## 4 Discussion  
### Ggo Segmentation  
The examples reported in Figures 3 and 4 show how the non-supervised segmentation method proposed in this paper is able to approximate the gold standard results with satisfactory results.  
This result has two strong implications for the Radiomics of the COVID-19 patients. First, given that the amount of information required for the k-means method training is considerably lower than CNN methods, while still retaining good results, this segmentation can be implemented with in-patient training. Secondly, this method can be used with success as a first segmentation method to be used as training for other, more specific methods. We remark that all the proposed techniques are voxel-based algorithms: this kind of method requires the whole patient's scan as input, drastically reducing the dimensionality of the dataset. As a reference, a 3D U-Net-based method [66] required two order of magnitude training samples to achieve comparable results.  
It is worth noting that the various segmentation scores are dependent on the class balance, and therefore tend to penalize this kind of segmentation where one class (the GGO class in our case) is substantially under-represented. This can be confirmed by confronting the results of the proposed segmentation with published methods such as those reported in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Survival** & **Fisher** & \(\chi^{2}\) & **PPV** & **Fisher** & \(\chi^{2}\)**TPR** & **Fisher F\({}_{1}\)** & \(\chi^{2}\)**F\({}_{1}\)** \\  & **1 = Dead** & **PPV** & **\(\chi^{2}\) PPV** & **TPR** & **\(\chi^{2}\) TPR** & **Fisher F\({}_{1}\)** & \(\chi^{2}\)**F\({}_{1}\)** \\ \hline Logistic & 0 & 0.88 & 0.90 & 0.82 & 0.82 & 0.85 & 0.85 \\  & 1 & 0.00 & 0.08 & 0.00 & 0.14 & 0.00 & 0.10 \\ Ridge & 0 & **0.93** & **0.95** & 0.82 & 0.82 & 0.87 & 0.88 \\  & 1 & 0.20 & 0.25 & 0.43 & 0.57 & 0.27 & 0.35 \\ KNN & 0 & 0.89 & 0.89 & 0.83 & 0.85 & 0.86 & 0.87 \\  & 1 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ R. Forest & 0 & 0.90 & 0.90 & **0.94** & **0.95** & **0.92** & **0.93** \\  & 1 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table}
Table 16: Precision, Sensitivity, and F\({}_{1}\) Score for each model and each feature selection strategy to predict patient survival. From the left: dichotomized score value, Precision obtained using the 3 best features identified by the Fisher test, Precision obtained using the 3 best features identified by the \(\chi^{2}\) test; Sensitivity obtained using the 3 best features identified by the Fisher test, Sensitivity obtained using the 3 best features identified by the \(\chi^{2}\) test; F\({}_{1}\) score obtained using the 3 best features identified by the Fisher test; F\({}_{1}\) score obtained using the 3 best features identified by the \(\chi^{2}\) test. For each column the maximum value was indicated with bold font.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Fisher** & \(\chi^{2}\) & **All** \\ \hline Logistic & 0.41 & 0.48 & 0.43 \\ Ridge & **0.62** & **0.70** & 0.41 \\ KNN & 0.41 & 0.42 & **0.50** \\ R. Forest & 0.46 & 0.48 & **0.50** \\ \hline \hline \end{tabular}
\end{table}
Table 15: Global adjusted accuracy of the models to predict mortality using different feature selection strategies. From the left: dichotomized score value, Precision obtained using the 3 best features identified by the Fisher test, Precision obtained using the 3 best features identified by the \(\chi^{2}\) test; Sensitivity obtained using the 3 best features identified by the 3 best features identified by the \(\chi^{2}\) test; F\({}_{1}\) score obtained using the 3 best features identified by the \(\chi^{2}\) test. For each column the maximum value was indicated with bold font.