## 3 Methodology
### Data Acquisition and Model Parameter Settings  
In this study, the Nanshan District of Shenzhen University in Shenzhen was chosen as the research area. The travel space-time trajectory data of four students and the location information of 13 PLCs within the test area were collected as the experimental data. Data collection employed an Amazfit smartwatch (Manufacturer: Zepp Health Corporation, Beijing, China, version: balance) equipped with a GPS module to capture the spatial and temporal location information of the students at a frequency of once every 5 s, as shown in Figure 5. The test data encompassed the longitude, latitude, speed, and time of the user's travel process, along with the longitude and latitude of the PLCs and the receiving points. The data processing, model construction, path planning solution, and visualization in this study were all implemented using Python3.8. It is important to note that the four volunteers in this study can hardly represent the entire population or all types of activity spaces. However, the study relied on terminal devices to record individual trajectories, and such information contains a wealth of personal data that is often difficult to collect. Furthermore, the primary focus of this research is on the innovative value of the methodology. Similarly, [PERSON] and [PERSON] et al. also collected trajectory activity data from only four volunteers to measure individual activity exposure to physical neighborhood environments in their study [39; 40]. Figure 5: Trajectory collection terminal. To ensure the reliability and validity of the data, trajectory data was collected using pre-calibrated mobile devices with a positioning accuracy of \(\pm\)10 m. Prior to the experiment, participants underwent standardized training to ensure proper device usage, such as avoiding signal obstruction, and device status was checked daily during data collection. A sliding window method with a window size of 10 data points was employed to detect and remove abnormal trajectory points, such as those with speeds greater than 5 km/h or sudden altitude changes exceeding 50 m. The data underwent spatiotemporal consistency validation by matching user-reported daily activity locations, such as dormitories and cafeterias, with GPS trajectories, achieving a matching accuracy of 98.7%. Hotspot locations were reverse-geocoded using the GaodeMap API(Web API service) to ensure alignment with actual points of interest (POIs), such as libraries and teaching buildings. Two independent clustering analyses, K-means and DBSCAN, were performed on user activity hotspots, yielding a clustering consistency index (Adjusted Rand Index) of 0.95, indicating high methodological reproducibility. This study selected trajectory data from four users within a relatively enclosed campus environment as a preliminary exploration, primarily based on the following considerations: (1) Behavioral consistency: Campus users (students) exhibit highly regular daily activities (e.g., the dormitory-classroom-canteen routine), facilitating the extraction of core characteristics in spatiotemporal behavior patterns. (2) Data controllability: A small sample size enables high-precision trajectory collection (5 s GPS intervals), avoiding common noise interference in large-scale data (e.g., positioning drift). (3) Reproducibility: A reproducible benchmark dataset is provided for subsequent research. Although the sample size is limited, the 1856 trajectories (averaging 464 per person) cover users' round-the-clock activities and can capture the principal components of their behaviors. This establishes a foundational framework for future work to expand into cross-city multi-group validation. The distance parameter \(L\) is set to 50 m. If the X and Y distances between two coordinates are within the tolerance range, these coordinates are considered to be within the same hotspot region. Consequently, the cluster coordinates are moved to the center of gravity of the point set.