Epilepsy Diagnosis Using Directed Acyclic Graph SVM Technique in EEG Signals

In this research, we analyze the EEG signal to diagnose epilepsy disorders. The following section explains the diagnosis procedure.

2.1 Data acquisition and preprocessing

We use the Bern-Barcelona EEG Dataset for both training and testing purposes. This dataset is publicly available online. Five patients' EEG signals, studied 80 hours at Bern University Department of Neurology, are included in this dataset, which consists of 7,500 EEG signal pairs categorized into non-focal and focal signals. All signals were sampled and tested at 512Hz for 20 seconds, and 3750 focal and 3750 non-focal EEG data were utilized for the evaluation. For further analysis, we divided 3400 focal and 3400 non-focal EEG data into the training set and 350 focal and 350 non-focal EEG signals into the testing set. The major partitioning allows the evaluation of the proposed methodology for epilepsy diagnosis. We recorded the EEG signals during preprocessing and used the Discrete Fourier Transform (DFT) method to remove noise artifacts and interferences [25].

2.2 Feature extraction

The present investigation used DWT since it is an appropriate method for analyzing nonlinear and non-stationary signals. This research examines the classification of epileptic EEG data and evaluates performance. This study compares multiple classifiers [26]. The DWT uses a single function known as the mother wavelet, to investigate signal features in the frequency and temporal domains [27].

$\psi(t)=\frac{1}{\sqrt{2}} \psi \frac{(t-y)}{x} \quad x, y, \in S, x>0$           (1)

x and y represent the scaling and shifting parameters, while S represents the wavelet space parameter. We illustrate the Wavelet Transform as follows:

$F(x, y)=\frac{1}{\sqrt{x}} \int \psi \frac{(t-y)}{x} d t$         (2)

$\begin{aligned} F(t)= & \sum_{k=-\infty}^{k=+\infty} D_{n, k} \emptyset\left(2^{-n} t-k\right) +\sum_{k=-\infty}^{k=+\infty} \sum_{k=-\infty}^{k=+\infty} 2^{\frac{-j}{2}} A_{j, k} \psi\left(2^{-j} t-\right)\end{aligned}$         (3)

where, A_j,k and D_n,k are the approximate coefficients, $\psi$ is the scaling function, and n is the depth. EEG signal analysis involves descriptive coefficients at each phase and approximating coefficients at the final phase. We create feature vectors using the following signal:

Logarithmic band power (LBP)

$L B P=\log \left(\frac{1}{N} \sum_{n=1}^N|S(n)|^2\right)$             (4)

where, number of signal samples implies by N whereas S(n) is a discrete signal with n=1,2, 3....N.

Standard deviation (SD)

$S D=\sqrt{\frac{1}{N} \sum_{n=1}^N(S(n)-\mu)^2}$           (5)

Variance (VAR)

$\operatorname{Var}=\frac{1}{N} \sum_{n=1}^N(S(n)-\mu)^2$           (6)

Kurtosis (KUR)

$K U R=E\left[\left(\frac{S(n)-\mu}{\sigma_s}\right)^4\right]$          (7)

The predicted value shown by E[], We represent the Mean with µ, while σ_s denotes the standard deviation of the sample signal.

Average energy (AE)

$A E=\sum_{n=1}^N|S(n)|^2$         (8)

Root Mean Square (RMS)

$R M S=\sqrt{\sum_{n=1}^N|S(n)|^2}$         (9)

Further, to extract spatial patterns, the common spatial filtering is applied using the below equations:

$\begin{aligned} C_{P D} & =\frac{E_{P D} E_{P D^{\prime}}}{\operatorname{trace}\left(E_{P D} E_{P D^{\prime}}\right)} \\ C_{H C} & =\frac{E_{H C} E_{H C^{\prime}}}{\operatorname{trace}\left(E_{H C} E_{H C^{\prime}}\right)}\end{aligned}$         (10)

where, E_PD E_HC denote the EEG segments respectively.

2.3 Feature selection

In this work, features extracted by DWT are based on their linear correlation with the target variable, as defined by the Pearson correlation coefficient (PCC). Computing the Pearson correlation coefficient for each feature can help identify the most significant features with a strong linear link to the target.

$P(x, y)=\frac{\operatorname{Cov}(x, y)}{\sigma_x \sigma_y}$          (11)

$\operatorname{Cov}(x, y)$ indicates a covariance between x and y, whereas $\sigma_x$ and $\sigma_y$ are the corresponding standard deviations of x and y [28].

