# Spatiotemporal Road Traffic Anomaly Detection: A Tensor-Based Approach
## 5 Results
### Anomalous Traffic Patterns  
This section shows the evaluation results using the real-life dataset. Figure 8 presents eight extracted characteristic matrices, with corresponding temporal components, in which the morning (07:25-08:20) and evening (15:30-17:05) rush hours are labeled with striped green lines. Figure 9 represents the spatial placement of the extracted anomalous cells, where every anomaly event is labeled with a letter that corresponds to the Figure 8 labels.  
All characteristic matrices, except for (c) example, represent the same anomaly type as the CoM placed at the matrix's lower-left corner. This traffic situation is characterized by sudden brakes and large speed decrease when traveling from origin to destination links. These situations occur when a vehicle is facing congestion ahead and represent a potentially serious safety threat. The (c) example is the opposite situation, where the CoM is placed in the upper right corner. Here, a different but potentially dangerous event occurs, where vehicles are accelerating from low to very high speeds.  
Most of the temporal components indicate that anomalous events occur at rush hours. It can be observed that the period between rush hours (08:20-15:30) and the evening rush hour is the most represented case. This claim is justified because in rush hours, many vehicles are on the roads, and the anomaly probability arises.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Number of GNSS traces** & 6.55 billion \\ \hline
**Sampling rate** & 100 m/5 min \\ \hline
**Time-span** & August 2008–October 2014 \\ \hline
**Number of vehicles** & 4200 \\ \hline
**Number of road segments (Croatia)** & 2,000,000 \\ \hline
**Number of road segments (Zagreb)** & 86,900 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Data summary.  
Figure 7: Result of the grid-based map segmentation and the data filtering process.  
Figure 9 represents the spatial placement of the extracted abnormal cells, where every anomaly event is labeled with a letter that corresponds to the labels in Figure 8. The spatial placement of the anomalies indicates two spatial clusters: (i) Edges of the city represented  
Figure 8: Results of the anomaly detection; (**a**–**h**) represent characteristic matrices which represent anomalous patterns (**left**) with corresponding temporal components (**right**).  
with the examples (a), (b), (d), (f), (h), and (ii) city center represented with the examples (c), (e), and (g). The cluster of transitions placed at the edges of the city points to the congestion related to daily commuters traveling to work from outside of the city center. By considering temporal components, it can be observed that the evening rush hour contributes mostly to the congestion and the anomalous events in the city, with the exception of example (f), where the anomalous events mostly occur at the morning rush hour. The city center cluster is characterized by the temporal components that point to the intervals between rush hours, evening rush hour, and the interval later in the day, after the evening rush hour. This behavior is mostly attributed to the inefficient traffic signalization, which leads to the prolongation of the anomaly events mostly caused by the rush-hour congestion. Similar behavior can be caused by the tourist attractions and other entertainment facilities provided at the city center. During the transition in example (e), the most congested bridge in the city was captured. This information indicates the possible usable information for the urban planners by suggesting the need to build a new bridge that will connect the north and the south parts of the city.