## 5 Discussion and Conclusions  
The negative impact of an earthquake on a building is primarily conceptualized as a function of its seismic vulnerability. This vulnerability is generally analyzed via computational simulation models of seismic response, such as push-over analysis. Although push-over analysis can provide sophisticated information about a building's seismic vulnerability in terms of a capacity curve, it is time-consuming, requiring an immense quantity and high quality of data on building characteristics; and precisely because of this extraordinary level of detail, it must be repeated on a building-by-building basis thousands of times when such computational analysis is applied at a regional scale. It was primarily for this reason that the present study developed an SVM model for rapidly assessing buildings' seismic vulnerability at the macroscale, in terms of spectral yield and ultimate points of their capacity curves, \(P_{Y}(S_{dy},S_{ay})\) and \(P_{U}(S_{du},S_{au})\). In each of our two case studies, one with 11 and the other with 20 building characteristics, 11 different sizes of training dataset ranging from 400 to 4400 samples were tested. In the first case, the results for output \(S_{dy}\) indicate that, with only 11 building characteristics as inputs, the proposed  
Figure 11: Test results of 4400 training samples for spectral-yield displacement \(S_{ay}\) with 20 building characteristics. Figure 10: Model accuracy for spectral-yield displacement \(S_{ay}\) with 20 building characteristics. SVM model could only achieve 52% prediction accuracy, even at the largest size of training dataset. In the second case study, taking the output \(S_{dy}\) as an example, model accuracy reached 64% with a training-dataset size of just 400, and improved to 74% at a size of 4400; and parallel results were obtained for \(S_{ay}\), \(S_{du}\) and \(S_{au}\). Importantly, our results imply that high reliability of prediction accuracy of the proposed model can be achieved if all 20 building characteristics are used as model inputs, regardless the size of training dataset, at least within the 400-4400 range that we studied. Additionally, comparing the first case study with the second case study, increasing training data can only slightly improve the prediction accuracy of models in the first case study, while increasing training data can significantly increase the prediction accuracy of models in the second case study, and such increasing trend seems to be continuous as the training dataset becomes larger. Such results indicate that the SVM model in the first case study could be underfitting, which means the number of building characteristics are too less to obtain high prediction accuracy even with a large training dataset. On the other hand, with more building characteristics, the prediction accuracy of the models in the second case study is expected to be improved with more training data. In short, the above case studies, and particularly the second one, confirm the effectiveness and reliability of our proposed new data-mining technique (SVM) for rapid, regional-scale assessment of buildings' seismic vulnerability in terms of their capacity curves. Coupled with seismic-demand curves, a seismic risk assessment of the buildings at a regional scale can also be done rapidly by determining their performance points using their capacity curves obtained by our proposed SVM model. As well as obviating the need to construct far more complex computational models for the same purpose, our technique could readily be extended to regional-scale estimation of other natural disaster risks to buildings, such as high winds and floods. Conceptualization, Z.Z., and T.-Y.H. ; Methodology, Z.Z. and H.-H.W., and J.-H.C.; Validation, Z.Z. and H.-H.W. ; Resources, T.-Y.H. ; Data curation, Z.Z., H.-H.W., and T.-Y.H. ; Writing--original draft preparation, Z.Z. and H.-H.W. ; writing--review and editing, H.-H.W. and J.-H.C. This research received no external funding. The authors declare no conflict of interest.