## 2 Technical Background
### 1D Cnn  
CNNs have a specialized architecture designed to reduce computational complexity and can handle overfitting. The architecture of a CNN includes several layers: input, convolutional, pooling, fully connected, and output layers. The input layer is where raw data are fed into the network. The convolutional layer then learns high-level abstract features from this input data through convolutional operations, whereby filters slide over the input to extract features. These features are enhanced by adding an activation function with different weights and biases. Following the convolutional layer, the pooling layer reduces the dimensionality of the data, decreasing computational load and helping to control overfitting. The fully connected layer integrates features learned by previous layers to make final predictions, and the output layer produces the classification or regression results. Equation (1) illustrates the convolutional operation within the CNN, demonstrating how these networks process data similarly to the visual cortex of the brain.  
\[C_{l}^{j}=f\left(\sum_{i\in P_{n}}C_{i}^{j-1}*w_{il}^{j}+b_{l}^{j}\right) \tag{1}\]  
where the number of layers is denoted by \(l\). Within each layer, the \(j\)-th component is represented by \(C_{i}^{j-1}\). The convolved region is shown as \(P_{n}\), with \(w\) representing the weights and \(b\) representing the biases.  
Discriminant features are important for the classification accuracy of a classifier. To enhance the quality of features extracted from the convolutional layer, a pooling layer is introduced. Max pooling is used to remove redundant information. It simplifies the representation by taking the maximum value from each region of the feature map, effectively reducing its dimensionality while retaining important features. The max pooling operation can be mathematically expressed as Equation (2) as follows:  
\[C_{l}^{j}=f\left(w_{l}^{j}*\max\left(C_{i}^{j-1}\right)+b_{l}^{j}\right) \tag{2}\]  
where the max pooling operation, denoted by \(\max\left(C_{i}^{j-1}\right)\), is illustrated. To linearly enhance the discriminative power of the features, this study uses sigmoid as the activation function. This operation helps to highlight the most prominent features, improving the robustness and accuracy of the classification process.  
To enhance the extraction of local information from input data in a CNN, multiple convolutional and pooling layers are utilized. These layers work together to gather important information from the input. Once this key information is obtained, the next step is to classify it into its respective classes. For this classification task, a fully connected layer is used.  
The fully connected layer classifies the important features obtained from the convolutional layers. Initially, these latent features are flattened into a 1D feature vector. This flattened feature vector is then provided as an input to the fully connected layer. The operation of the fully connected layer is illustrated in Equation (3), demonstrating how the network translates the learned features into classification outputs.  
\[fC^{j+1}=\left(\sum_{i=1}^{n}w_{il}^{j}a^{i(i)}+b_{l}^{j}\right) \tag{3}\]In the context of a neuron, \(w\) represents the weighted value and \(b\) represents the bias in the \(j\)-th layer. The output value \(fC^{j+1}\) denotes the activation of the \(i\)-th neuron at layer \(l+1\).  
To prevent overfitting, a dropout strategy is implemented in the CNN. Dropout involves randomly deactivating neurons in certain layers of the network during training using probabilistic techniques. By reducing the reliance on specific neurons, dropout enhances the network's ability to generalize to new data, improving its performance on unobserved data. Figure 1 represents the basic architecture of a one-dimensional CNN.