## 2 Materials and Methods
### Training and Internal Testing of the Model
#### 2.2.2 Classification of Segmented Aortic Arch and Supra-Aortic Vessels
The last layers of DensNet-201 consist of one average pooling layer and one fully connected layer, followed by an SVM classifier layer. Moreover, we were interested in investigating whether a feature representation learned using a different number of layers (SqueezeNet: 18 layers; ResNet-50: 50 layers; DenseNet-201: 201 layers), which is reflected in a shallower or deeper level of abstraction, respectively, could have an influence on the automatic-classification results. It should be noted that these deep networks include different convolutional filters that are able to learn a rich feature representation of the input image classes during training and to use this learned representation for classifying new images. Basic feature detection filters are learned through the first layers, filters able to detect parts of the target object are learned through the middle layers, while high-representation filters able to detect the entire target are learned through the last layers. These differences can be more emphasized the higher the number of layers. For each patient considered in this study, the SIAA, obtained from the fully automatic segmentation step, was automatically down-sampled in order to match the ResNet-50 input image size (224 by 224 pixels), the SqueezeNet input image size (227 by 227 pixels), and the DenseNet image size (224 by 224 pixels). For the training and cross-validation of the deep learning classifiers, we considered the first dataset of CTs, obtained from half of the dataset of Center 1, consisting of 50% of CTs with CILCA and 50% CTs without CILCA, together with 75% of the Center 2 dataset, consisting of 15% of CTs with CILCA and 85% CTs without CILCA. For internally testing the deep learning classifiers, we considered the CTs from both Center 1 and Center 2 datasets consisting of 50% of CTs with CILCA and 50% CTs without CILCA. In order to increase image diversity among different training phases (epochs), we applied data augmentation and image manipulation techniques to the training image set, as follows: (i) reflections in the top-bottom direction and reflections in the left-rightdirections applied randomly (50% probability); (ii) planar rotations, with the rotation angle picked randomly from a continuous uniform distribution from \(-5^{\circ}\) to \(+5^{\circ}\); (iii) horizontal and 100 vertical shears, with shear angle picked randomly from a continuous uniform distribution from \(-0.05^{\circ}\) to \(+0.05^{\circ}\). TRACE4 allowed a fine-tuning of the three CNNs architectures to specialize for our binary classification task (CILCA versus non-CILCA), replacing the fifth last layers for SqueezeNet, and the two last layers for ResNet-50 and DenseNet-201. After editing these specific layers, TRACE4 proceeded with the re-training of the CNNs. Specifically, TRACE4 optimized (during training of each CNN) the maximum number of epochs to 300, with an optimal mini-batch size of 8 (the samples of the training set were randomized before each epoch in order to avoid issues related to the choice of samples to include in the mini-batches--e.g., always discarding the same samples). An Adam optimization was used for stochastic gradient computation [25]. TRACE4 did not optimize the learning rate that was maintained at \(1\times 10^{-4}\) constantly throughout the whole training. A 5-fold cross-validation method was chosen. The division ratio between the training set and the validation set was 4:1 (124:31). For each fold of the cross-validation, each of the three CNNs was trained on the training set and used to classify the validation set. Each of the three CNN was then used to obtain the classification performance on both the training and the validation sets. This resulted in five different CNN-derived classification models and a set of five classification performances (one for each fold). For each of the three CNNs, the final training and validation performance was calculated as the mean of the performances obtained on each of the five CNN-derived classification models.