i, j}^{2}}\left(x_{j}-x_{i}\right)+\beta_{0} e^{-\gamma r_{i, \text { best }}^{2}}\left(x_{\text {gbest }}-x_{i}\right)\right)+\alpha \in+\lambda \in\left(x_{i}-g_{\text {best }}\right)$      (13)

Here i^th because the firefly came up with the best solutions if there was no perfect local best solution in the neighborhood. This above algorithm thus decreases the algorithm randomness so that convergence is achieved rapidly and affects fireflies’ movement towards global optimal, thus decreasing the algorithm's probability caught in several local optima.

In Eq. (13) α is the randomization parameter and ∈ is the random number vector. Although the algorithm has no specific selection criterion, it changes each firefly in each iteration step and ranks it by fitness value and then selects individual potential. The classifier learning accuracy decides the fitness value and the firefly with the higher value that is known as a potential individual. The fitness function considered here for evaluating the feature sub-set is seen in the updated Eq. (13)

$\begin{align}  & \mathop{Fitness}_{val}=\eta *\mathop{predictive}_{acc} \\ & +\left( 1-\eta  \right)*\mathop{feature}_{redu} \\\end{align}$      (14)

In Eq. (14) η(1-η) and (1-η) are the parameters corresponding to weight of the learning accuracy.

Chaotic Maps: Chaos is a stochastic movement defined by a deterministic equation which varies from the phenomena of irregularity and disorder. Chaos has a perfect internal structure. Random, ergodic and regular with three characters. Ergodic property can test all states in a certain range by its formulas. This has made chaos a technique accessible that keeps them from getting trapped in local optima and increases the search efficiency globally. In this paper, the firefly’s population is instantiated and we substitute the continuous absorption of the coefficient value with chaotic maps (see Figure 3).

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Figure 3. Chaotic map processing

Three parameters regulate an initial feature, i.e. the random movement step size α, attractiveness β and absorption coefficient γ. In Eq. (14), the first parameter affects the randomized term α$\in $i, in which we set the randomized parameter $\in $i using chaos time series.

$\mathop{\in }_{i}=\mathop{C}_{i}^{(k)}$      (15)

Following chaotic-enhanced form,

$\mathop{\beta }_{i}=\mathop{\beta }_{0}\mathop{C}_{i}^{(k)}$       (16)

Remarkably, the firefly social factor of move can be specified by approximately overviews based on Yang' study [21]. The most commonly utilized chaotic activity is the logistic map and tent map. They are both close and exhibit chaotic dynamics. Chaotic sequences can rapidly and efficiently be produced and processed, without long sequence storage. In this paper, chaotic sequences incorporated in ICFFA is used to calculate the initial weight values where k shows the number of iterations and the logistic map and the tent map.

Logistic maps are expressed as

$\mathop{x}_{k+1}=\mathop{\mu x}_{k}\left( \mathop{1-x}_{k} \right)$     (17)

where, $\mu \in [0,4]$ and $x\in [0,1]$, x_ktakes any value from 0 to 1 belongs to the feature-extraction input value. k is the number of iterations; μ is the interval control parameter (1, 4) to decide how many maps numbers to complete the function collection are needed. A number sequence provided by the iteration of a logistic map (orbit also) with μ = 4 is chaotic. For values above 4 (μ > 4). The maps return negative values that reduce the efficiency of the algorithm.

Tent Map: It is an iterated method that shapes a discreet dynamic system is in the shape of a tent. It begins on the actual line from a point x_k and maps it to a different end. It is an equation with a certain value of the control parameter (μ). With chaotic behavior, it is rather dynamic. It describes the map of the tent as

$x_{k}+1=\left\{\begin{array}{c}\mu x_{k} / 2, \text { for } x_{k}<0.5, \\ \mu\left(1-x_{k}\right) / 2, \text { for } x_{k} \geq 0.5\end{array}\right.$      (18)

where, μ is in the range [0, 2] and it is a positive real constant.

Tent map suffers from periodic window conflicts. Conversely, the classical chaotic systems such as the tent and logistic maps have certain inadequacies such as non-uniform data distribution. In the current article, we use Joint Logistic-Tent Map (JLTM) to ease periodic window issues. The multiple chaotic map shows a stable chaotic distribution between 0 and 4.

Similarly, Lyapunov’s exponent of multiple chaotic map like Logistic-Tent Maps (LTM) are seen in Figure 4(a) shows positive values that lies in the range of (0, 4), while in Figure 4(b) and Figure 4(c), Lyapunov’s one-dimensional map exponent has a set of non-positive values for logistic map (LM) and tent map (TM). So we used Logistic-Tent Maps (LTM) in the current paper to study.

