## 6 Results and Discussion
### Gaussioan Kernel Versus Linear Kernel and Linear Regression Method  
To demonstrate the advantage of Gaussian kernel SVR, the prediction performances of SVR with linear kernel and linear regression are also calculated. For brevity, only the results of best models with one, two, and seven features are shown here. The linear regression using least square on the training dataset for the three cases are as follows:  
\[\text{MSI}=1.330\log(\text{PGA})+3.863 \tag{18}\]  
\[\text{MSI}=0.416\log(\text{PGA})+1.024\log(A_{0.3})+3.980 \tag{19}\]  
\[\text{MSI}=0.196\log(\text{PGA})+0.945\log(A_{0.3})+1.007\log(\text{ASI})-2. 638\log(\text{HI}) \tag{20}\]  
\[+1.471\log(\text{PGV})+0.898\log(\text{VSI})-0.260\log(Ic)+3.019\]  
The predicted MSIs versus actual ones on the testing dataset are shown in Figure 8a-c for one, two, and seven features, respectively. To show the scatter for the third method more clearly, the result of the linear regression is off to the left side of a Gaussian kernel, with a linear kernel SVR to the right side. It can be seen from Figure 8a that most of predicted values are within a \(\pm 0.5\) range of the actual values for the Gaussian kernel. The predicted points of MSI VI are well concentrated in a smaller range, and even MSI IX is well predicted. On the other hand, more points are out of the \(\pm 0.5\) range for the linear  
Figure 7: Performance of best SVRs with 1–9 features.  
SVR and linear regression. This means that Gaussian kernel SVR has better prediction performance than the other two methods. Figure 8b for two features and Figure 8c for seven features show similar results. Since Gaussian kernel SVR gives the lowest MSE and highest accuracy percentage, it is the best of the three regression models. Comparing Figure 8a with Figure 8c, it can also be seen that the performance of predicted MSIs using PGA is almost the same as the one using seven features.  
Present empirical relationships for the MMI or MSI are mainly based on PGA and PGV [1; 2; 3; 4; 5; 7; 8; 9; 10], and the Gaussian SVR versus linear regression of PGA and PGV are also studied. As the dataset is not the same as those used in previous studies [1; 2; 3; 4; 5; 7], the linear regression equation should be obtained on this training set again. The model of the PGA is given by Equation (18), and the model of the PGV is given by  
\[\text{MSI}=1.442\log(\text{PGV})+5.299 \tag{21}\]  
The performance results are shown in Table 2. The linear regression model of PGV is better than that of PGA, and the accuracy percentage increases from 44.3% to 66.7%. The MSE decreases from 0.374 in the linear regression of PGV to 0.214 in the Gaussian kernel SVR of PGA, and the predicted accuracy increases from 66.7% to 74.1%. It is noted that the Gaussian kernel SVR of PGV is not better than that of PGA, which can also be seen from Figure 6. The well-accepted conception that PGV is better than PGA for estimating MSI assumes linear regression. The Gaussian SVR of PGA and PGV has almost the same MSE and correlation coefficient as that of PGA, but the accuracy percentage decrease from 74.1% to 68.6%. From the comparison, it was found that the Gaussian kernel SVR of PGA gave the best regression model for predicting MSI, and was much better than the linear regression of PGV or PGA.  
Figure 8: Performance comparison of regression models with Gaussian kernel and linear kernel SVRs and linear regression. (**a**) One feature; (**b**) two features; (**c**) seven features.