EEG-Based Autism Detection Using Multi-Input 1D Convolutional Neural Networks

In this section, the related materials and methods are given to carry out the EEG-based ASD detection where each channel of the EEG signal is used as input to the multi-input 1D CNN model [15-17]. Figure 1 shows the illustration of the proposed method.

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Figure 1. Illustration of the proposed method

As depicted in Figure 1, the model architecture incorporates a series of one-dimensional convolutional layers, each responsible for processing an individual channel signal. After the initial convolutional layer, the model employs batch normalization and Rectified Linear Unit (ReLU) layers. Following the first ReLU layer, another set of three layers, comprising convolution, batch normalization, and ReLU layers, is sequentially arranged. The final ReLU layers' outputs are subjected to flattening and concatenation to form an input structure for the fully connected layer. To finalize the model architecture, softmax, and classification output layers are employed. The model is trained utilizing the 'Adam' optimization algorithm.

2.1 Data augmentation

Data augmentation of EEG signals can be achieved through the implementation of an overlapping sliding window technique [18]. In this method, the continuous EEG signal is divided into fixed-length windows or segments, which serve as the fundamental units for analysis or machine learning model training. To introduce variability and capture temporal dependencies, these windows overlap with each other, meaning that certain sections of adjacent windows share common EEG data [19]. The degree of overlap, typically specified as a percentage of the window size, can be adjusted to control the level of augmentation. This strategy demonstrates its utility across a range of EEG applications, including tasks like categorizing brain states or detecting disorders. It empowers the model to capture finer-grained features and temporal patterns from the data, enhancing its effectiveness in these applications. Moreover, overlapping sliding windows find utility in time-frequency analysis, facilitating the exploration of frequency components over time. However, the choice of window size and overlap percentage is application-dependent and may require experimentation to optimize the data augmentation process for a specific EEG analysis task, ultimately enhancing the robustness and performance of the analysis or machine learning model. Figure 2 shows an illustration of an overlapping sliding window method.

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Figure 2. Data augmentation procedure

2.2 The dataset

The dataset utilized in this investigation was sourced from the King Abdulaziz University Hospital in Jeddah, Saudi Arabia [14]. It comprises 20 children diagnosed with ASD, aged between 6 and 20 years. Additionally, a control group consisting of nine children with no history of neurological conditions was included for comparison. EEG signals were recorded from participants in a relaxed state using a G-tec EEG cap equipped with Ag/AgCl electrodes, G-tech USB amplifiers, and BCI2000 software, ensuring the acquisition of artifact-free EEG data. The data collection involved recordings from 16 channels (FP1, FP2, F7, F3, Fz, F4, F8, T3, C4, Cz, C3, T5, Pz, O1, Oz, and O2) following the international 10–20 systems configuration, with AFz serving as the ground reference and the right ear lobe as specified in [20]. It's essential to highlight that this dataset is publicly accessible, and all requisite ethical approvals were obtained [14]. The architecture referred to as "-18" denotes a deep CNN architecture with 18 layers.

2.3 Multi-input 1D CNN

A CNN stands as a profound architecture in the realm of machine learning, particularly influencing tasks related to image analysis and recognition [14, 20, 21]. CNNs are composed of multiple layers, encompassing convolutional layers, pooling layers, and fully connected layers, collaboratively designed to progressively extract and process features from the input data. Convolutional layers employ learnable filters to convolve over the input, enabling the network to discern and identify local patterns. Pooling layers then down sample the feature maps, reducing spatial dimensions and computational complexity. Lastly, fully connected layers amalgamate the extracted features to make predictions or classifications. This architecture has proven transformative in various applications, solidifying its significance in the field.

In this paper, as the input is a signal, a one-dimensional convolution layer is employed at the beginning of the developed model [15]. The convolution operation for a 1D signal in a CNN involves applying a convolutional layer to the input signal using a set of learnable filters or kernels. The 1D convolution operation for each filter k is computed as follows:

$y^k[n]=\sum_{m=0}^{M-1} W^k(m) \cdot x(n-m)$                  (1)

In the above equation, n represents the current position in the output map y^k. m is the position within the filter W^k, ranging from zero to M-1. x(n-m) corresponds to the element of the input signal x at position m-n. W^k(m) represents the filter coefficient at position m for filter k. This operation is applied independently to each filter k, resulting in a set of output feature maps y¹,y²,…,y^k. These feature maps are then typically passed through an activation function to introduce non-linearity and form the final output of the convolutional layer. Batch normalization is a technique utilized to standardize the outputs of individual layers within a neural network model. In the training phase, this method calculates a scaling factor to transform the mean to zero and the variance to one for each batch of data. Following this standardization, the outputs undergo activation functions. Mathematically, batch normalization can be described by the following equations:

$\mu_B=\frac{1}{m} \sum_{i=1}^m x_i$                  (2)

$\sigma_B^2=\frac{1}{m} \sum_{i=1}^m\left(x_i-\mu_B\right)^2$                   (3)

