## 4 Model Verification
As can be seen from Figure 5, which shows the relationship between the predicted and target values of \(S_{dy}\) in the 11-building-characteristic case with a sample size of 4400. From Table 6 and Figures 6 and 7, all the above discussions regarding the results of output \(S_{dy}\) apply broadly to \(S_{ay}\), \(S_{du}\), and \(S_{au}\). Figure 4: Model accuracy for spectral-yield displacement \(S_{dy}\) with 11 building characteristics. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**Size of Training Dataset**} \\ \cline{2-13}  & **400** & **800** & **1200** & **1600** & **2000** & **2400** & **2800** & **3200** & **3600** & **4000** & **4400** \\ \hline Max. & 0.61 & 0.63 & 0.64 & 0.59 & 0.63 & 0.63 & 0.61 & 0.61 & 0.62 & 0.58 & 0.62 \\ Min. & 0.26 & 0.23 & 0.34 & 0.31 & 0.35 & 0.41 & 0.34 & 0.38 & 0.39 & 0.46 & 0.42 \\ Average & 0.51 & 0.51 & 0.51 & 0.52 & 0.52 & 0.53 & 0.53 & 0.53 & 0.54 & 0.54 & 0.54 \\ SD & 0.08 & 0.10 & 0.07 & 0.06 & 0.07 & 0.06 & 0.07 & 0.05 & 0.05 & 0.04 & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Model accuracy with testing 11 building characteristics for spectral-yield displacement \(S_{dy}\). Figure 5: Test results of 4400 training samples for spectral-yield displacement \(S_{dy}\) with 11 building characteristics. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{10}{c}{**Size of Training Dataset**} \\ \cline{2-13}  & **400** & **800** & **1200** & **1600** & **2000** & **2400** & **2800** & **3200** & **3600** & **4000** & **4400** \\ \hline Max. & 0.63 & 0.59 & 0.61 & 0.61 & 0.61 & 0.62 & 0.60 & 0.60 & 0.62 & 0.59 & 0.60 \\ Min. & 0.03 & 0.03 & 0.03 & 0.29 & 0.33 & 0.36 & 0.37 & 0.39 & 0.38 & 0.42 & 0.51 \\ Average & 0.49 & 0.49 & 0.50 & 0.50 & 0.51 & 0.51 & 0.51 & 0.52 & 0.52 & 0.52 & 0.52 \\ Standard Deviation (SD) & 0.12 & 0.11 & 0.09 & 0.08 & 0.07 & 0.06 & 0.05 & 0.05 & 0.04 & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Model accuracy with testing 11 building characteristics for spectral-yield acceleration \(S_{ay}\). Figure 6: Model accuracy for spectral-yield displacement \(S_{ay}\) with 11 building characteristics. In the second case study, which used all 20 of the building characteristics in Table 2 as model inputs, we also tested the influence of all 11 training-dataset sizes on prediction accuracy, again running 30 trials for each training-dataset size using samples randomly selected from the NCREE's buildings. The \(S_{dy}\) output results are shown in Table 7 and Figure 8, where we can observe that the average values of model accuracy \(A\) increase along with the size of the training dataset: from 0.64 at 400 samples, to 0.74 at 4400. In other words, when our selected 20 building characteristics are used as the inputs, our SVM model can achieve an average accuracy of 64% in the prediction of buildings' seismic vulnerability \(S_{dy}\) using a relatively small training dataset of 400, but its average accuracy increased to 74% if the training-dataset size is increased to 4400: i.e., a 42% improvement over the 11-building-characteristic model with a dataset of the same (largest) size. Figure 8: Model accuracy for spectral-yield displacement \(S_{dy}\) with 20 building characteristics. Figure 7: Test results of 4400 training samples for spectral-yield displacement \(S_{ay}\) with 11 building characteristics.