## 3 Machine Learning Performance Indexes  
When addressing a simple two classes classification problem, usually one class is defined as the \"positive\" one while the other as \"negative\". Without any implications on benefits or values, the positive class is usually the object of the study [5]. This distinction starts from the training samples given to the model, which can be either positive or negative; for example, in identifying a fracture, a positive sample could be a bone fracture vs. the negative sample being that of a healthy bone. Hence, once positive and negative examples are fed to the model, predictions made via the latter can be categorized and allocated as one of the following: true positive (TP), that is, a prediction of a positive result for a positive sample; true negative (TN), that is, a prediction of a positive result for a negative sample; false positive (FP), that is, a prediction of a positive result that in reality is negative; and false negative (FN), that is, a prediction of a negative result that is actually labeled as positive. The formulas of the main performance indicators rely on these concepts. To better understand the performance of the models that will be discussed later, the main performance metrics must thus be introduced since only one index might not be enough to describe the performance of a model. It is to be highlighted that the formulas reported herein are valid for a binary classifier, but the concepts can be extended to multi-class classification problems. **Accuracy**: expresses how good a classifier is in its job of finding all the correct predictions related to the total number of predictions, i.e., the proportion of the total number of test samples in which the model identifies the positive labels [18]. \[Accuracy=\frac{TP+TN}{TP+FP+FN+TN} \tag{1}\]  
**Sensitivity**: indicates how well the model is performing in terms of classifying the positive results related to the total number of predictions made regarding positive samples. It is also known as _true positive rate_[5] since it measures the ability of the model to predict positive results (all the actually pathologic subjects that were classified as pathologic by the model). \[Sensitivity=\frac{TP}{TP+FN} \tag{2}\]  
**Specificity**: quantifies how well the model is performing in terms of classifying the negative results related to the total number of predictions regarding truly negative results. It is also called the _true negative rate_ as it quantifies how many true negatives (for example people that did not have a certain pathology that were actually recognized by the model as not having that pathology) were obtained. \[Specificity=\frac{TN}{TN+FP} \tag{3}\]  
**Precision**: computes what proportion of the positive predictions were actually true and is used when the goal is to limit the number of false positives [5]:  
\[Precision=\frac{TP}{TP+FP} \tag{4}\]  
**F1-score**: denotes the harmonic mean of precision and sensitivity [18]. It is used to assess whether our model has a high precision, a high sensitivity or both. In fact, the F1-score is high if both are high and thus optimized, it is medium if only one of the two metrics is optimized, and if it is low both metrics are low. \[F1\ score=2\times\frac{Precision\times Sensitivity}{Precision+Sensitivity} \tag{5}\]  
**ROC curve**: known as Receiver Operator Characteristic curve, it is plotted (as seen in Figure 4) on a graph with the \"True Positive Rate\" or \"Sensitivity\" on the \(y\)-axis and \"False Positive Rate\" or \"\(1-\)Specificity\" on the \(x\)-axis. The different values of the two rates are measured for different threshold levels in order to see how different values would influence the performance of the model. This curve also shows the trade-off between sensitivity and specificity. **AUC**: is the Area Under the Curve between the ROC curve and the bisector. It measures the ability of a classifier to distinguish between the two or more classes, and it summarizes the ROC curve.