Trajectory Similarity Measure Research Articles

A movement-aware measure for trajectory similarity and its application for ride-sharing path extraction in a road network

Recognizing common travel paths of crowds in a road network is valuable for understanding human mobility patterns and developing intelligent ride-sharing services. To achieve this, it is critical to measure the similarity of their trajectories. Although many measures have been proposed in the past decades, they often ignore movement consistency, exhibit one or more deficiencies in the face of noise and misaligned trajectories, or require extra parameters to tune predictions. In this paper, we propose an improved similarity measure called the directed segment path distance (DSPD), which considers the spatial proximity and movement consistency of trajectories. By integrating the spatial proximity distance and moving direction similarity between trajectories, the DSPD is a competitive parameter-free similarity measure that can effectively distinguish trajectories with different movement characteristics. To verify the effectiveness of the DSPD, we conducted a quantitative comparative study between the DSPD measure and 11 state-of-the-art trajectory similarity measures on six simulated trajectory datasets and applied the DSPD to two typical application scenarios: trajectory clustering for road network generation and retrieving common trajectories for ride-sharing path planning. The results demonstrate the effectiveness, robustness, and superiority of the DSPD and its great potential in trajectory search, clustering, and classification.

Trajectory Similarity Measurement: An Efficiency Perspective

Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, trajectory similarity is quantified by means of non-learned measures, e.g., Hausdorff, that operate directly on the trajectories. Recent studies exploit deep learning to map trajectories to d -dimensional vectors, called embeddings. Then, some distance measure, e.g., Manhattan, is applied to the embeddings to quantify trajectory similarity. The resulting similarities are inaccurate: they only approximate the similarities obtained using the non-learned measures. As embedding distance computation is efficient, focus has been on obtaining embeddings of high accuracy. Adopting an efficiency perspective, we analyze the time complexities of both the non-learned and the learning-based approaches, finding that the time complexities of the former approaches are not necessarily higher. Through extensive experiments on open datasets, we find that only a few learning-based approaches can deliver the promised higher efficiency, when the embeddings can be pre-computed, while non-learned approaches are more efficient for one-off computations. Among the learning-based approaches, the self-attention-based ones are the fastest and the most accurate. These results have implications for the use of trajectory similarity approaches given different application requirements.

A Principled Distributional Approach to Trajectory Similarity Measurement and its Application to Anomaly Detection

This paper aims to solve two enduring challenges in existing trajectory similarity measures: computational inefficiency and the absence of the ‘uniqueness’ property that should be guaranteed in a distance function: dist(X, Y ) = 0 if and only if X = Y , where X and Y are two trajectories. In this work, we present a novel approach utilizing a distributional kernel for trajectory representation and similarity measurement, based on the kernel mean embedding framework. It is the very first time a distributional kernel is used for trajectory representation and similarity measurement. Our method does not rely on point-to-point distances which are used in most existing distances for trajectories. Unlike prevalent learning and deep learning approaches, our method requires no learning. We show the generality of this new approach in anomalous trajectory and sub-trajectory detection. We identify that the distributional kernel has (i) a data-dependent property and the ‘uniqueness’ property which are the key factors that lead to its superior task-specific performance, and (ii) runtime orders of magnitude faster than existing distance measures.

Retrieving Similar Trajectories from Cellular Data of Multiple Carriers at City Scale

Retrieving similar trajectories aims to search for the trajectories that are close to a query trajectory in spatio-temporal domain from a large trajectory dataset. This is critical for a variety of applications, like transportation planning and mobility analysis. Unlike previous studies that perform similar trajectory retrieval on fine-grained GPS data or single cellular carrier, we investigate the feasibility of finding similar trajectories from cellular data of multiple carriers, which provide more comprehensive coverage of population and space. To handle the issues of spatial bias of cellular data from multiple carriers, coarse spatial granularity, and irregular sparse temporal sampling, we develop a holistic system cellSim . Specifically, to avoid the issue of spatial bias, we first propose a novel map matching approach, which transforms the cell tower sequences from multiple carriers to routes on a unified road map. Then, to address the issue of temporal sparse sampling, we generate multiple routes with different confidences to increase the probability of finding truly similar trajectories. Finally, a new trajectory similarity measure is developed for similar trajectory search by calculating the similarities between the irregularly-sampled trajectories. Extensive experiments on a large-scale cellular dataset from two carriers and real-world 1,701 km query trajectories reveal that cellSim provides state-of-the-art performance for similar trajectory retrieval.