2.4 Classification model

A support vector machine (SVM) is a supervised machine learning model used for regression and classification. It finds the feature space hyperplane that most successfully separates classes [29]. The approach adopted in SVM is to find relevant patterns and differentiate non-epileptic and epileptic patients using EEG dataset recordings.

Decision DAG Classification Tree-DDAG tree has internal nodes that describe decision rules based on features, and leaf nodes indicate class labels. In their findings, Montanés et al. [30] suggested an outline of multiclass classification.

DAGSVM Classifier- DAGSVM is a machine-learning classifier for epilepsy diagnosis. It uses directed acyclic networks, which are ideal for making complex relations in EEG patterns. The process for detecting epileptic seizures described in this paper assembles binary classifiers in a directed acyclic graph and employs layered multiclass SVM and fuzzy-rule-based sub-band features. This method increases classification processing efficiency and high accuracy [31].

In contrast to existing multiclass SVM algorithms, this approach has more rapid testing and training times.

According to a power law $T={c m}^\gamma$, where m is the iteration count $\gamma \approx 2$ for decomposition-based algorithms, and c is a constant of proportionality. The training data generates all N classifiers using the conventional l-v-r multiclass SVM training technique.

Training for l-v-r takes,

$T_{\mathrm{l}-\mathrm{v}-\mathrm{r}}=c N m^\gamma$          (12)

If the classes are all the same size, the number of training examples needed to train each l-v-I SVM is merely 2m/N. Therefore, training in K l-v-I SVMs would be needed.

$T_{\mathrm{l}-\mathrm{v}-\mathrm{r}}=c \frac{N(N-1)}{2}\left(\frac{2 m}{N}\right)^\gamma \approx 2^{\gamma-1} c N^{2-\gamma} m^\gamma$     (13)

Training all 1-v-1 SVMs takes twice as long as training a solitary 1-v-r SVM, but this duration is independent of N. Therefore, we recommend a combination method for training one 1-v-1 SVM, where γ=2.

The paper proposes large-margin Directed Acyclic Graphs (DAGs) for multiclass classification. Their technique uses big-margin concepts to optimize classification accuracy while decreasing computational complexity by arranging SVM classifiers in a DAG framework [32].

Figure 2 represents the diagram of the three-layer classification decision DAG. The Decision DAG have internal and leaf nodes, each of which may belong to a distinct class. Until reaching a final diagnosis, the algorithm navigates through the Decision DAG, eliminating classifications along the way.

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Figure 2. Decision DAG classification tree [30]

Figure 3 illustrates epilepsy diagnosis using Decision DAGs, and we provide the steps for this process.

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Figure 3. Epilepsy diagnosis using decision DAGs

Execution of Epilepsy Diagnosis Using Decision DAG:

1. The flowchart begins by taking EEG data (input) as x for epilepsy diagnosis.
2. The data enters the root node of the Decision DAG, where we evaluate a binary function.
3. Depending on the outcome of the binary function evaluation, the algorithm proceeds either to the left edge or the right edge.
4. The internal nodes (internal node-1 and internal node-2) also perform binary function evaluations, and the algorithm navigates through the Decision DAG accordingly.
5. Every leaf node records the class connected with the leaf.
6. The function that makes the ultimate choice The class linked to the final leaf node in the evaluation route is D(x).
7. The result of the epilepsy diagnosis is determined based on the decision function, and the flowchart ends.

Decision DAGs are part of DAGSVM, which provides an improved representation of decision trees by allowing for the removal of unnecessary repetitions and redundancies between nodes. These are especially helpful for issues involving numerous classes, such as epilepsy diagnosis and generalizing the class of Decision Trees.

In Figure 4, the proposed methodology for EEG signal analysis and epilepsy disease diagnosis is shown.

