## 3 Method
### Evaluation of 15-min Walkability to Elderly Care Facilities  
#### 3.3.1 Machine Learning-Based Analysis of Facility Importance Weights  
This study employs a random forest algorithm to construct a computational model for determining indicator weights, achieving methodological innovation compared to traditional questionnaire-based approaches. Existing research often relies on resident or expert surveys to derive POI facility attribute weights. While this method effectively captures \begin{table}
\begin{tabular}{c c c} \hline \hline
**First Level Indicators** & **Second Level Indicators** & **Example** \\ \hline Settlement [72] & Resident [73] & Jinyuan Community \\ \hline Transportation & Bus station [17] & Xihu Bridge Bus Station \\ [17; 61] & Subway station [61] & Orange Island Subway Station \\ \hline  & General hospital [17] & Hunan Provincial People’s Hospital \\ Medical care & Specialized hospital [19] & Carnation Geriatric Hospital \\ [11; 17; 19; 61] & Clinic [19] & Wangping Clinic \\  & Pharmacy [11] & People’s Pharmacy \\ \hline Leisure & Park and square [21; 22] & Meixi Lake Park, Jiangwan Cultural Square \\ [11; 21; 22] & Landscape [11] & Orange County \\ \hline Finance & Bank [17] & the People’s Bank of China, postal savings bank \\ [17; 73] & ATMs [17] & China Construction Bank 24-h self-service banking \\ Insurance [73] & China Life Insurance Company \\ \hline Government & Government [11] & Xifu Village Committee \\ [11; 17; 73] & Tianxin District Government Service Center \\  & Social organization [73] & Nursery Planting Professional Cooperative \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._subjective perceptions of 15-min living circles, it suffers from spatial representativeness: geographically uneven sampling distributions risk compromising the reliability of findings. To address the challenge, we computationally quantified facility weights through decision tree recursive partitioning within the Random Forest framework, analyzing 8 primary indicators and 23 secondary indicators. The feature importance evaluation incorporated dual dimensions: spatial accessibility and service coverage. Furthermore, stratified analyses were conducted for urban core areas and peri-urban townships to objectively quantify the heterogeneous impact weights of facilities on elderly care location suitability across distinct geographic contexts. This study utilized a Random Forest classifier with the following configurations: A balanced dataset was constructed through equal sampling of grid units containing elderly care facilities and control units, followed by stratified random splitting into training (70%) and testing (30%) subsets to preserve distributional characteristics. For node splitting, the Gini impurity criterion was adopted due to its robustness in handling class-imbalanced data. To prevent overfitting, tree depth was constrained to 8 layers, and a minimum of 15 samples per node was required for splitting. The ensemble comprised 300 decorrelated decision trees to enhance prediction stability via variance reduction. Model performance (Table 3) was assessed using accuracy (overall correctness), precision (positive predictive value), recall (sensitivity), and the F1-score (harmonic mean of precision and recall). The proposed Random Forest classifier demonstrated robust and consistent predictive capabilities across both urban and rural study areas, as evidenced by comparable accuracy (0.792 vs. 0.793) and recall (0.792 vs. 0.793) values. The marginally higher precision in urban areas (0.814) suggests enhanced reliability in identifying elderly care facilities with fewer false positives. In contrast, the rural region achieved a slightly superior F1-score (0.791), indicating a more balanced trade-off between precision and recall. As evidenced in Tables 4 and 5, marked disparities exist in the weighting influences of various facilities on elderly care facility location selection between urban and township areas.