## 3 Research Content and Methodology
### Research Methodology  
(a) Kernel Density Analysis  
The objective of this study is to examine the distribution and evolution of fast-moving consumer goods (FMCGs) enterprises within the vicinity of 16 metro station areas in the Chengguan District of Lanzhou. In contrast to conventional mapping techniques, this research employs point of interest (POI) data. We sourced commercial POI data for the Chengguan District from the open-source resources available through the BaiduMaps Development API platform, subsequently filtering these data according to specific categories. Additionally, we acquired building contour lines and road network data from the same platform, aggregating pertinent information within radii of 300 m, 500 m, and 1000 m surrounding each metro station. This methodology facilitates the precise identification of commercial distribution locations and enhances the visual and operational capabilities for the quantitative analysis of urban space. This paper analyzes the distribution characteristics of POIs in metro station areas during three time periods (2016, 2018, and 2020). It conducts a comparative analysis of their spatial distribution logic across these intervals. This study aims to explore the influence of metro stations on urban configuration. In the examination of the spatial distribution logic of POIs, we utilize kernel density analysis as a methodological approach to visualize both POIs and road networks. Kernel density analysis is commonly employed to depict variations in spatial density values and is effective in representing the spatial distribution patterns associated with point and line elements. The calculation formula is articulated as follows:  
\[f(x)=\frac{1}{h^{2}}\sum_{i=1}^{n}k\left(\frac{s\times c_{i}}{h}\right) \tag{1}\]  
In Formula (1), '\(s\)' denotes the position of the target point; '\(f\)(s)' represents the kernel density calculation function; '\(h\)' indicates the distance attenuation threshold; '\(n\)' signifies the number of element points whose distances from position '\(s\)' are less than or equal to '\(h\)'; '\(K\)' refers to the spatial weight function; and '\(c_{i}\)' represents each core element indexed by '\(i\)'. The kernel density value attains its maximum at each core element '\(c_{i}\)' and is equal to zero when the distance from '\(c_{i}\)' equals '\(h\)' [51; 52]. (b) Urban Gravity Model  
This research employed the urban gravity model to illustrate the appeal of stations located within an 800-m radius to high-traffic commercial establishments. The gravity model, which is frequently utilized to represent the attraction dynamics between urban centers, is derived from the gravitational formula in physics and functions as a foundational framework for characterizing spatial interactions [53; 54]. Consequently, this theoretical framework is applicable not only for elucidating the attractions among urban centers but also for analyzing both macroscopic and microscopic environments. The calculation formula is presented as follows:  
\[\text{I}_{\text{ij}}=\text{G}\frac{\text{Q}_{\text{i}}\text{Q}_{\text{j}}}{ \text{d}^{\text{b}}} \tag{2}\]  
In this context, '\(\text{I}_{\text{ij}}\)' denotes the mutual attraction between station '\(\Gamma\)' and point of interest (POI) '\(\gamma\)'. The variable '\(\text{Q}_{i}\)' signifies the traffic volume associated with station '\(\Gamma\)', while '\(\text{Q}_{i}\)' reflects the quality of POI \(\gamma\)'. The parameter d represents the distance separating station '\(\Gamma\)' from POI '\(\gamma\)'. The distance attenuation coefficient, denoted as 'b' [12], is considered negligible in this analysis due to the relatively short distances involved, as supported by previous studies [12; 55]. Furthermore, G represents the gravitational constant, which, in alignment with the principles of the physics gravity model, is assigned a value of 1 for the purposes of this study.