An approach for traffic pattern recognition integration of ship AIS data and port geospatial features

ABSTRACT Recognition of ship traffic patterns can provide insights into the rules of navigation, maneuvering, and collision avoidance for ships at sea. This is essential for ensuring safe navigation at sea and improving navigational efficiency. With the popularization of the Automatic Identification System (AIS), numerous studies utilized ship trajectories to identify maritime traffic patterns. However, the current research focuses on the spatiotemporal behavioral feature clustering of ship trajectory points or segments while lacking consideration for multiple factors that influence ship behavior, such as ship static and maritime geospatial features, resulting in insufficient precision in ship traffic pattern recognition. This study proposes a ship traffic pattern recognition method that considers multi-attribute trajectory similarity (STPMTS), which considers ship static feature, dynamic feature, port geospatial feature, as well as semantic relationships between these features. First, A ship trajectory reconstruction method based on grid compression was introduced to eliminate redundant data and enhance the efficiency of trajectory similarity measurements. Subsequently, to quantify the degree of similarity of ship trajectories, a trajectory similarity measurement method is proposed that combines ship static and dynamic information with port geospatial features. Furthermore, trajectory clustering with hierarchical methods was applied based on the trajectory similarity matrix for dividing trajectories into different clusters. The quality of the similarity measurement results was evaluated by quality criterion to recognize the optimal number of ship traffic patterns. Finally, the effectiveness of the proposed method was verified using actual port ship trajectory data from the Tianjin Port of China, ranging from September to November 2016. Compared with other methods, the proposed method exhibits significant advantages in identifying traffic patterns of ships entering and leaving the port in terms of geometric features, dynamic features, and adherence to navigation rules. This study could serve as an inspiration for a comprehensive exploration of maritime transportation knowledge from multiple perspectives.

Measuring Trajectory Similarity Based on the Spatio-Temporal Properties of Moving Objects in Road Networks

Advancements in navigation and tracking technologies have resulted in a significant increase in movement data within road networks. Analyzing the trajectories of network-constrained moving objects makes a profound contribution to transportation and urban planning. In this context, the trajectory similarity measure enables the discovery of inherent patterns in moving object data. Existing methods for measuring trajectory similarity in network space are relatively slow and neglect the temporal characteristics of trajectories. Moreover, these methods focus on relatively small volumes of data. This study proposes a method that maps trajectories onto a network-based space to overcome these limitations. This mapping considers geographical coordinates, travel time, and the temporal order of trajectory segments in the similarity measure. Spatial similarity is measured using the Jaccard coefficient, quantifying the overlap between trajectory segments in space. Temporal similarity, on the other hand, incorporates time differences, including common trajectory segments, start time variation and trajectory duration. The method is evaluated using real-world taxi trajectory data. The processing time is one-quarter of that required by existing methods in the literature. This improvement allows for spatio-temporal analyses of a large number of trajectories, revealing the underlying behavior of moving objects in network space.

QuadGridSIM: A quadrilateral grid‐based method for high‐performance and robust trajectory similarity analysis

AbstractMeasuring trajectory similarity is a fundamental algorithm in trajectory data mining, playing a key role in trajectory clustering, pattern mining, and classification, for instance. However, existing trajectory similarity measures based on vector representation have challenges in achieving both fast and accurate similarity measurements. On one hand, most existing methods have a high computational complexity of O(n × m), resulting in low efficiency. On the other hand, many of them are sensitive to trajectory sampling rates and lack of accuracy. This article proposes QuadGridSIM, a quadrilateral grid‐based method for trajectory similarity analysis, which enables high‐performance trajectory similarity measure without the cost of low effectiveness. Specifically, we first realize the multiscale coding representation of trajectory data based on quadrilateral discrete grids. Then, a novel trajectory similarity measure is defined to reduce the computational complexity of O(n). Several effectiveness properties of QuadGridSIM are further optimized, including the spatial overlap, directionality, symmetry, and robustness to sampling rate variations. Experimental results based on real‐world and simulated taxi trajectory data indicate that QuadGridSIM outperforms most of the other tested algorithms developed previously in terms of effectiveness, particularly in its robustness regarding trajectory sampling rates. Furthermore, QuadGridSIM exhibits superior performance and is approximately one order of magnitude faster than previous methods in the literature. QuadGridSIM provides a solution to the low‐efficiency problem of massive trajectory similarity analysis and can be applied in many application scenarios, such as route recommendation and suspect detection.

