The proposed patient-independent epileptic seizures detection model is illustrated in Figure 1, which includes three subnets. (1) Multi-level temporal-spectral feature extraction network, (2) feature separation network, and (3) invariant feature extraction network. The feature extraction network extracts temporal feature information and frequency domain feature information from EEG data (Li et al., 2020), and performs enhanced characterization by the Squeeze-and-Extraction Network (Hu et al., 2018), so that the extracted features are discriminable; the feature extraction network is illustrated in Figure 2. The feature separation network disentangles the features into category-related features and patient-related features. Finally, the invariant feature extraction network extracts the invariant patient-independent features by aligning the marginal distribution and the conditional distribution; so the generalization ability of the model is improved.

Electroencephalogram data is two-dimensional data similar to images, which has uncertainties and incidences; therefore, it is necessary to preprocess the original data; we use min-max regulation technology to regulate the data. You can also refer to Rahim et al. (2016) and Versaci and Morabito (2021) for preprocessing.

As convolution operators are essentially equivalent to a low-pass filter (Azimi et al., 2019), the embedding block, the embedding block, that is, successive temporal convolution and batch normalization (BN) operations, is first adopted to infer an optimal filter-band for the subsequent analysis. As a result, after stacking original data and output embeddings with a channel-wise concatenation function, the embedding block obtains a sub-band matrix, which provides a subsequent network with adaptive sub-band responses and also original data. Finally, the data is fed into the multi-level spectral feature extraction module and the multi-level temporary feature extraction module for feature extraction.

In the multi-level temporal-spectral feature extraction network, in order to prevent the deformation of the boundary data caused by zero padding in the convolution operation, the head and tail of the data are filled according to formula (1):

Where, | is a concatenating operator, x(i) is the i-th element of input x, R representing the parameter kernel size in the convolution operation.

In order to reduce the time of data computation, the proposed method adopts convolution operation to perform multi-level wavelet decomposition, which is defined as follows:

Where, ⊗ is the convolution operation, g and h represent a pair of scaling and wavelet filter, s represents the parameter stride in the convolution operation, y_A(i) is the approximation (low pass) coefficients, and y_D(i) is the detail (high pass) coefficients.

In the multi-level spectral feature extraction module, to extract the corresponding wavelet coefficients under standard physiological sub-bands δ(0∼4 Hz), θ(4∼8 Hz), α(8∼16 Hz), β(16∼32 Hz), and γ(32∼64Hz), we select Daubechies order-4 (Db4) wavelet, since previous studies reported that Db4 mother wavelet is useful for epileptiform transient detection due to its high correlation coefficients with the epileptic spike signal (Indiradevi et al., 2008). Finally, the frequency features (f_δ, f_θ, f_α, f_β, f_γ) are obtained.

In the multi-level temporal feature extraction module, considering the data distribution shift between subjects, we use five independent convolution, batch normalization and empirical linear unit (ELU) operations to capture multi-level temporal feature information with different receptive fields. The convolution kernel size is set to [S, 1], the value of S is {k, k, k/2, k/4, k/8}, k = 2⁵, and finally, the temporary features (f_t1,f_t2,f_t3,f_t4,f_t5) are obtained.

To further extract discriminative feature information, the features extracted by the multi-level spectral feature extraction module and the multi-level temporal feature extraction module are combined according to the feature dimensions:

The combined features f_all are fed into Squeeze-and-Excitation Network to enhance feature discrimination.

The feature information (category information, patient information, etc.) is contained in each dimension and intertwined. If the features can be disentangled by the feature separation network, the separability and discriminability of the features will be improved. Therefore, according to the prior knowledge, we separate the features which are obtained from the feature extraction network into two parts, the first half of the features is the category-related component, which is recorded as F_{category_related}, the second half of the features is the patient-related component, which is recorded as F_{patient_related}. In addition, to ensure the first half of the features are the category-related component, the category classifier and cross-entropy loss function are used, to ensure the second half of the features are the patient-related component, the patient classifier and cross-entropy loss function are used, to ensure better separation of the features of the two parts, the maximum divergence loss function is used to ensure the maximum separation of the category-related component and the patient-related component (Bui et al., 2021).

The loss function of the category classifier and the patient classifier is:

Where, N is the number of samples, x_i is the data sample, G_f is the feature extraction network, G_c1 is the category classifier, G_p is the patient classifier, L is the cross-entropy loss function, y_i is the category label (seizure or normal), d_i is the patient label, D_s ∈ D₁ ∪ D₂… ∪ D_n (D₁,D₂,……, D_n are the data of each patient).

To separate category-related component (F_{category_related}) and patient-related component (F_{patient_related}), we use the maximum divergence loss function:

Then combine the separated features to create new features:

The feature separation network effectively disentangles the features and improves the discrimination of the features, but the current features are not the invariant features of each patient. To improve the generalization ability of the model, the proposed method is based on the methods of DANN (Domain-adversarial training of neural networks) (Ganin et al., 2016; Yu et al., 2019) and MADA (Multi-adversarial domain adaptation) (Pei et al., 2018) to achieve better invariant feature learning. The global patient discriminator aligns the features of each patient according to the marginal distribution. The local patient discriminator aligns the features of each category according to the conditional distribution. The global adversarial loss function and the local adversarial training loss function are as follows:

Where, L is the cross entropy loss function, G_f is the feature extraction network, G_g and Glk (k = 1,2) are the patient discrimination network, d_i is the patient label, yik (k = 1,2) is the first and second dimensional data of the original label after one-hot encoder, D_s ∈ D₁ ∪ D₂… ∪ D_n is the patient sample set.

