## 3 Results
### Feature Importance  
This subsection presents our main results analyzing of the importance of the RVS features for the relative classification of structures, which we performed using the SHAP values, as explained in Section 2.5. Note that there is some inherent variability in the \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Hyperparameter**} & \multirow{2}{*}{**Tuning Range**} & \multicolumn{3}{c}{**Optimal Value per Pair**} \\ \cline{3-5}  & & **(Green, Yellow)** & **(Yellow, Red)** & **(Red, Black)** \\ \hline max\_depth & [3; 11] & 3 & 5 & 3 \\ n\_estimators & [50; 300] & 297 & 50 & 293 \\ min\_samples\_leaf & [1; 10] & 9 & 8 & 10 \\ learning\_rate & [0.05, 0.25] & 0.086887 & 0.120314 & 0.182278 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameter tuning. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **(Green, Yellow)** & \multicolumn{3}{c}{**(Yellow, Red)**} & \multicolumn{3}{c}{**(Red, Black)**} \\ \cline{2-5}  & \(-\mathbf{1}\) & \(+\mathbf{1}\) & \(-\mathbf{1}\) & \(+\mathbf{1}\) & \(-\mathbf{1}\) & \(+\mathbf{1}\) \\ \hline Precision & 0.69585 & 0.76301 & 0.90943 & 0.86933 & 0.93992 & 0.90379 \\ Recall & 0.73221 & 0.72928 & 0.84995 & 0.92183 & 0.88501 & 0.95024 \\ F1-score & 0.71357 & 0.74576 & 0.87869 & 0.89481 &  
computations of the \(\phi_{i}\), and consequently in \(\overline{\phi}\) from (3) and (4). This can stem from how the algorithm splits the dataset between training and testing at each iteration or from the computation of the SHAP values themselves. To mitigate the sensitivity of the results to these factors, we performed 100 runs of our proposed methodology and averaged the obtained feature importances. This heavily reduces the variability of the computations and increases the reliability of the extracted feature importance values. Thus, we constructed a matrix \(\mathbf{\Theta}\in\mathbb{R}^{100\times 13}\), where \(\theta_{ij}\) is the value \(\overline{\phi}_{j}\) from (4) for the \(j^{\text{th}}\) feature at the \(i^{\text{th}}\) iteration. From this, we calculated the average value per column/feature, i.e., we defined  
\[\lambda_{j}=\frac{1}{100}\sum\limits_{i=1}^{100}\theta_{ij}. \tag{5}\]  
Finally, in order to normalize these coefficients, we divided them with their sum, i.e.,  
\[\overline{\lambda}_{i}=\frac{\lambda_{j}}{\sum\limits_{j=1}^{13}\lambda_{j}}. \tag{6}\]  
With this normalization, we now have \(0\leq\overline{\lambda}_{i}\leq 1\) and \(\sum\limits_{i=1}^{13}\overline{\lambda}_{i}=1\); therefore, these coefficients can be interpreted as the percentage of the contribution of the corresponding features to the overall predictions of the model. We carried out the above using both of the alternatives used in (4). The results are shown in Figure 4.  
Figure 4: _Cont_. This figure presents the comparative results of the contribution of each feature to the model predictions expressed as a percentage of the total. As previously discussed, these correspond to the mean contributions for all pairs of structures, which, given that we are averaging over thousands of pairs, are representative of the the overall parameter effect on seismic behaviour across the various limit states of all the structures in the dataset. The left subfigures in Figure 4a-c pertain to \(\mathcal{L}_{1}\), i.e., the absolute values of these features, while the right subfigures pertain to \(\mathcal{L}_{2}\), i.e., their squares. The results demonstrate a basic hierarchy of the structural properties that influence the seismic vulnerability of the studied structures and contribute to the observed degrees of damage. In general, the results are in agreement with the existing structural mechanics literature and the seismic behaviour of reinforced concrete structures. We analyze and discuss each of Figure 4a-c separately.