## 2 Materials and Methods
### Research Methods
#### 2.2.3 Data Preprocessing  
In this study, data preprocessing is divided into three parts. The first part involves the preprocessing of research samples from 12 settlements within Jiexiu City using satellite imagery and GIS technology. Based on the site plans from settlement protection planning documents, the settlement buildings were precisely located, and raster base maps of settlement buildings with 1 m precision were created using AutoCAD software (Version 2018), with building areas filled in black. Meanwhile, 5 m precision elevation data from Jiexiu City were used to conduct the slope analysis, identifying suitable construction areas with slopes of less than 10\({}^{\circ}\). Raster base maps of these suitable construction areas, also with 5 m precision, were generated and filled in black as well. This step aims to generate settlement building distribution maps and suitable construction area distribution maps (Figure 3) where the slope is less than 10\({}^{\circ}\)[35], which will facilitate subsequent calculations of fractal dimensions and correlation validation.  
The second part focuses on the subspace regional division of Xingdi Village, which is characterized by a relatively high fractal dimension among the 12 settlements and a minimal difference in fractal dimension compared to the suitable construction areas. This  
Figure 3: Building and suitable construction area distribution.  
village is divided into 67 regions using a grid size of 150 m \(\times\) 150 m (Figure 4), and the fractal dimensions of building patches within each grid cell are calculated accordingly.  
After verification, it was found that the explanatory power of independent variables in sub-regions derived from a 100 m \(\times\) 100 m grid segmentation is insufficient for the dependent variable. Conversely, excessively large grids may lead to an inadequate sample size during MGWR regression [16]. The third part involves mapping the independent and dependent variables of MGWR regression. We selected the fractal dimension values of subspace grid building patches as the dependent variable, while different levels of slope and aspect distribution ratios were utilized as independent variables (Figure 5). The classification of slopes is defined as follows: flat (0-5\({}^{\circ}\)), gentle slope (5-10\({}^{\circ}\)), and unsuitable for construction (above 10\({}^{\circ}\)) [35]. Additionally, only the proportion of south-facing areas is considered for the aspect ratio. X\({}_{1}\) is defined as the ratio of flat areas (0-5\({}^{\circ}\)) to the total grid area, X\({}_{2}\) represents the average elevation of each grid, and X\({}_{3}\) is the ratio of south-facing slope areas to the total grid area. Compared to the average slope, the slope-area ratio better reflects topographical characteristics, as the average slope may obscure terrain details. For example, steep regions may also contain flat areas, which cannot be captured by the average value. Meanwhile, the slope-area ratio is less sensitive to extreme values and is less affected by outliers. The inclusion of elevation height considers the vertical height factor of mountain settlements, making the results closer to 3D analysis.  
Data source: The settlement layout maps are derived from the traditional village protection plans of each settlement, with the diagrams accurately drawn based on coordinate  
Figure 4: Zoning map.  
Figure 5: Slope and aspect division.  
systems to ensure high precision. Elevation data were obtained from a third-party online platform, featuring a spatial resolution of 5 m. The temporal coverage of the elevation data corresponds to the year 2022, and the acquisition date was March 2024. To meet the specific requirements of this study, the data underwent additional preprocessing, including cropping and refinement.