A novel trajectory similarity measurement method based on node‐sequence hierarchical digraph

AbstractTrajectory similarity measurement is a basic and vital task in trajectory data mining, which has attracted extensive research in the past decades. Recent works focused on the sequence and hierarchy property of trajectories to construct similarity measurements. However, these methods ignore the user information on the visiting locations, such as semantic and time distribution. In light of this, a novel trajectory similarity measurement based on Node‐Sequence Hierarchical Digraph (NSHD) framework is proposed in this article. We first propose a Time‐Weighted Stay Point Detection (TWSPD) method to extract real visiting locations of users more accurately. Then, the nodes of digraph are obtained by clustering users' stay points and the edges of digraph are sequence information that users move between these nodes. An Advanced Earth Mover's Distance (AEMD) is proposed to measure the node similarity between users, considering visiting time distribution and semantic information simultaneously. Both node and sequence similarities are used to calculate the similarity score to obtain the final trajectory similarity measurement. Experiments on Geolife and T‐Drive datasets show that our proposed method offers competitive performance with mean reciprocal rank values reaching 96.01 and 81.26%, which outperforms related trajectory similarity measurements by more than 10 and 15%.

A Trajectory-Based User Movement Pattern Similarity Measure for User Identification

Recently, matching the cross-site user accounts based on user trajectory similarity has been attracting much attention, which benefits many applications. Most of existing works measure the user trajectory similarity based on the proximity of stay points. However, since the user trajectory is noisy, sparse and biased, the trajectory similarity measure is not a trivial task. In theory, the user movement pattern inherent in user trajectory is unique to the user and site-independent, which may be the key to address the above question. Thus, we propose a trajectory-based user movement pattern similarity measure for user identification. Specifically, we first find the frequent user stay points at each time slot to represent the user daily activities, and then present a similarity measure method for user daily activities, where we assign a global popularity and local popularity to stay point with the aim of accurately characterizing the contribution of stay point to the similarity. To represent the user-specific and site-independent movement pattern, we propose a trajectory-oriented embedding method, called T-LINE, which preserves the similarity of user daily activities. Finally, based on the similarity of movement patterns between a user and his/her candidates, we select top <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> similar users as the matching users. The experiments conducted on three ground-truth datasets show a significant improvement compared to the representative works.

A novel ship trajectory clustering analysis and anomaly detection method based on AIS data

The increasing volume of ship traffic has resulted in new challenges for the supervision of maritime safety administration. The conventional manual monitoring approach for maritime traffic is inefficient and lacks specifics, particularly for supervising ships with abnormal trajectories. To address this issue, this study proposes utilizing the minimum description length criterion to extract features from ship trajectory data provided by the automatic identification system (AIS). This approach simplifies the compression of ship trajectories. Additionally, the dynamic time warping trajectory similarity measurement algorithm is employed to optimize the density-based spatial clustering of applications with noise algorithm. This optimization enables the clustering of ship trajectories and the acquisition of normalized ship motion trajectories. Furthermore, a ship trajectory prediction method based on a transformer model is proposed, and the normalized motion trajectory is used as the training set for model training. The trained ship trajectory prediction model is subsequently utilized to predict the target ship trajectory. The AIS ship trajectory data in the vicinity of Yantai Port were used for experimental verification. The results demonstrate the effectiveness of the proposed approach in identifying abnormal ship trajectories.

