## 5 Results
### Damage Validation  
In this section, the estimated damage maps from each of the Naive, SVM, and deep learning algorithms were validated using the official damage map at three county, city, and 10 by 10 km grids scales. The official damage map, which was computed based on the FEMA HAZUS loss model, is shown at the three, county, city, and 10 by 10 km grid, scales in Figure 13.  
Figure 12: The estimated damage map from (**a**) Naive Bayes, (**b**) SVM, and (**c**) deep learning algorithms at the 10 \(\times\) 10 km grids scale. Figure 13: Cont. * Damage validation at the county scale Table 3 presents the results of the validation of the estimated damage map from Naive Bayes, SVM, and deep learning at the county scale with official data. Based on the validation results by the three indices of Kendall's tau, Pearson correlation, and Spearman's rho, the deep learning classifier was selected as the best model at the county scale. In additino, Kendall's tau and Spearman's rho indexes, which were used to rank values, performed better than Pearson indices, which worked with the values themselves. * Damage validation at city scale Table 4 presents the results of the validation of the estimated damage map from Naive Bayes, SVM, and deep learning at the city scale with official data. Based on the validation results by the three indices of Kendall's tau, Pearson correlation, and Spearman's rho, the SVM classifier was selected as the best model at the city scale. \begin{table}
\begin{tabular}{c c c c} \hline
**Algorithm** & **Spearman’s Rho** & **Pearson Correlation** & **Kendall’s Tau** \\ \hline Naive Bayes & 0.647 & 0.539 & 0.550 \\ \hline Deep Learning & 0.8205 & 0.5217 & 0.6666 \\ \hline SVM & 0.6655 & 0.5191 & 0.5714 \\ \hline \end{tabular}
\end{table} 
Table 3: The results of validation of the estimated damage map from Naive Bayes, SVM, and deep learning at the county scale. Figure 13: Official damage map at the county (**a**), city (**b**), and 10 by 10 km grids (**c**) scales. * Damage Validation at the 10 \(\times\) 10 km grids scale  
Table 5 presents the results of the validation of the estimated damage map from Naive Bayes, SVM, and deep learning at the 10 \(\times\) 10 km grids scale. Table 6 presents the results of validation of the estimated damage map from Naive Bayes, SVM, and deep learning at the 10 \(\times\) 10 km raster grids scale with accuracy, precision, recall, and F-score indices. These indices were obtained from the confusion matrix. Based on the validation results by the four indices of accuracy, precision, recall, and F-score, the Naive Bayes classifier was selected as the best model at the 10 \(\times\) 10 km raster grids. Figure 14 shows the area values (km\({}^{2}\)) included by each class in our estimated damage map and FEMA HAZUS loss model map for the Naive Bayes, SVM, and deep learning algorithms. Obviously, the area covered by the four classes in the FEMA HAZUS loss model map for all three algorithms must be equal. In addition, the areas covered by the four classes in the estimated damage map for the two Naive Bayes and SVM algorithms were approximately equal. However, the obtained area corresponded to the results of the four classes in the damage map for the deep learning algorithm, on average 2.8 times more than the same value in the two Naive Bayes and SVM algorithms. In general, the results of the deep learning algorithm in the area covered by four classes were closer to the FEMA HAZUS loss model map (official damage map). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Accuracy** & **Precision** & **Recall** & **F-Score** \\ \hline Naive Bayes & 35.20\% & 35\% & 42.7\% & 38.66\% \\ \hline Deep Learning & 30.20\% & 30.2\% & 32.85\% & 31.47\% \\ \hline SVM & 29.40\% & 29.69\% & 32\% & 30.80\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The results of validation of the estimated damage map from Naive Bayes, SVM, and deep learning at the 10 \(\times\) 10 km raster grids scale with accuracy, precision, recall, and F-score indices.