## 4 Experimental Results and Analysis
### Data Synchronization  
To obtain the final format of the Vehicle Activity Dataset, a crucial step involves the integration of both PEMS data and image data. This amalgamation necessitates a meticulous synchronization process to align these two disparate data sources cohesively. As explained earlier, PEMS and images are acquired at different frequencies--1 Hz for PEMS and 5 frames per second (fps) for images. This proximity in frequency implies an inevitable incongruity in the data counts, with the image count exceeding that of the available PEMS data.  
The methodology involves aligning the timestamp of each captured PEMS data entry. With a fixed timestamp for each collected PEMS dataset, we determine the closest corresponding image by examining the temporal proximity between the timestamps. Through this meticulous comparison, we ensure a cohesive alignment between the PEMS data and their corresponding image snapshot.  
This synchronization process not only bridges the temporal gap between data sources but also fortifies the integrity of our dataset, facilitating an accurate correlation between the captured road scenes and the concurrent traffic and environmental measurements.  
After completing the synchronization process, our dataset attains its ultimate format, comprising 28,972 data rows. The dataset incorporates PEMS data detailed in Table 1, covering emissions, ambient data and vehicle data. Additionally, it includes road data  
Figure 9: Identifying 70 km/h Speed Limit Signs in Our Dataset  
from Table 3, encompassing information about traffic signs, traffic lights, and traffic density. The finalized dataset is structured as a CSV file for ease of accessibility and utilization.  
To enhance our understanding of the correlation between vehicle emissions and road data, we employ a statistical measure known as the point-biserial correlation coefficient. This coefficient facilitates the calculation of the correlation between our continuous vehicle gas emissions and categorical road data. The formula for the point-biserial correlation coefficient (\(r_{pb}\)) is given by:  
\[r_{pb}=\frac{\bar{X}_{1}-\bar{X}_{0}}{s_{p}} \tag{2}\]  
where \(\bar{X}_{1}\) is the mean of the vehicle gas emissions for the group with existing road data (1), \(\bar{X}_{0}\) is the mean for the group with non-existing road data (0), and \(s_{p}\) is the pooled standard deviation defined as:  
\[s_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{0}-1)s_{0}^{2}}{n_{1}+n_{0}-2}} \tag{3}\]  
Here, \(n_{1}\) is the number of observations in the group with existing road data, \(n_{0}\) is the number of observations in the group with non-existing road data, \(s_{1}\) is the standard deviation of the vehicle gas emissions for the group with existing road data, and \(s_{0}\) is the standard deviation for the group with non-existing road data. The correlation factor estimates the point-biserial correlation coefficient between certain road data and the emissions of CO, CO\({}_{2}\), NO, and NO\({}_{2}\) from vehicles, as illustrated in Figure 10. Notably, there is a strong correlation observed between stop signs and speed limits with all types of vehicle gas emissions. Traffic lights exhibit a moderate correlation with CO\({}_{2}\), NO, and NO\({}_{2}\), but a weaker one with CO. On the other hand, yield signs show a low correlation with vehicle gas emissions, with a negative correlation specifically noted with NO and NO\({}_{2}\) emissions.