Hierarchical Method for Mining a Prevailing Flight Pattern in Airport Terminal Airspace

Due to the variety of flight patterns in airport terminal airspace, as well as the high global similarity of different flight patterns entering and leaving from the same runway or corridor, it is difficult for current mainstream methods to achieve good clustering. To this end, this paper first constructs a truncated dynamic time warping (TDTW) trajectory similarity measurement to characterize different trajectory patterns with high global similarity and large local differences. Furthermore, a hierarchical flight pattern mining method is proposed, which is divided into four layers according to different characteristics. The first three layers of the method classify trajectories according to takeoff and landing types, runways, and corridors; whereas the fourth layer uses a -medoid clustering method based on TDTW, thereby making the mining process more controllable and in line with actual operation. Compared to dynamic time warping, the experimental results show that the intraclass compactness and interclass separation of the cluster obtained by the proposed method have decreased and increased by 44.6 and 20.1%, respectively, and the overall performance has improved by 54.1%. More refined and reasonable flight patterns have been obtained.

Leveraging similarity analysis to understand variability in movement behavior

AbstractThe increasingly large volume of trajectories of moving entities obtained through GPS and cellphone tracking, telemetry, and other location‐aware technologies motivates researchers to understand the implicit patterns hidden in movement trajectories and understand how movement is influenced by the environmental context. Trajectory similarity serves as an important tool in computational movement analysis and as the foundation of revealing those patterns. However, there are various trajectory similarity measures, each of which has its own strengths and weaknesses. In this article, we present a hierarchical clustering framework that integrates five commonly used similarity measures, including Fréchet distance, dynamic time warping, Hausdorff distance, longest common subsequence, and normalized weighted edit distance, a special kind of edit distance for movement analysis. The framework aims at clustering similar patterns and identifying variability in movement. The optimal number of clusters are first obtained. Then, the clusters are characterized by environmental variables to explore the associations between variability in movement and the environmental conditions. We evaluate the proposed framework using 15 years of tracking data of turkey vultures, tracked at 1‐ to 3‐h sampling intervals, during their fall and spring migration seasons. The results suggest that, at 5% significance level, turkey vultures select their movement paths intentionally and those selections appear to be related to certain environmental context variables, including thermal uplift, vegetation state (observed indirectly through Normalized Difference Vegetation Index), temperature, precipitation, tailwind, and crosswind. And interestingly, there exist preferential differences among individuals. Although the preference of the same turkey vulture is not strictly consistent over different years, each individual tends to preserve a more similar preference over different years, compared with the preferences of other turkey vultures.

Improvements (or not!) in the hand trajectory of stroke patients due to practice of a virtual game

Movement trajectories contain important spatio-temporal information to characterise human activities that require displacements (eg grasp an object). A trajectory (dis)similarity measure is highly relevant in trajectory data analysis. The main purpose of this study was to develop a running version of the Procrustes Method to quantify dissimilarity between trajectories along time, as a method that can be used in further research. Empirical data was used to quantify changes in stroke patients’ movements in a daily life task (drinking water) after participating in a combined rehabilitation program (virtual reality plus conventional therapy). Results of the simulation study reflected the reliability of the Running Procrustes Method to quantify the dissimilarity between trajectories continuously over time. For the empirical data, this method identified critical parts of the drinking water task, providing information that might suggest beneficial effects of the combined program in stroke patients’ daily life tasks.

Spatiotemporal Companion Pattern (STCP) Mining of Ships Based on Trajectory Features

Spatiotemporal companion pattern (STCP) mining is one of the means to identify and detect group behavioral activities. To detect the spatiotemporal traveling pattern of ships from massive spatiotemporal trajectory data and to understand the movement law of group ships, this article proposes a feature-driven approach for STCP mining that consists of (1) generating the grid index via the rasterizing of geospace and characterizing trajectory points via the spatiotemporal trajectory grid sequences (STTGSs) of ships; (2) designing filtering rules with the constraints of range, time and distance to construct a candidate set for ship STCP mining; and (3) measuring the STTGS similarity of the associated ships and setting the confidence threshold to realize spatiotemporal companion mining. The effectiveness of the proposed method is practically validated on a real trajectory dataset which is collected from the Taiwan Strait waters. The experimental results are as follows: 825 pairs of associated ships and 225 pairs of accompanying ships are mined when the grid size is 0.05° and the confidence is 0.5. Larger grid sizes can increase the inclusiveness of the associated ship trajectory similarity measurement, which can result in an increase in confidence of pattern. A large number of pseudo-accompaniment ships are extracted to the result set, resulting in a more dispersed distribution of pattern confidence. By verifying the proposed method, accompanying behavioral activities such as ship cooperative operation, companion navigation method, and so on, can be detected. These results can provide a reference for the research of ship group behavior identification and have an important application value for water transportation management.

