# Machine Learning for Evaluating Hospital Mobility: An Italian Case Study
## 4 Experimental Results and Discussions  
The results achieved by the model have highlighted high performance, with an area under the curve (AUC) of 0.969, an accuracy (CA) of 87.6%, an F1 score of 0.869, a precision (PREC) of 87.1%, a recall rate of 87.6%, and a Matthews correlation coefficient (MCC) of 0.758. For a more in-depth analysis of the model's performance, the analysis of the confusion matrix and the receiver operating characteristic (ROC) curves were included. The confusion matrix (Figure 4) showed a significant match between the model's predictions and the actual classifications, with 90.2% of low mobility cases correctly identified (low-low), 83.3% of high mobility cases accurately classified (high-high), and 75.0% of medium mobility cases correctly recognized (medium-medium).  
Classification errors were found in cases of medium mobility, with 12.5% mistakenly classified as low mobility and 12.5% as high mobility; 9.8% of low mobility cases were classified as medium, and 16.7% of high mobility as medium. The ROC curves for the three classes (low, medium, and high mobility) provided an effective visual representation of the model's ability to discriminate between these categories, demonstrating excellent separation with high AUC values, a sign of the model's strong ability to correctly classify hospitals based on their active mobility (Figures 5-7). The confusion matrix and the ROC curve representations are produced using the Confusion Matrix widget and the ROC Analysis widget, respectively, as shown in the dark red box in Figure 2.  
The ROC curves for the low, medium, and high mobility classes provide a graphical representation of the model's ability to discriminate between these different categories. The prominently marked performance curve in black that we see in the graphs is the visual representation of the true positive rate (sensitivity) as a function of the false positive rate (1-specificity) across various decision thresholds. Sensitivity, depicted on the vertical axis, shows the extent to which the model correctly identifies actual cases of each class,  
Figure 5: ROC curve for target class LOW.  
while the horizontal axis indicates the percentage of cases erroneously classified, known as false positives.  
The ROC curve stands out in the graph as a trajectory exploring the trade-off between sensitivity and specificity: a curve that arches towards the top-left corner signals high-quality discrimination by the model. In each of the graphs, the area under the curve, represented by the gray zone, reveals the overall classification capability of the model; an area approaching unity signals excellent predictive capacity. The red lines indicate the  
Figure 6: ROC curve for target class MEDIUM.  
Figure 7: ROC curve for target class HIGH.  
chosen optimal cut-off points, balancing the capture of true positives against the increase in false positives. High AUC values in these curves demonstrate the model's strong ability to accurately classify hospitals based on the degree of active patient mobility, as highlighted in the graphs for the three mobility classes.