# Anomalous Vehicle Recognition in Smart Urban Traffic Monitoring as an Edge Service +
## 6 Experimental Results
### mSSA-Based Anomalous Behavior Detection
#### 6.2.2 Tests on the Public NGSIM Data Set  
A subset is extracted from the NGSIM US-101 data for our experimental study. This subset contains four kinds of vehicle motions, and there are 35 vehicles in total in each video frame, and 50 frames are used in this study. There are two kinds of anomalous vehicle trajectories among the four. The first is one vehicle moving with a much lower speed and the second is that the \(x\) position of a vehicle is significantly different from other vehicles. This study compares the mSSA approach with a widely used approach, the KMeans clustering method. Parameters are set as follows: \(N=20,\ L=10,\ K=2,\ h=0.5\). \(K\) is set as two for clustering: normal and abnormal vehicles. The weights of \(x,y\), and speed are the same.  
The experimental results reported in Figure 6 verifies that our mSSA approach outperforms the K-means clustering in terms of detection accuracy. When there are two anomalous vehicles, the mSSA achieves a high detection accuracy of 97%. When the number of anomalous vehicles increases, the mSSA maintains a higher detection accuracy than the K-Means clustering method obtained. In this experimental study, a very large percentage of anomalous vehicles was considered, where ten out of 35 vehicles are misbehaved, which is very unlikely to happen in practice. Additionally, the K-Means algorithm can only detect one out the two types of anomalies when the number of anomalous vehicles grows to eight and ten. This comparison study verifies that the similarity based anomaly detection methods always require a thorough prior knowledge about the monitoring scenario and the rules. However, this requirement leads to a poor adaptation for different testing scenarios.  
This experimental study also explores the selection of parameters for the mSSA algorithm. With different numbers of misbehaved vehicles among the total 35 vehicles, the window size \(L\) and time series length \(N\) are investigated to get deeper insight on their impacts on the detection accuracy. The threshold is set as \(h=0.5\) based on the experimental experiences with different thresholds. As shown by Figure 7, the time series length  
Figure 6: Detection accuracy comparison.  
changes from \(N=16\) to \(N=36\) with iteration 4. With different numbers of misbehaved vehicles, the detection accuracy shows the same trend, going up as \(N\) increases.  
The experimental study reveals that the proposed mSSA-based anomalous vehicle detection approach is sensitive enough, and it achieves a good performance when the length is the time series is small. The trade-off is, however, that a relatively longer time series provides more information, which potentially will be more reliable in some application scenarios. Hence, \(N\) and \(L\) should be adjusted accordingly for different scenarios. Meanwhile, larger values of \(N\) and \(L\) also imply longer detection delays, which must be taken into consideration specifically for delay-sensitive, mission-critical tasks.  
Figure 8 plots the ROC curve that illustrates the trade-offs between the false alarm rate and the detection rate. It is very encouraging that, when the detection rate of the proposed approach comes to 100%, the false alarm is still low. For example, as shown in Figure 8, when the number of anomalous vehicles is below eight, the operator can set the threshold to get a detection rate of 98%, and the false alarm is still below 15%.