## 3 Data and Methods
### Methods
#### 3.2.2 Cluster Extraction with Spatial Statistical Analysis  
After extracting ground deformation through the SBAS-InSAR analysis, potential landslides in the mountainous areas were identified by selecting ground deformation with a specific deformation rate threshold (DRT) [62]. This analysis is based on the assumption  
Figure 5: Workflow of the data processing in this study.  
that the deformation rate is higher in landslide-prone areas than in non-landslide areas [63]. However, considering the spatial variation in the geological conditions and the failure mechanism of landslides, the DRTs may vary among different regions and cannot be defined by a fixed rule. Nevertheless, the deformation of the landslide body is controlled by the failure mechanism and is continuously distributed in space but cut off at the landslide boundary [42]. This suggests that, from the spatial statistic viewpoint, the deformation would cluster in the landslide body. Therefore, the cluster analysis of the deformation rate obtained from the InSAR technique can be used to determine potential landslide sites. Compared with the DRT method, the cluster analysis is considered to be a more effective and general tool for determining landslide sites in mountainous areas. In this study, one of the famous cluster analysis methods, termed the hot spot analysis, was used to cluster the InSAR results and further determine potential landslide sites [64]. In the analysis, the \(G_{i}^{*}\) value, an indicator for potential landslide, is calculated as follows [65; 66]:  
\[G_{i}^{*}=\frac{\sum_{j=1}^{n}w_{ij}x_{j}-\overline{X}\sum_{j=1}^{n}w_{ij}}{S \sqrt{\frac{\left[n_{j=1}^{\overline{x}}w_{ij}^{2}-\left(\sum_{j=1}^{n}w_{ij} \right)^{2}\right]}{n-1}}} \tag{1}\]  
where \(x_{j}\) is the deformation rate obtained by InSAR analysis; \(n\) is the number of the measured points; \(w_{ij}\) is the spatial weight of points \(i\) and \(j\), which are used in statistics; and \(\overline{X}\) and \(S\) are the mean and standard deviation of the deformation rate, respectively.  
In the processes of calculating \(G_{i}^{*}\), the \(z\)-score and \(p\)-value were also obtained. For a statistically significant positive \(z\)-score, the higher the \(z\)-score, the more concentrated the cluster (hot spot). For a statistically significant negative \(z\)-score, the lower the \(z\)-score, the more concentrated the cluster (cool spot). The critical values of the \(z\)-score at clustering confidence coefficients of 90%, 95%, and 99% were \(\pm\)1.65 (\(p\)-value = 0.10), \(\pm\)1.96 (\(p\)-value = 0.05), and \(\pm\)2.85 (\(p\)-value = 0.01), respectively [67]. In general, a higher confidence coefficient reflects a better clustering result. However, a higher confidence coefficient could also narrow down the landslide deformation area as well as ignore some small landslides. Thus, the critical \(z\)-score was set as \(\pm\)1.96 (95% confidence coefficient) to maximize the potential landslide detection in this study.  
After the hot spot analysis, the clustered ground deformation velocity was obtained. However, some noised measure points (MPs) still appeared and obstructed the identification of potential landslide sites. To eliminate the noised MPs, buffer analysis was conducted following the procedure described by [PERSON] et al. [68]. In the analysis, a potential landslide area is determined by clusters with a minimum of three MPs and a maximum buffer size of 50 m for each MP [67; 68]. However, considering the large distance between the MPs on the slope because of the large slope in the study area, the maximum buffer size was set to be 75 m through several runs of trial-and-error analysis.