## 2 Materials and Methods
We design an evaluation composed of three different steps: the first one is a statistics evaluation, where we compare the populations of MRIs related to different Gleason scores: the aim is to understand whether the radiomics features exhibit different values when extracted from MRIs related to Gleason score; the second step is the hypotheses testing that is related to understanding whether the features exhibit different distributions of the MRIs; the third step is a classification analysis which aims to understand if the exploited radiomic features are able to rightly discern different unknown MRIs related to different Gleason scores. For the statistics evaluation, we compare the MRI population through a violin plot, aimed at showing in a graphical way groups of numbers with the detail about the quartiles (in particular, the first and the third one). Violin plots are related to highlight variation in statistical populations without any kind of assumptions of the statistical distribution. Relating to the second step i.e., the hypotheses testing, the null hypothesis to be tested is the following:  
**Hypothesis 0**. : _\"prostate cancer MRIs labelled with different Gleason Scores exhibit similar values for the exploited radiomic feature set\"._  
For the null hypothesis test, the Wald-Wolfowitz and the Mann-Whitney Test are exploited. For both of the tests, the \(p\)-level is fixed to 0.05. With regard to the classification, supervised machine learning algorithms are exploited. These kinds of algorithms to build models require two different steps i.e., _Training_ and _Testing_. The first one, the _Training_, is shown in Figure 1: from the the radiomic features gathered from MRIs, these algorithms are able to build a model. The inferred model is aimed at discerning between radiomic features belonging to Gleason scores. \begin{table}
\begin{tabular}{c c c} \hline \# & **Radiomic Feature** & **Category** \\ \hline \(F1\) & _Mean_ & _FO_ \\ \(F2\) & _Run Variance_ & _GLRLM_ \\ \(F3\) & _Gray Level Non Uniformity_ & _GLSZM_ \\ \(F4\) & _Gray Level Non Uniformity Normalized_ & _GLSZM_ \\ \(F5\) & _Gray Level Variance_ & _GLSZM_ \\ \(F6\) & _High Gray Level Zone Emphasis_ & _GLSZM_ \\ \(F7\) & _Large Area Emphasis_ & _GLSZM_ \\ \(F8\) & _Large Area High Gray Level Emphasis_ & _GLSZM_ \\ \(F9\) & _Large Area Low Gray Level Emphasis_ & _GLSZM_ \\ \(F10\) & _Low Gray Level Zone Emphasis_ & _GLSZM_ \\ \(F11\) & _Size Zone Non Uniformity_ & _GLSZM_ \\ \(F12\) & _Size Zone Non Uniformity Normalized_ & _GLSZM_ \\ \(F13\) & _Small Area Emphasis_ & _GLSZM_ \\ \(F14\) & _Small Area High Gray Level Emphasis_ & _GLSZM_ \\ \(F15\) & _Small Area Low Gray Level Emphasis_ & _GLSZM_ \\ \(F16\) & _Zone Entropy_ & _GLSZM_ \\ \(F17\) & _Zone Percentage_ & _GLSZM_ \\ \(F18\) & _Zone Variance_ & _GLSZM_ \\ \hline \end{tabular}
\end{table} 
Table 1: The feature set with relative categories. Figure 1: Training phase. The second step, once the model is generated, is the evaluation of its effectiveness: the _Testing_ one is shown in Figure 2.  
We evaluate radiomic features belonging to MRIs that are not considered in the training data: as a matter of fact, the aim of the _Testing_ step is to evaluate the effectiveness of the models with unseen MRIs. To evaluate all MRIs, the cross validation is exploited. In a nutshell, with the cross validation, the full dataset is split into two different parts: the first part is used for model training, while the second one is exploited to test the model. This process is repeated several times, each time considering different MRIs for both the training and testing dataset in order to evaluate all the MRIs belonging to the full dataset. To enforce the conclusion validity, four different classifiers are considered. Furthermore, once the best classifier is selected in terms of performance, we will calibrate it.