## 2 Materials and Methods
### Classification  
Following the application of the FS algorithm, the most prominent features are fed into a classifier to estimate the class (ASD vs. TD) of each individual/instance. Specifically, a linear kernel SVM was employed to discriminate between the different classes, based on the premise that linear models represent better the importance of the feature within the model (compared to non-linear models such as neural networks) [38]. In detail, SVM is a supervised binary classifier that utilizes known variables (training set; selected from all the available data) to create a projection on a multi-dimensional space. Then, a hyperplane is generated corresponding to the maximum distance from all the training instances of both classes. The unknown data elements (testing set; the non-selected data) are then evaluated as to the class they belong to and according to the side of the hyperplane separator they are subsequently mapped.  
The classification precedure utilized the RFE-CBR ranked set by adding one by one the most common feature from all folds and evaluating the overall performance. Consequently, in each iteration, the SVM classifier estimated the accuracy of the features set deriving from the previous iterations with the inclusion of the next ranked feature in succession, starting from a null feature subset. The overall process was performed until all features were included in the classification subset, in order to investigate the optimal number of features that would provide the highest performance, optimizing internal parameters with a Bayesian procedure aiming at minimizing the error as shown in Equation (3) [39]:  
\[\text{error}=1-\text{AUC} \tag{3}\]  
where AUC is the area under curve (Equation (4)):  
\[\text{AUC}=1-\sum_{\text{k}=1}^{\text{n}}(\text{X}_{\text{k}}-\text{X}_{\text {k}-1})(\text{Y}_{\text{k}}+\text{Y}_{\text{k}-1}) \tag{4}\]  
with X denoting the false positive rate and Y the true positive rate.  
Similar to the FS process, the classification framework employed a nested 10-fold CV scheme. Specifically, in order to tune SVM's hyperparameters and select the optimal  
Figure 1: The workflow of the proposed approach.  
classification model based on the selected features, the nine initial folds are further split into training and validation sets using an inner new 10-fold CV scheme coupled with a grid search approach. The maximum number of epochs for SVM training is 50 (determined by varying the epoch number from 40 to 60 with a step of 1). The best model (optimal set of hyper-parameters) according to the validation procedure is retrained on the whole 90% of the initial dataset and is tested on the remaining 10%, evaluating the overall performance. The process is repeated for all folds (10 \(\times\) 10), and the average results on the testing data are presented.  
The performance of the classification process is assessed in terms of accuracy, sensitivity, and specificity using the equations:  
\[\text{Accuracy}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+ \text{FN}} \tag{5}\]  
\[\text{Sensitivity}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{6}\]  
\[\text{Specificity}=\frac{\text{TN}}{\text{TN}+\text{FP}} \tag{7}\]  
where TP is true positive, TN is true negative, FP is false positive, and FN is false negative.