Anomalous taxi trajectories are those chosen by a small number of drivers that are different from the regular choices of other drivers. These anomalous driving trajectories provide us an opportunity to extract driver or passenger behaviors and monitor adverse urban traffic events. Because various trajectory clustering methods have previously proven to be an effective means to analyze similarities and anomalies within taxi GPS trajectory data, we focus on the problem of detecting anomalous taxi trajectories, and we develop our trajectory clustering method based on the edit distance and hierarchical clustering. To achieve this objective, first, we obtain all the taxi trajectories crossing the same source–destination pairs from taxi trajectories and take these trajectories as clustering objects. Second, an edit distance algorithm is modified to measure the similarity of the trajectories. Then, we distinguish regular trajectories and anomalous trajectories by applying adaptive hierarchical clustering based on an optimal number of clusters. Moreover, we further analyze these anomalous trajectories and discover four anomalous behavior patterns to speculate on the cause of an anomaly based on statistical indicators of time and length. The experimental results show that the proposed method can effectively detect anomalous trajectories and can be used to infer clearly fraudulent driving routes and the occurrence of adverse traffic events.

In a conventional P-median model, demanding points are likely assigned to the closest supplying facilities, but this method exhibits evident limitations in real cases. This paper proposed a modified P-median model in which exact and approximate strategies are used. The first strategy aims to enumerate all of the possible combinations of P facilities, and the second strategy adopts simulated annealing to allocate resources considering capacity constraint and spatial compactness constraint. These strategies allow us to choose optimal locations by applying visual analytics, which is rarely employed in location allocation planning. This model is applied to a case study in Henan Province, China, where three optimal healthcare centers are selected from candidate cities. First, the weighting factor in spatial compactness constraint is visually evaluated to obtain a plausible spatial pattern. Second, three optimal healthcare centers, namely, Zhengzhou, Xinxiang, and Nanyang, are identified in a hybrid transportation network by performing visual analytics. Third, alternative healthcare centers are obtained in a road network and compared with the above solution to understand the impacts of transportation network types. The optimal healthcare centers are visually detected by employing an improved P-median model, which considers both geographic accessibility and service quality. The optimal solutions are obtained in two transportation networks, which suggest high-speed railways and highways play a significant role respectively.

In road networks, an ‘optimal’ trajectory is a geometrically optimal drive from the source point to the destination point. In reality, the driver’s driving experience or road traffic conditions will lead to differences between the ‘actual’ trajectory and the ‘optimal’ trajectory. When the differences are excessive, these trajectories are considered as anomalous trajectories. In addition, these differences can be observed in various trajectory features, such as velocity, distance, turns, and intersections. In this paper, our aim is to fuse these trajectory features and to quantitatively describe this difference to infer anomalous trajectories. The Dempster-Shafer (D-S) evidence theory is a theory and method that uses different features as evidence to infer uncertainty. The theory does not require prior knowledge or conditional probabilities. Therefore, we propose an automatic, anomalous trajectory inference method based on the D-S evidence theory that considers driving behavior and road network constraints. To achieve this objective, we first obtain all of the ‘actual’ trajectories of drivers for different source-destination pairs in taxi Global Navigation Satellite System (GNSS) trajectories. Second, we define and extract five trajectory features: route selection ( $RS$ ), intersection rate ( $IR$ ), heading change rate $\left(\mathrm{HCR}\right)$ , slow point rate ( $\mathrm{SPR}$ ), and velocity change rate $\left(\mathrm{VCR}\right)$ . Then, different features of each trajectory are combined as evidence according to Dempster’s combinational rule. The precise probability interval of each trajectory is calculated based on the D-S evidence theory. Finally, we obtain the anomalous possibility of all real trajectories and infer anomalous trajectories whose trajectory features are significantly different from normal ones. The experimental results show that the proposed method can infer anomalous trajectories effectively and that it can be used to monitor driver behavior automatically and to discover adverse urban traffic events.