$\hat{x}_i=\frac{x_i-\mu_B}{\sqrt{\sigma_B^2+\epsilon}}$                 (4)

$y_i=\gamma \hat{x}_i+\beta$                  (5)

In the provided equations, x_i represents the i-th example within a batch, $\mu_B$ denotes the batch mean, and $\sigma_B^2$ stands for the batch variance. $\hat{x}_i$ represents the normalized output. γ and β are the scale factor and bias parameters, respectively. ϵ is a small value introduced to prevent division by zero errors. These equations illustrate the process of first computing the batch mean and variance, then utilizing these values to obtain the normalized output, and finally applying the scale factor and bias terms. This operation can be applied to normalize the output of any layer within a neural network model. Batch normalization often contributes to a faster and more stable training process, thereby enhancing the overall performance of neural networks.

The Rectified Linear Unit (ReLU) is a widely used activation function in neural network models. The ReLU function outputs the input value directly if it is greater than zero, and assigns an output value of zero if the input is less than zero [21]. Mathematically, the ReLU function is expressed as follows:

$f(x)=\max (0, x)$                      (6)

In this equation, x represents the input value, and f(x) represents the output value. The graph of the function exhibits a value of zero on the x-axis for negative input values and rises linearly with a slope of x for positive input values. The ReLU function can be employed as the activation function for any layer within a neural network model. Notably, in deep neural network models, utilizing the ReLU function helps mitigate the problem of vanishing gradients for input values near zero, resulting in faster learning.

The flattening layer is a layer within a neural network model that transforms the output of any preceding layer into a single vector. This layer is commonly used, especially in the processing of image inputs. The flattening layer can be expressed mathematically by the following equation:

flatten $(X)=X^{\prime}$                  (7)

In this context, X represents a tensor that comes from the previous layer, while X' refers to the tensor that has been flattened or transformed into a one-dimensional vector. The Concatenation layer is a layer that combines two or more tensors to create a new tensor. This layer is particularly useful in neural network models when there is a need to merge multiple pathways or when input data has distinct features. Mathematically, the Concatenation layer can be expressed using the following equation:

$\operatorname{concat}\left(X_1, X_2, \ldots, X_n\right)=\mathrm{Y}$                   (8)

Here, $X_1, X_2, \ldots, X_n$ represent the tensors to be concatenated, and Y is the resulting tensor. The numbers $1,2, \ldots, n$ respectively indicate the number of channels in each tensor. A FC Layer, alternatively referred to as a Dense Layer, is a neural network layer designed to process vectorized input data and generate an output vector through matrix multiplication. Typically employed in the concluding layers of a neural network, this layer produces outputs utilized in tasks like classification or regression. The mathematical expressions governing a FC Layer are outlined below:

$y=\sigma(W x+b)$                   (9)

In this context, x is an n-dimensional vector representing the input to the layer. W is the weight matrix with dimensions m×n, where m represents the size of the output vector. b is the bias term, a vector of size m. σ is the activation function. The Softmax layer is an output layer commonly used in classification problems. It interprets the input vector data as probabilities belonging to different classes and selects the most likely class. The Softmax function calculates the probability of each class by normalizing the individual class scores concerning the total probabilities. The mathematical equations for the Softmax layer are as follows:

$y_i=\frac{e^{z_i}}{\sum_{j=1}^C e^{z_j}}$              (10)

Here, $y_i$ represents the probability of the ith class, and $Z_i$ is the net output value for the ith class. C is the total number of classes. The Softmax function calculates the ratio of $e^{z_i}$ contributing to the total probability of class C to $e^{z_i}$, where $Z_i$ is the net output for class i. Consequently, the probability of each class is normalized relative to the sum of $e^{z_i}$ divided by C. Consequently, the sum of probabilities assigned to all classes by the Softmax function always equals one. Another noteworthy characteristic of the Softmax function is its adaptability to different numbers of classes, making it well-suited for diverse classification problems with varying class counts. The Classification Output layer is a commonly employed output layer in classification tasks. Specifically designed for these problems, this layer calculates the probabilities associated with belonging to different classes for a given example, ultimately carrying out the classification. The predetermined number of classes denoted as C, corresponds to the number of output neurons, with each neuron representing a distinct class. Activation functions like sigmoid, softmax, or others are applied to transform output neuron values into probability values. In classification scenarios, the cross-entropy loss is frequently used. This loss function measures the disparity between the actual class label and the predicted probability values, aiming to minimize this difference to enhance the model's accuracy. The mathematical representation of cross-entropy loss is articulated as follows:

$L=-\sum_{i=1}^C y_i \log \left(\widehat{y}_l\right)$                   (11)

In this context, $y_i$ represents the actual class label, and $\widehat{y}_l$ is the probability value predicted by the model. The computation of cross-entropy loss involves comparing the probability values assigned to all output neurons with the correct class label.

Table 4. Comparison of the proposed approach with existing approaches.