Joint Logistic-Tent map (JLTM): It is multiple chaotic maps that can solve the problem of one-dimensional chaotic map can be inferred as stated earlier non-uniform distribution over output series that causes false selection in the features. To resolve we embed functions and weights to the model as (19a).

$x_{k+1}=G_{\mu}\left(x_{k}\right):$$=\left\{\begin{array}{l}\omega_{1} f_{1}^{\circ} F\left(\mu, x_{k}\right)+\alpha_{1} g_{1}\left(\mu x_{k}\right) \\ +\xi_{1} \frac{\left(\beta_{1}-\mu\right) x k}{2} \bmod 1, \text { when } x_{k}<0.5 \\ \omega_{2} f_{2}^{\circ} F\left(\mu, x_{k}\right)+\alpha_{2} g_{2}\left(\mu_{x k}\right) \\ +\xi_{2} \frac{\left(\beta_{1}-\mu\right)\left(1-x_{k}\right)}{2} \bmod 1, \text { when } x_{k} \geq 0.5\end{array}\right.$      (19a)

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Figure 4. Lyapunov Exponent of multiple and Single Chaotic Map (a) Logistic-Tent map (LTM) (b) Logistic map (LM) (c) Tent map (TM)

where, F(μ, x_k) is Logistic map. In (19a), f_i(x) and g_i(x) (i = 1, 2) for all the trigonometric functions. Correspondingly the terms, ω_i, α_i, ξ_i and β_i (i = 1, 2) are real numbers and parameter μ $\in $ (0, 4]. For discrete time system (DTS) as (19a), the Lyapunov exponent for an orbit beginning with x₀ is demarcated as

$LE(\mathop{x}_{0},\mu ):=\underset{n\to \infty }{\mathop \lim \frac{1}{n}}\,\sum\limits_{i=0}^{n-1}{\ln \left| \mathop{G}_{\mu }^{'}(\mathop{x}_{i}) \right|}$       (19b)

The degree of “sensitivity to initial conditions” measured with the help of the Lyapunov exponent. The pseudocode of a FFA with Joint Logistic-Tent map (ICFFA) for feature optimization (see Figure 5), the different parameter values for the ICFFA model (see Table 1).

Table 1. Parameter settings for the ICFFA model

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Figure 5. Pseudocode of an FFA with Joint Logistic-Tent map (ICFFA)

3.5 Classification

Several optimal feature subsets are supplied to the classifier to improve the performance. The viability of the framework is supported by comparison metrics with literature works. Taking advantage of extending binary classifier to multi-class classifier using SVM, we opted this for classification of EEG data. In this current study we dealt with three-class case, so the Multi-class SVM classifier is adopted by allocating code word with length N given as

$t(c)\in \mathop{\{-1,0,1\}}^{N}$       (20)

$t(c)\in \mathop{\{0,1\}}^{N},t(c)\in \mathop{\{-1,1\}}^{N}$      (21)

or for each class c. To eliminate over fitting problem in learning process some sort of slack terms is embedded with function f that can be written as

$Maximize\frac{\lambda }{M}\sum\limits_{m=1}^{M}{\mathop{\ell }_{m}}+\Omega \{f\}(m\arg in)$       (22)

To maintain the minimal distance between embedded function f, correct class target of interest t(y) and non-target of interest t(c). Then it can be generalized to optimized problem to the minimizing as

$Minimize\frac{\lambda }{M}\sum\limits_{m=1}^{M}{\mathop{\ell }_{m}}+\Omega \{f\}$       (23)

From the above analysis, it is explicitly that MSVM classifier optimal problem is w.r.t the soft margin and distance function d.

In this paper we proposed an integrated framework to Detect the epilepsy by proposing the framework of EEG signal exploration with the Multi-class SVM and Improved Chaotic Firefly algorithm (ICFFA). To accomplish the process of training/testing the classifier, this approach used the features obtained by statistical (DWT) and entropy-based examination for each subject of EEG data. After we built the feature set, a feature selection based on a chaotic mapping-based firefly version called ICFFA was used, which decreased the insignificant features to result in optimal feature subset. For obtaining this, two types of chaotic maps, a logistic map and a tent map, are used in combined form on FFA. However theses chaotic maps display different dynamic behavior between [0, 1]. The behavior affects the search ability of ICFFA. Then an MSVM classifier was trained with 70%, 80%, and 90% of data and tested with 30%, 20%, and 10% of the data, respectively. The Experimental results shows that the proposed technique (ICFFA+MSVM) attained a satisfactory accuracy of 99.63% for Normal data (Set A and B) and an accuracy of 98.10%, 97.3% of the JC, and 85.77% of precision (averaged for Normal, Inter-ictal and Ictal classes of data with 90% training). Also experimental results show that ICFFA with joint Logistic-tent map obtained higher success rate than CFFA alone with a logistic OR Tent map alone.