## 2 Materials and Methods
### Data Analysis
#### 2.4.1 Baseline Analysis  
The IR images of the dorsum of both participants' hands during the baseline condition were used as the input of the DCNN model implemented to differentiate PRP from SSc and HC. The DCNN model was developed according to the following processing steps:  
Figure 2: Raw thermal IR image of a representative healthy participant within the dataset. Black circles represent the regions of interest manually selected. * **Input images preprocess**. Firstly, the IR images were down sampled from 320 \(\times\) 240 to 80 \(\times\) 107 pixels and normalized by subtracting the average value of the entire set of images. A Principal Components Analysis was then adopted to reduce the number of spatial features while keeping the information characterizing the object to be analyzed. The number of components kept was 20 with a cumulative explained variance ratio of 0.95. * **Model architecture design. ** The DCNN structure employed in this work was heuristically chosen in similarity with previously reported DCNN structures on biological images or signals classification [41]. The DCNN was composed of 3 convolutional layers, 3 pooling layers, and 1 fully connected prior to the output layer. The first convolutional layer consisted in 32 filters (size 5 \(\times\) 5) applied to the input images to obtain 32 feature maps of the images. The other 2 convolutional layer were both composed of 10 filters (size 5 \(\times\) 5). The activation function employed in all the 3 convolutional layers to add nonlinearity to the network, were the Rectified Linear Unit (ReLU) function. Then, as pooling layer (or down-sampling layer) a MaxPooling were chosen, where the largest element from the rectified feature map was retained. A filter size of 3 \(\times\) 3, 3 \(\times\) 4 and 2 \(\times\) 2 for the 3 MaxPooling layers, respectively, was implemented to reduce the dimensionality of each feature to 1 after the 3 convolutional layers and before the fully connected layer. The fully connected layer consisted in 20 neurons employed to summarize information and compute the class score. Lastly, a softmax function was used in the output layer, which outputs a probability value from 0 to 1 for each of the 3 classification classes (PRP, SSc, and healthy). All the biases of the DCNN were initialized to a small constant, i.e., 0.1, whereas the weights were initialized in a pseudo-random manner employing a truncated normal distribution (standard deviation = 0.1). The DCNN architecture is shown in Figure 1a. * **Model optimization. ** The model optimization was primarily focused on how to reduce overfitting. Indeed, developing a DCNN model with a small sample size inevitably involves high risk of overfitting. A technique used to address overfitting is regularization [42]. In this study, a Ridge Regression (L2 regularization) was implemented by adding the sum of the squared values of the model coefficient (weights) as a penalty term to the loss function. The loss function employed in this study was the categorical cross-entropy, therefore after performing the regularization technique it resulted in the following Equation: \[Loss_{r}=-\sum y_{k}\ \log\hat{y}_{k}\ +\frac{\lambda}{2}\sum{{\omega_{i}}^{2}}\] (1) where \(\hat{y}_{k}\) is the \(k\)th scalar value of the model output, \(y_{k}\) is the corresponding target value, and the constant \(\lambda\) times the sum of the squared weight (\(\omega\)) values is the regularization term. The \(\lambda\) value was set to 0.01. This was intended to reduce model complexity and make the model less prone to overfitting. In addition, instead of using a fixed learning rate hyperparameter for the presented model, which could lead the model to converge too quickly to a suboptimal solution, a tunable learning rate over the training process was implemented. In detail, a function was implemented to reduce learning rate by a factor of 0.1 once learning stop improving during at least 10 epochs. * **Model evaluation.