## 2 Materials and Methods
### InSAR Hotspot Clustering Analysis  
Typically, a cluster of PSs representing relative high deformation velocities tends to aggregate in unstable areas, which are often recognized as active landslides or ground subsidence areas. However, point-based deformation rate maps are scattered and noise-affected, especially in mountainous areas where coherence varies largely in space. Such results can hardly provide reliable information indicating the spatial difference of landslide local deformation [32]. Thus, only point-based PSs with the absolute displacement velocity value above a basic threshold (>10 mm/yr in this study) and showing obvious spatial aggregation can be used to discern active deformation areas from stable regions.  
In this study, we employed the hotspot and clustering analysis (HCA), which uses a statistics approaches, namely Getis-Ord Gis\({}^{*}\) statistics [33], to identify the hot and cold spots of point clustering. The obtained \(Z\) scores measured the extent of the clustering, and the Gi-Bin value identified the hot and cold spots of statistical significance with different levels of confidence intervals. PSs with Z-scores over 2.9 were extracted as 'hotspots' and used to identify mass ground movements, which corresponded to an approximate 99% confidence interval. Represented by the Gi-Bin values, positive values were rendered with blue and negative values with red. Both colors indicate the location of relevant clustering of PSs, with deeper colors standing for a higher clustering status. The clustering of elements with no statistical significance were rendered with light yellow, which means they provide no reliable information in identifying active landslides or ground deformation. The result is shown in Figure 5a.  
Figure 4: Displacement velocity (Vslope) map of the area generated from the Sentinel-1 data stack.  
Hotspots, PSs, and landslide polygons can be overlaid on high-resolution Google Earth images in a GIS system to obtain substantial information regarding the exact deformation area, which, in turn, can provide exact targets for further field investigation. Landslide polygons with hotspots insides its boundaries were considered as suspected active landslides, and then a second confirmation step was conducted at the slope scale to verify the effectiveness of the engineering remedial measures for controlled landslides. Different colors were rendered on landslides polygons representing their active level, orange representing active controlled landslides, pink for active uncontrolled landslide and yellow for the remaining inactive landslides (Figure 5b).  
Figure 5: (**a**) Persistent Scatterer Interferometry (PSI) hotspot maps of the entire study area including the main district from Wanzhou to Yunyang county. Red hotspots and blue hotspots correspond to the clustering of PSs with high deformation rates. (**b**) Landslide polygons rendered with different colors according to the hotspot map. Orange: Active landslides with engineering remedial works. pink: Active landslide area without engineering remedial works. Yellow: Other inactive landslides. Four numbered landslides are representative landslides combining field investigation and ground monitoring data, which will be discussed in the following section.