## 3 Methods
### Hot-Spot Analysis  
Generally, the most reliable deformation-area data in the monitoring results obtained by SBAS\(-\)IPTA do not appear as single deformation points. Instead, there are obvious clusters of low or high values. In contrast, errors are usually distributed discretely andrandomly across the results [52]. Hotspot analysis is usually used to judge whether spatial values have clustering properties. Therefore, this paper uses hotspot analysis to identify the effective deformation and error areas in the deformation rate. It is important to determine the appropriate distance for spatial analysis. In this paper, the spatial incremental auto-correlation analysis is used to determine the optimal analysis distance [53]. The whole process is based on the [PERSON]'s \(I\) statistic, which calculates the z-score of the feature at different distances and finally uses the z-value peak as the distance threshold parameter of the spatial analysis. The equation is as follows:  
\[I=\frac{n}{\mathbb{S}_{0}}\frac{\sum_{i=1}^{n}\sum_{j=1}^{n}\omega_{ij}( \mathrm{x_{i}-\overline{x}})\big{(}\mathrm{x_{j}-\overline{x}}\big{)}}{\sum_{j =1}^{n}\big{(}\mathrm{x_{j}-\overline{x}}\big{)}^{2}} \tag{1}\]  
where \(n\) is the total number of elements when performing spatial clustering, \(\overline{x}\) is the average value of all elements, \(\omega_{ij}\) is the spatial weight of the element, and \(\mathbb{S}_{0}\) is the sum of all spatial weights. The formula is as follows:  
\[\mathbb{S}_{0}=\sum_{i=1}^{n}\sum_{j=1}^{n}\omega_{ij} \tag{2}\]  
From the results of Global Moran's \(I\) index, the \(z\)-value is used to determine the degree of spatial auto-correlation, which is calculated as follows:  
\[z=\frac{I-\mathrm{E}[I]}{\sqrt{\mathrm{Var}[I]}} \tag{3}\]  
where the calculation of \(\mathrm{E}[I]\) and \(\mathrm{Var}[I]\) is as follows:  
\[\mathrm{E}[I]=-\frac{1}{\mathrm{n}-1} \tag{4}\]  
\[\mathrm{Var}[I]=-\mathrm{E}\Big{[}I^{2}\Big{]}-\mathrm{E}[I]^{2} \tag{5}\]  
After the optimal distance threshold is obtained, the statistical model \(\mathrm{G_{i}^{*}}(d)\) can be used to see whether the monitoring feature points within a certain distance have significant spatial clustering:  
\[\mathrm{G_{i}^{*}}(d)=\frac{\sum x_{j}+x_{i}-n_{ij}\times\overline{x}^{*}}{ \sqrt{s^{*}\Big{\{}\Big{[}\big{(}n\times n_{ij}\big{)}-n_{ij}^{2}\Big{]}/n-1 \Big{\}}}} \tag{6}\]  
where \(n\) is the total number of elements, \(n_{ij}\) is the total number of elements within the distance threshold, \(x_{i}\) is the deformation value, and \(\overline{x}^{*}\) is the average value of the elements. The Getis-Ord \(\mathrm{G_{i}^{*}}\) statistics for each element are represented by their \(z\)-value and \(p\)-value. The \(p\)-value is the significance level in the hypothesis test [54]. The \(z\)-value indicates the statistical significance of the clustering at the 90% (\(p\) value 0.10), 95% (\(p\) value 0.05), and 99% (\(p\) value 0.01) confidence levels, and the corresponding values are \(\pm\)1.65, \(\pm\)1.96, and \(\pm\)2.58, respectively. In this experiment, the element points (99% confidence level) are set to be reliable deformation points with spatial-clusteringthe radar sensor to monitor the steep back slope [56; 57]. Assuming that the incident angle of the satellite sensor is \(\theta\) and that \(\alpha\) is the surface slope, the geometric distortion of the deformation observations corresponding to different incident angles and slopes is shown in Figure 4 and Table 3. It can be seen that when the local surface slope and the satellite incident angle are in a certain geometric relationship, the satellite will not detect the surface deformation. This error will result in missing detection of the landslide, so this situation is an important indicator in data evaluation. In this paper, we classify the fully monitored and foreshortened area as the visible area and layover and shadow area as the invisible area.