## 3 Experimental Results  
The results of the experimental analysis are presented in this section. Figure 3 shows the violin plots. For reason space, we report the violin plots for the Mean (\(F1\)), the Zone Entropy (\(F16\)), the Small Area Low Gray Emphasis (\(F15\)), the Gray Level Non Uniformity (\(F3\)), the Size Zone Non Uniformity (\(F11\)) and the Run Variance (\(F2\)). The violin plots for the Zone Entropy feature show that the \(3+4\) Gleason score distribution shows greater maximum values if compared with the ones with \(4+3\) and \(4+4\)  
Figure 3: Violin plots for the Gleason score distributions. Figure 2: Testing phase. Gleason scores. Furthermore, the \(4+4\) population values in the third quartile are ranging in a greater interval than the ones of the \(3+4\) and \(4+4\) Gleason score distributions. The Small Area Log Gray Emphasis violin plots are showing that the third quartile distribution is ranging in value similar to the Zone Entropy feature, while the first quartile distributions are ranging in a greater range interval: in this case, the violin plot whose distributions are ranging in a greater interval is the \(4+4\) Gleason score one. The Mean feature violin plots show that the \(3+4\) Gleason score distribution exhibits values ranging in a similar interval for the first and third quartiles, while, with regard to the \(4+3\) and \(4+4\) ones, the first quartile values are ranging in a smaller interval if compared with the ones of the \(3+4\) Gleason score distribution. The Gray Level Non Uniformity violin plots show that the numeric values for the first and third quartiles are really similar. Furthermore, the \(3+4\) distribution shows higher values if compared to the remaining ones. The Size Zone Non Uniformity violin plots show a similar trend to the one exhibited by the Gray Level Non Uniformity violin plots. The Run Variance violin plots show that the \(4+3\) distribution exhibits higher values than the other ones, while the values of the first and third quartiles are ranging in similar values. The aim of the hypothesis testing is to evaluate if the radiomic features exhibit different distributions for the \(3+4\), \(4+3\) and \(4+4\) populations of the Gleason Score MRI features with statistical evidence. We consider valid the results we obtained when the null hypothesis is rejected by both of the tests. Table 2 shows the results of the the null hypothesis \(H_{0}\) test. From Table 2 results, the features not passing the null hypothesis \(H_{0}\) test are the following: \(F1\), \(F2\), \(F3\), \(F4\), \(F5\), \(F6\), \(F7\), \(F8\), \(F9\), \(F10\), \(F11\), \(F12\), \(F13\), \(F14\) and \(F17\). In the classification analysis, this radiomic feature set will be considered, resulting from the most discriminating for \(3+4\), \(4+3\) and \(4+4\) Gleason scores. The classification step is related to the classifier building with the aim to evaluate the feature vector ability to discriminate \(3+4\), \(4+3\) and \(4+4\) Gleason scores. For training the classifier, we defined \(T\) as a set of labeled MRI instances (_M, l_), where each \(M\) is associated with a label \(l\in\{3+4\), \(4+3\), \(4+4\)}. For each \(M\), we built a feature vector \(\text{F}\in R_{y}\), where \(y\) is the number of the features used in the training phase (\(y=15\)). In detail, \(\text{F}\in\{F1\), \(F2\), \(F3\), \(F4\), \(F5\), \(F6\), \(F7\), \(F8\), \(F9\), \(F10\), \(F11\), \(F12\), \(F13\), \(F14\), \(F17\}\). Relating to the training phase, we exploit a 10-fold cross-validation: the dataset is randomly partitioned into 10 different subsets. In order to obtain a single estimate, the average of the \(k\) results from the folds is computed. Each classification of the cross-validation was performed using the 80% of the dataset for the training and the remaining 20% for testing. Four different supervised machine learning algorithms are considered: \(C\)_4.5_[24,25], _SVM_[26,27], _Gaussian_[28,29] and _RandomForest_[30].