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Figure 4. Proposed methodology

2.5 Proposed algorithm for EEG signal analysis and epilepsy disease diagnosis

Start

Step 1: Read the Bern-Barcelona EEG dataset as input variable → X

Step 2: Preprocessing (sampling, Noise artifact removal, Bandpass elliptic filtering, segmentation) using DFT (Discrete Fourier Transform):

$X_{ {preprocessed }}=$ $preprocess$ $(X)$

Step 3: Feature extraction using DWT (Discrete Wavelet Transform):

$D W T_{ {features }}=$$Extract$ $D W T$ $features$ $\left(X_{ {preprocessed }}\right)$

Step 4: Feature selection using Pearson correlation coefficient (PCC):

When comparing two characteristics, x and y, the PCC is considered as follows:

$P(x, y)=\frac{\operatorname{Cov}(x, y)}{\sigma_x \sigma_y}$

Selected_features=Select Features (DWT_Features)

Step 5: Classification using ML models (SVM, LS-SVM, DAGSVM, KNN, RF):

Model=Train Model (Selected_features)

Step 6: Test the model by classifying the test data as focal and non-focal EEG signals:

$Test \,data$ = $LoadTesData ()$

$Predictions$$=$ $Model.predict$$(Test$$_{ {data }})$

Step 7: Performance evaluation using (acc., press., recall, F-1 score):

True_lables=LoadTrueLables()

Metrics=Evaluate Model (Predictions, True_lables)

where,

X: Raw EEG signal dataset, $X_{ {preprocessed }}$: EEG data after preprocessing.

$D W T_{ {features }}$: Feature set obtained from Discrete Wavelet Transform.

$Selected _{ {features }}$: Feature set after feature selection.

Model: Trained ML model, ${Test}_{ {data }}$: Unseen test data for validation.

Predictions: Predicted labels (focal and non-focal) for the test data.

$True _{{labels }}$: True labels for the test data.

Metrics: Evaluation metrics, including accuracy, precision, specificity, and sensitivity

End

The proposed approach uses preprocessing, feature extraction, feature selection, and DAGSVM classification to enhance efficiency and address EEG data complexities. This novel method provides an accurate automated epilepsy diagnosis, which validates further real-time implementation and clinical validation for wider healthcare significance.

This study presents a novel machine-learning approach for classifying EEG signals. The EEG data is preprocessed using Discrete Wavelet Transforms to extract time and frequency domain features. With a 99.71% accuracy, 99.71% precision, 99.43% sensitivity, 99.71% specificity, 99.71% positive predictive rate (PPR), and 99.42% negative predictive rate (NPR), the DAGSVM classifier achieves the most suitable results. It better classifies EEG signals from all the classifiers used in this study.

Figure 8 shows the discrimination of features at different DWT (Discrete Wavelet Transform) decomposition levels. It illustrates the distinct behaviors and significance of the feature values for EEG signal analysis throughout the wavelet decomposition stages.

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Figure 8. Analysing feature discrimination across various DWT levels

In Table 2, P-values were determined and displayed to assess the discriminative features and their effectiveness. The fifth-level approximation sub-band signal's log energy entropy shows the lowest p-value, representing superior discriminative power among all features.

Table 3 contrasts the accuracy rates of several machine-learning methods that classify EEG signals. The sample EEG signals consisted of 350 focal and 350 non-focal signals. RF, KNN, SVM, LSSVM, and DAGSVM classified the signals as 342 focal and 345 non-focal, 347 focal and 345 non-focal, and 349 focal and 349 non-focal, respectively. RF obtains the lowest accuracy at 98.1%, while DAGSVM gets the best accuracy at 99.71%.

Figure 9 contrasts the accuracy rates of these models are as follows: DAGSVM (99.71%), KNN (98.80%), LSSVM (99.40%), RF (98.1%), and SVM (98.8%).

Table 2. Analysing feature discrimination across various DWT levels

Table 3. Machine learning models for EEG signal classification

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Figure 9. Machine learning models for EEG signal classification

Table 4 compares the performance of several machine-learning techniques for classifying EEG signals. It also displays PPR, NPR, accuracy, sensitivity, specificity, and precision. Table 4 illustrates that the DGSVM classifier attains the maximum sensitivity (99.43), specificity (99.71), precision (99.71), PPR (99.71), and NPR (99.42) among all the ML classifiers.

Table 5 compares the DAGSVM model with conventional techniques, presenting accuracy, sensitivity, and specificity values for SVM, Bidirectional LSTM, and Random Forest classifiers from different references.

Table 4. Machine learning models for performance analysis

Table 5. DAGSVM model comparison with various traditional methods

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Figure 10. Machine learning models for performance analysis

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Figure 11. Performance metrics for different models

Figures 10 and 11 visually display the assessment of machine learning models using performance metrics such as accuracy, sensitivity, specificity, precision, positive predictive rate (PPR), and negative predictive rate (NPR).