# Anomalous Vehicle Recognition in Smart Urban Traffic Monitoring as an Edge Service +
## 6 Experimental Results
### mSSA-Based Anomalous Behavior Detection
#### 6.2.1 Results with Local Traffic Data  
Figure 3 shows an example scenario of the videos collected by the drone overseeing the local traffic. The video streams record the traffic on a road near our campus, which is a local highway with the speed limit of 72 Km/h. For testing purposes, multiple types of anomalous behaviors are created. Three parameters are selected to describe the trajectory for each vehicle: \(x\) position and \(y\) position of a vehicle in a video frame and the driving speed. The sample frequency on the video is ten samples per second. Five trajectories are selected mainly to validate the feasibility and effectiveness of our method. The five vehicles are labelled as \(ID1\), \(ID2\), \(ID3\), \(ID4\), and \(ID5\), and the anomalous vehicle is \(ID4\). Grouping is the most important step in the mSSA procedure. Elaborated selections will allow the decomposition of the components of a time series to be conducted efficiently and achieve a higher precision. Figure 4 illustrates the eigenvalues corresponding to the driving speed of vehicle \(ID1\). The larger the eigenvalue, the more significant information is contained in the corresponding dimension. In the example shown by Figure 4, the largest eigenvalue is almost \(10^{3}\), and all the others stay below ten. This substantial difference leads to the decision that only the largest eigenvalue is applied for reconstruction operation. The others are discarded due to the limited influences. Figure 5 presents the results of reconstruction for different components of testing trajectories. The time series length \(N\) is 30 within three seconds and the window length \(L\) is 15. By default, in this paper, the window length \(L\) for the construction of the trajectory matrix is set as half of \(N\) unless explicitly noted. Figure 5a shows the original speed of the five vehicles. The anomalous vehicle, marked as \(ID4\), stops on the road. The curves in Figure 5a verified that the original time series of speed contains noises. The noises mainly result from the vehicle detection algorithms, which are not able to obtain the position information of a vehicle from the same part on the vehicle body in all the frames. Meanwhile, it is very encouraging that the SSA algorithm performs robustly and noises are efficiently attenuated at the grouping step. Figure 3: An example traffic scenario collected by the drone. In contrast, Figure 5b is the reconstruction result from the subspace that contains only the largest eigenvalue. It is obvious that the interference from noises is removed, and the trend for each vehicle is very clear. After the grouping step, time series for normal vehicles become closer, which is very helpful to increase the detection accuracy. Figure 5c,d show the reconstruction results of the second and third components of the original time series for speed information. The curves in Figures 5c,d do not show a clear trend or any periodic patterns; they change randomly. This result clearly verified the effectiveness of the grouping strategy. It is worth noting the significant distance from \(ID4\) to the base (average) that is constructed from all vehicles in the set. In this experimental study, we have also compared the computation time on two different edge devices. One is a laptop computer with the i7-6820 HQ processor, 32 GB  
Figure 4: Eigenvalues for different dimensions. Figure 5: Components of testing vehicle trajectories. (**a**) Original speed data sequence; (**b**) The first component; (**c**) The second component; (**d**) The third component. memory space, and the maximum frequency is 2.7 GHz. The experimental results show that, when the number of vehicles increases from five to 35, the computing time grows from around 10 ms to almost 100 ms. Since the sampling frequency is still ten samples per second, this performance is sufficient to meet the requirement for anomaly detection in real time. In our data set, with a different number of total vehicles, the percentage of anomaly behaved vehicles is around 20%.