## 2 Materials and Methods
### Data Analysis
#### 2.4.1 Baseline Analysis
** To evaluate the model performance, a categorical cross-entropy was employed, which is suitable for multiclass classification task. The optimization procedure was iterated for 100 epochs with a batch size of 6 samples. To address the model generalization performance, a leave-one-out cross-validation procedure was performed [43]. The metrics used for evaluating the model was the accuracy, sensitivity, and specificity. Accuracy represents the percentage of correct predictions out of the total number of test samples. Sensitivity is the proportion of predicted true positives out of all patients with the disease, whereas specificity represent the percentage of the predicted true negatives out of all participants who do not have the disease [44]. Those metrics were performed by counting the number of correct DCNN predictors after an argmax evaluation of the DCNN output vector, averaged among the plateau iterations. This procedure was conducted following the leave one-out cross-validation. The overall sensitivity and specificity of the classifier were obtained by averaging the sensitivity and specificity of each class, respectively. The described DCNN model was implemented in Python using Keras API with TensorFlow backend. For model evaluation, the scikit learn library was utilized. Figure 3 shows an example of the input images, respectively, for HC, SSc, and PRP participants, and the related feature maps resulting as output from the first two convolutional layers. Feature-Based Analysis  
A feature extraction algorithm was then implemented to extract features of interest from the same IR-images of the baseline condition. In detail, a region of interest present on each fingers' nail bed was manually selected. For each region of interest, the temperature average value was extracted. Region of interests are shown in Figure 2. The extracted temperature data were then normalized by subtracting the average value of the entire dataset. In addition, for each participant, features related to the 10 fingers normalized temperature distribution were estimated. These features were: the standard deviation (STD), kurtosis, skewness, range (i.e., the difference between the largest and smallest values  
Figure 3: Deep Convolutional Neural Network (DCNN) feature maps. (**a**) Input image of a representative healthy participant within the dataset together with the features map resulting from the first two convolutional layers (s.u. = standardized units). (**b**) Input image of a representative systemic sclerosis (SSC) participant within the dataset and the features map resulting from the first two convolutional layers. (**c**) Input image of a representative primary Raynaud’s phenomenon (PRP) participant within the dataset and the features map resulting from the first two convolutional layers. The images’ axes units represent the images’ pixels number. of the distribution), and the inter-quartile range (i.e., the difference between the third and first quartile). Figure 4 shows the group mean and standard deviation of the 10 fingers' temperature average value, and of all the other features z-score normalized. As a machine learning approach, the SVC was implemented. Specifically, the SVC was computed using radial basis function (RBF) as a kernel function (non-linear). Such a function has the following formula for two vectors \(\mathrm{u}\) and \(\mathrm{v}\):  
\[\mathrm{RBF}\left(\mathrm{u},\mathrm{v}\right)=\exp(-\gamma\parallel\mathrm{ u}-\mathrm{v}\parallel^{2}) \tag{2}\]  
where \(\gamma\) is a hyperparameter used as similarity measure between two data point. For the purpose of our study \(\gamma\) was set as follows:  
\[\gamma=1/(\mathrm{number\ of\ features}=15) \tag{3}\]  
whereas the regularization hyperparameter C was set to 5. The SVC generalization capabilities were assessed through cross-validation. The same cross-validation procedure employed for the DCNN model were utilized. The metrics employed to be evaluated were the accuracy, sensitivity, and specificity. The z-score normalized features constituted the SVC inputs.