In category classifier, to centralize the character of data, the central loss function is adopted. The loss function is (Wen et al., 2016):

Where, c_yi is the category center.

Through the above operations, the marginal distribution and conditional distribution of features are aligned, and the features are gathered to the central point of each category, so the invariant features are obtained. The loss function of the category classifier (Rahim et al., 2015; White et al., 2020; Versaci et al., 2022; Waheed et al., 2023) is:

Where, G_c2 is the category classifier, y_i is the category label.

We propose an adversarial training strategy to train all the loss functions jointly (Matsuura and Harada, 2020):

Where, λ = 0.1. θg,θl1,θl2 are trained by a special layer called Gradient Reversal Layer (GRL), this GRL is omitted during forward propagation, and the gradient is reversed in backpropagation. Finally, we search for the optimal parameters θf∧f,θc⁢2∧c⁢2,θg∧g,θl1∧1,θl2∧2 to meet the following requirements:

Where, θ_f are the parameters of multi-level temporal-spectral feature extract network, θ_c1 are the parameters of category classifier in feature separation network, θ_p are the parameters of patient classifier in feature separation network, θ_c2 are the parameters of category classifier in invariant feature extraction network, θ_g are the parameters of global patient discriminator in invariant feature extraction network, θl1,θl2 are the parameters of local patient discriminator in invariant feature extraction network.

During training, if the training samples are trained by minibatch, the features of all the training samples cannot be obtained in time, so we feed all the training samples into the network as a batch for training. The Adam optimizer is used for the model; the learning rate is set to 0.005; the center loss function is optimized using the Stochastic Gradient Descent (SGD) optimizer, and the learning rate is set to 0.05; the training rounds are 200. We use the grid search method to set the hyperparameters in the experiment.

The proposed approach is evaluated on a benchmark dataset, the TUH corpus (Obeid and Picone, 2016), which is a neurological seizure dataset of clinical EEG recordings associated with 22 channels according to the international 10/20 system. We form a subset of the TUH with 14 subjects by selecting the subject with more than 250 s of seizure state. For each subject, we use 500 s (half normal and half seizure) of EEG signals with a sampling rate of 250 Hz. Each EEG fragment has 250 sample points (lasting 1 s) and adjacent fragments with 50% overlap. For each EEG fragment, those belonging to the epileptic seizure state are labeled as 1, while those belonging to the normal state are labeled as 0. Then the sample set is divided into a training set and a test set.

The experiment used accuracy (ACC), sensitivity (SN), and specificity (SP) to quantify the performance of the algorithm (Yang et al., 2023).

Where, TP (True Positive): The sample which is positive is judged to be positive, TN (True Negative): The sample which is negative is judged to be negative, FP (False Positive): The sample which is negative is judged to be positive, FN (False Negative): The sample which is positive is judged to be negative.

The adopted baseline models include:

● Zabihi et al. (2013) applied Discrete Wavelet Transform (DWT) and calculated metrics such as relative scale energy and Shannon entropy as features; SVM is used for data classification.

● Fergus et al. (2015) applied Power Spectral Density (PSD) and calculated metrics such as peak frequency and max frequency as features; KNN is used for data classification.

● Schirrmeister et al. (2017) applied convolutional neural networks to distinguish seizure segments by decoding task-related information from EEG signals.

● Kiral et al. (2018) designed a deep neural network for seizure diagnosis and further developed a prediction system on a wearable device.

● Zhang et al. (2020) proposed an adversarial representation learning strategy, which achieves robust and explainable epileptic seizure detection.

● Dissanayake et al. (2021) used the CNN network structure and Siamese network structure to improve the generalization ability of the model.

The six comparison methods and my experiment used the same data segment length on the TUH dataset, using leave-one-out cross-validation, and obtained the comparison results in Table 1.

Through comparative analysis, the methods in literature (Schirrmeister et al., 2017; Kiral et al., 2018) only used a deep neural network to train a model with the data of multiple patients together, without considering the negative impact of inter-patient differences on the training model, resulting in poor detection accuracy when applied to new patients. In literature (Zabihi et al., 2013), relative scale energy and Shannon entropy, etc., were used as features, in literature (Fergus et al., 2015), peak frequency and max frequency, etc., were used as features, these methods were able to extract the obvious common features, but were unable to extract the deeper common features, so the detection accuracy of the methods was higher than the results in Schirrmeister et al. (2017) and Kiral et al. (2018) and lower than the results in Zhang et al. (2020) and Dissanayake et al. (2021). For the methods mentioned in the literature (Zhang et al., 2020; Dissanayake et al., 2021), which applied a neural network to eliminate the negative impact of the data distribution shift between patients, the results were higher than those without considering the elimination of the negative impact of the data distribution shift between patients. For the method proposed in this paper, which uses feature separation and adversarial training to disentangle features in the latent space while learning domain-invariant features to achieve the goal of mitigating the influence of inter-patient differences, its experimental results are the best, with an average detection accuracy of 85.7% by leave-one-out cross-validation.

In addition, the confusion matrix and the receiver operating characteristic (ROC) curve with the area under the curve (AUC) value are shown for a closer look at the detection results. The results of one of the best-performing subjects (patient 6) are illustrated in Figure 3. From the confusion matrix we can see that our approach achieves a sensitivity of 98.4% and a specificity of 100%.