## 4 Evaluation Metrics  
In this section, we briefly describe the performance metrics used to objectively evaluate the classifiers implemented in this study. Let \(P(i)\) and \(N(i)\) represent the total numbers of actual positive and actual negative cases for the \(i\)-th class, respectively. Additionally, let \(TP(i)\), \(TN(i)\), \(FP(i)\), and \(FN(i)\) denote the numbers of true positives, true negatives, false positives, and false negatives, respectively, as identified by the classifier for the \(i\)-th class. Based on these quantities, the following metrics can be defined:  
\[TPR(i) = \frac{TP(i)}{P(i)} \tag{1}\]  
\[TNR(i) = \frac{TN(i)}{N(i)} \tag{2}\]  
\[FNR(i) = \frac{FN(i)}{P(i)} \tag{3}\]  
\[FPR(i) = \frac{FP(i)}{N(i)} \tag{4}\]  
These metrics can be interpreted as follows:  
* \(TPR(i)\), also known as _Recall_ or _Sensitivity_, represents the proportion of actual positives correctly classified as belonging to the \(i\)-th class. High values of \(TPR\) indicate a good performance at identifying positive cases. For simplicity, the Recall for the \(i\)-th class is denoted as \(r(i)\).
* \(TNR(i)\), or _Specificity_, represents the proportion of actual negatives correctly classified as not belonging to the \(i\)-th class. High values of \(TNR\) indicate the effective exclusion of negatives.
* \(FNR(i)\) indicates the proportion of false negatives in the \(i\)-th class with respect to all actual positives in the class. Lower \(FNR\) values are desirable as they imply fewer missed positives.
* \(FPR(i)\) represents the proportion of false positives in the \(i\)-th class relative to the total number of actual negatives in the class. Lower \(FPR\) values are desirable as they indicate fewer incorrect positive classifications.  
Based on these definitions, we can define the Positive Predictive Value (_PPV_), or _Precision_, for the \(i\)-th class as follows:  
\[PPV(i)=\frac{TP(i)}{TP(i)+FP(i)} \tag{5}\]  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model** & **Params (\(\times\)10\({}^{6}\))** & **Layers** & **Input Size** \\ \hline ViT & 86.0 & 12 & 224 \(\times\) 224 \\ \hline DeiT & 86.0 & 12 & 224 \(\times\) 224 \\ \hline SwinTransformer & 88.0 & 12 & 224 \(\times\) 224 \\ \hline PVT & 45.0 & 13 & 224 \(\times\) 224 \\ \hline CvT & 20.0 & 7 & 224 \(\times\) 224 \\ \hline TNT & 23.8 & 12 & 224 \(\times\) 224 \\ \hline LeViT & 9.2 & 6 & 224 \(\times\) 224 \\ \hline Twins-SVT & 60.0 & 12 & 224 \(\times\) 224 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of Vision Transformer models: parameters, layers, and input image sizes.  
In the following, the Precision for the \(i\)-th class is denoted as \(p(i)\).  
Together with \(r(i)\) and \(p(i)\), we also consider the \(f_{1}\)-score, a combined metric that balances Precision and Recall for the \(i\)-th class. It is defined as follows:  
\[f_{1}(i)=\frac{2 TP(i)}{2 TP(i)+FP(i)+FN(i)} \tag{6}\]  
A useful tool for visualizing these performance metrics is the Confusion Matrix (CM), which provides a breakdown of classifier outcomes for each class. In a CM, rows correspond to the true classes (Target Classes), and columns correspond to the predicted classes (Output Classes). Diagonal cells represent correctly classified observations, while off-diagonal cells indicate misclassifications.