## 3 Method
### Parameter Settings  
Besides the models' architecture, parameter settings are vital in finding the most optimal classification performance. In this section, we examine the parameter settings of both models. * Normalization: The distribution of each layer's input varies throughout training, slowing down the process. Batch normalization is a technique for minimizing the influence of internal covariance on the training process, thus speeding up the training process [52]. We imputed batch normalization right after the convolutional layer. For each input \(x\), batch normalization normalizes each dimension \(k\) and computes the training set's expectation and variance: \[\tilde{x}^{(k)}=\frac{x^{(k)}-\mathrm{E}\Big{[}x^{(k)}\Big{]}}{\sqrt{\mathrm{ Var}\big{[}x^{(k)}\big{]}}}\,.\] (6) When it comes to nonlinear representations, normalizing each input may modify what the layer represents. For each activation, batch normalization has a shift and scale function to account for this constraint: \[y^{(k)}=p^{(k)}\tilde{x}^{(k)}+q^{(k)}\,,\] (7) where \(p^{(k)}\) and \(q^{(k)}\) scale and shift each activation \(x^{(k)}\), respectively. These parameters are learnt in tandem with the model's initial parameters, restoring the network's representation power. * Fully Connected Layer: Before the final classification layer, the models are provided with a fully connected layer. This layer is used to identify global compositions of the final convolutional output and is equivalent to a fully connected layer in a multilayer perceptron. The fully connected layer is denoted as follows: \[FC^{l}=f\Big{(}\omega^{l}*x^{l}+b^{l}\Big{)}\,,\] (8) for layer \(l\), where \(\omega^{l}\) is the weight matrix and \(x^{l}\) is the input for the fully connected layer, represented as a flattened vector of the output from the previous pooling layer. A dot product operation is denoted by \(*\), while a bias term is denoted by \(b^{l}\). The Sigmoid activation function employed in the layer is represented by \(f(\cdot)\). * Classifier: In the last layer of both models, a Sigmoid classifier is used, which is expressed as: \[\sigma(x_{i})=\frac{e^{x_{i}}}{1+e^{x_{i}}}\,,\] (9)where \(x\) is the value of the preceding layer's \(i\)th output, and \(e\) is [PERSON]'s mathematical constant. This results in output values that are independent of each other and are not constrained to sum up to 1. Therefore, we chose Sigmoid because it excels in classifying signals of any length with modest or no variations across classes, necessitating the calculation of each probability separately. * Optimization: An Adam stochastic optimizer is used to optimize the networks. For each individual parameter, it makes use of the power of adaptive learning rates. The optimizer is computationally efficient and memory-light, making it ideal for models with a large number of trainable parameters that process high dimensional data. Adam is particularly well suited for noisy and non-stationary signals [53]. Adam optimization can be denoted as: \[g_{t}=\
abla_{\theta}f^{t}\left(\theta^{t-1}\right),\] \[m_{\theta}^{t}=\beta_{1}m_{\theta}^{t-1}+\left(g_{t}-\beta_{1}g_{t} \right),\] \[v_{\theta}^{t}=\beta_{2}v_{\theta}^{t-1}+\left(g_{t}^{2}-\beta_{2}g_{t} ^{2}\right),\] \[\widehat{m}_{\theta}=\frac{m_{\theta}^{t}}{1-\left(\beta_{1} \right)^{t}}\,,\] (10) \[\widehat{v}_{\theta}=\frac{v_{\theta}^{t}}{1-\left(\beta_{2} \right)^{t}}\,,\] \[\theta^{t}=\theta^{t-1}-\alpha\cdot\frac{\widehat{m}_{\theta}}{ \left(\sqrt{\widehat{v}_{\theta}}+\epsilon\right)}\,.\]  
At epoch \(t\), \(f(\cdot)\) represents the stochastic objective function with parameters \(\theta^{t}\), yielding gradient \(g_{t}\). The first and second biased moment estimates are designated as \(m_{\theta}^{t}\) and \(v_{\theta}^{t}\), respectively, where the decay rates are \(\beta_{1}=0.9\) and \(\beta_{2}=0.999\). The bias-corrected momentum is represented by \(\widehat{m}_{\theta}\) and \(\widehat{v}_{\theta}\).