## 4 System Description
### Deep Learning Analysis  
Subsequently, we performed classifications and determined the condition of the user concerning their body temperature. Explicitly, we fed the measurements of the touch temperature sensors to identify an increase in the body temperature potentially caused by pathogenesis, thus signifying fever. The models employed for this task were unidimensional Convolutional Neural Networks. CNNs are a class of deep learning neural networks that display excellent capabilities in pattern recognition schemes. Their ability to extract regional features enables researchers to deal with complex tasks that are not possible with classic ANNs. Although, our signals stemmed from one device, and thus we did not possess a plethora of samples; we were prompted to select unidimensional CNNs as our classifier to provide proof of feasibility for our application in this task. This selection also delineates our future directions regarding the simultaneous acquisition of multiple signals from interconnected devices in the context of family members wearing this device and obtaining feedback in real-time concerning their condition and relatives. In this vein, these networks present excellent scaling capabilities, thus rendering them great candidates to constitute the foundation for our analysis. Furthermore, these networks were also employed in our previous work [44], where they demonstrated significant efficacy in classifying the condition of vessel equipment. Therefore, it is deemed necessary to use methodologies established in other domains and determine their transferability. The primary functionalities of CNNs are explicated in detail, as follows:  
Feature extraction: First, the convolution is characterized as a linear element-wise multiplication as a small array called the kernel glides through the input tensor of the layer and convolves the value of each time step. Equation (3) delineates this operation. \[F(x)=K^{\circ}S(x)=\sum_{i=-N}^{N}K(i)S(x-i) \tag{3}\]  
The emerging output tensor was fed into a nonlinear activation function. Recently, the rectifier linear unit (ReLU) has started to gain popularity, as it has been evinced capable of yielding remarkable results while also solving gradient problems related to other popular activation functions of the past, such as the sigmoid and the tanh. Classification: The output feature map of the last convolution layer was converted into a vector, which was input into a traditional Feed-Forward Neural Network (FFNN) carrying out the assignment of the samples to the output labels. Loss: The main objective of the optimization procedure is the minimization of the loss function. The utilized loss function was concluded based on the nature of the problem at hand. Explicitly, for our application, the Categorical Cross Entropy was utilized in the present study. Afterward, we assumed a dataset with M labels and N observations, and the vector of ground truth measurements is denoted as \(\mathbf{y}=[y_{1},\ y_{2},\ \dots,\ y_{n}]\). Similarly, the predicted values are denoted as \(\mathbf{a}^{[L]}=[a_{1}^{[L]},\ a_{2}^{[L]},\ \dots,\ a_{n}^{[L]}]\). Accepting CCE as our loss function then gives:  
\[E=\mathcal{C}CE(\mathbf{y},\mathbf{a}^{[L]})=-\sum_{i=1}^{M}y_{i}\log\Bigl{(}a_{i}^{[L ]}\Bigr{)} \tag{4}\]  
Subsequently, the backpropagation succeeded the forward pass. The gradient, namely the partial derivative of the loss, was calculated concerning the model's output. Through this computation, the model was capable of updating its learnable parameters, namely weights and biases, achieving convergence of the inferred values and actual measurements, hence augmenting the model's accuracy. Mathematically, we can formulate the aforementioned procedure as follows:  
\[p=p-a\ \frac{\partial L}{\partial p} \tag{5}\]where \(p\) represents any learnable parameter and \(\alpha\) denotes the learning rate of the optimizer of the model. For our application, we had continuous time-series signals pertinent to the variables monitored by the watch's sensors.