## 3 Experiments and Results
### Qualitative Analysis  
We scrutinized the distributions and relationships between each two features, and clarified the meaning of each cluster by matching each cluster's classification rules and the degree of PPRE. This section consists of three parts: (1) Boxplot analysis for single feature by cluster, (2) scatter analysis for two features, and (3) rule analysis by decision tree. First, we viewed the boxplot grouped by cluster, as illustrated in Figure 10a-e, as distributions of VV, VA, PV, DVP, and DVC features, respectively. In Figure 10a, cluster #5 is skewed higher than others, and this would distinguish it from the others overall. In Figure 10b,e, most frames are evenly allocated to each cluster, and a clear line does not seem to exist for their classification. In Figure 10c, we can see that in cluster #4, most frames are associated with high walking speed. In Figure 10d, cluster #0 and #1 are skewed higher than others, and have similar means and deviations. Comprehensively, cluster #5 has high VV and low PV, and cluster #4 has low VV and high PV. Cluster #0 and #1 have high DVP, but cluster #0 has moderate VV, and cluster #1 has low VV. As above results reveal, partial clusters have distinguishable features. However, boxplot analysis only illustrates a single feature, limiting its use in clearly defining the degrees of PPRE. Figure 10: Boxplots of (**a**) VV; (**b**) VA; (**c**) PV; (**d**) DVP; and (**e**) DVC by clusters. Second, we performed the correlation analysis between two features by using scatter matrices as illustrated in Figure 11. This figure describes the comprehensive results for labeled frames by hue and correlations between each feature. We studied three cases which are well-marked in detail (see Figure 12a-c). Figure 12a represents the distributions between VV and PV features by cluster. Cluster #5 features high-speed cars and slow pedestrians. This could be interpreted as moments when pedestrians walk slowly or stop to wait for fast-moving cars to pass by. Cluster #4 could be similarly interpreted as moments when cars stop or drive slowly to wait for pedestrians to quickly cross the street. Figure 12b illustrates the scatterplot between VV and DVP features. Remarkably, most clusters appear well-defined except for cluster #4. For example, cluster #3 has low VV and low DVP, for cars slowing or stopped while near pedestrians. Cluster #2 has higher VV than those of cluster #3 and low DVP, representing cars that move quickly while near pedestrians. Cluster #5 seems to capture vehicles traveling at high speeds regardless of their distance from pedestrians. Finally, Figure 12c shows the relationships between PV and DVP. In this figure, cluster #1 has low PV and high DVP, capturing pedestrians walking slowly even when cars are far from them. In cluster #4, regardless of distance from cars, pedestrians run quickly to avoid approaching cars. Through these analyses, it is possible to know features' distributions as allocated to each cluster, and to simply infer the type of PPRE that each cluster represents. Figure 11: Result of correlation analysis using scatter matrices by clusters. Figure 12: Cluster distributions of (**a**) VV-PV; (**b**) VV–DVP; and (**c**) PV–DVP. Finally, we visualized the decision tree and analyzed it in order to figure out how each cluster could be matched to degrees of PPRE. Note that the decision tree makes it possible to analyze the classified frames in detail in the form of _\"if-then\"_ rules. Figure 13 shows the result of the full decision tree without pruning, representing all of the complicated rules in detail. However, for the purpose of this paper, we chose to simplify the tree and the derived rules by limiting their maximum depth to 5 levels. Figure 14 shows the simpler decision tree and Table 4 lists its derived rules. In this figure, VV serves as the root node, reflecting its importance in classifying the given data.