## 4 Data Analysis
### Spatiotemporal Patterns
#### 4.2.2 Cluster Analysis  
According to the analysis above, the usage patterns of Mobike around different subway stations are different at different times. Hierarchical clustering, one of the most widely used clustering methods, was adopted to classify 277 rail stations with the distribution probabilities of trips from origin and trips to destination on weekdays. The clustering started with a set of clusters, each consisting of one station. A merging criterion, such as single link, complete link, centroid, average or Ward method, should be selected to merge these one-object clusters. Compared with other merging techniques, the average method and Ward method are most commonly used. Considering that [PERSON]'s minimum variance method outperforms other hierarchical clustering methods to some extent, we applied the Ward criterion in this study. Common evaluation methods, including the scree test and Kaiser-Harris criterion, were conducted to determine the number of clusters to retain. The scree plot can display the shape of the resulting curve, indicating the maximum number of components to retain, and the Kaiser-Harris criterion suggests the retention of clusters with eigenvalues above 1. Finally, the clusters can be divided into four categories. The curves of temporal patterns of all categories are drawn and reflected on the map, as illustrated in Figure 4. The abscissa represents time (from 0:00 to 22:00), and the ordinate represents how many trips from origin start (arrive by shared bike at the station) or how many trips to destination finish (depart by shared bike from the station) at this time. In general, the curve shapes of all categories exhibit apparent variations. Cluster 1 exhibits a triple-peak characteristic. The peak time (8:00) in the morning rush is later than the average peak time (7:00, Figure 2b). These stations are mainly distributed on the east and west sides in the vicinity of the central area of the city. The commuters depart later from their residences because of the shorter average commuting distance. Compared with the other three categories, it exhibits the highest proportion of flexible travel; thus, the discrepancy of peak-to-trough is small. The curve of Cluster 2 is similar to the overall probability density curve (Figure 2b). The curves of the temporal distribution of trips departing from or arriving at the station are generally overlapping; the stations are mainly located in the periphery of the urban core, with a well-proportioned distribution of stations and moderate variation between trips from origin and to destination. With regard to the stations of Cluster 3, the proportion of trips departing from and arriving at this kind of station during rush hour exhibits significant variation. In the  
Figure 4: Temporal patterns and geographical distribution of each cluster of subway stations on weekdays: (**a**) Cluster 1 stations; (**b**) Cluster 2 stations; (**c**) Cluster 3 stations; (**d**) Cluster 4 stations. morning rush, the number of Mobike used for departure from origin is significantly higher than that for trips to destination; its peak value is a maximum of 0.24, approximately two times that of the other categories. The situation in the evening rush is opposite to that of the morning rush. This category of station is mainly distributed over the periphery of the city. The longer commuting distance results in earlier departure times in a more concentrated time period. The trip purpose of this category is relatively straightforward--for commuting in most cases. The number of trips departure from origin in the morning rush is apparently higher than the number of trips arriving at destination during the evening rush. On the one hand, the travel in the morning rush is more concentrated; on the other hand, at this category of station, the use of Mobikes is generally counterproductive because during the morning rush, bikes fill the area around the station, leaving no available space for parking, whereas in the evening rush, passengers cannot find a bike to ride.