Bidirectional Multiple Object Tracking Based on Trajectory Criteria in Satellite Videos

Multiple object tracking (MOT) in satellite videos requires to detect all objects belonging to specified categories and identify each object, which plays a basic and necessary role in automatic driving, traffic surveillance and smart city. The traditional MOT methods in satellite videos mostly follow the detection-association framework. However, detection-association framework works under a strict assumption that all objects are correctly localized by the detector. In practice, MOT in satellite videos faces challenges such as low resolution, tiny objects, and the wide field of view, which leads to the degradation of detector performance. In order to reduce the impact of detector degradation, we propose a bi-directional multiple object tracking framework based on trajectory criteria (BMTC) in satellite videos. In BMTC, the SOT tracker carries out locating the objects between consecutive frames and the detector is just used for finding new objects. Therefore, it is less dependent on the detector performance. According to the characteristics of satellite videos, the trajectory criteria are designed to control the state of the tracker, which includes trajectory density, the limit of consecutive virtual motion predictions, and trajectory similarity measurement. Invalid fragment trajectory backtracking is implemented to alleviate the misalignment caused by the above subsection trajectory criteria. The method is validated on the VISO benchmark and SkySat-1 dataset. The experimental results show the improvement of completeness and accuracy, and the proposed tracker achieves state-of-art performance.

Behavior pattern mining based on spatiotemporal trajectory multidimensional information fusion

Trajectory data mining is widely used in military and civil applications, such as early warning and surveillance system, intelligent traffic system and so on. Through trajectory similarity measurement and clustering, target behavior patterns can be found from massive spatiotemporal trajectory data. In order to mine frequent behaviors of targets from complex historical trajectory data, a behavior pattern mining algorithm based on spatiotemporal trajectory multidimensional information fusion is proposed in this paper. Firstly, spatial–temporal Hausdorff distance is proposed to measure multidimensional information differences of spatiotemporal trajectories, which can distinguish the behaviors with similar location but different course and velocity. On this basis, by combining the idea of k-nearest neighbor and density peak clustering, a new trajectory clustering algorithm is proposed to mine behavior patterns from trajectory data with uneven density distribution. Finally, we implement the proposed algorithm in simulated and radar measured trajectory data respectively. The experimental results show that the proposed algorithm can mine target behavior patterns from different complex application scenarios more quickly and accurately compared to the existing methods, which has a good application prospect in intelligent monitoring tasks.

GLTC: A Metro Passenger Identification Method Across AFC Data and Sparse WiFi Data

In this paper, we investigate an efficient way for identifying passengers in a metro system across two heterogeneous but complementary trajectory data sources: AFC data recording two points per trip about when and where a passenger enters or leaves the metro system, and WiFi data recording a few points passed by a passenger in the way of some of his/her trips. The identification result can help us to complete individuals’ mobility, and benefits to lots of services, e.g., individual route choice analysis, epidemic case detecting and so on. The problem is similar to calculate the similarity between two trajectories from two data sources, where a trajectory refers to a sequence of points where a passenger appeared in a metro system on observed days. However, due to the small location space in a metro network, large number of passengers with similar travel pattern, and so on, there are lots of trip overlaps or point co-occurrences between different passengers. That results in a large number of passengers mismatched by existing trajectory similarity measurement. To address the problem, this paper proposes a novel global-local correlation based trajectory similarity measurement GLTC. Specifically, GLTC first extracts all overlapping trip pairs of two trajectories by considering the spatiotemporal inclusions from global level. Then it gets the similarity by aggregating each overlapping trip pair’s local similarity, which is calculated by considering some data-driven insights helpful to uniquely identify a passenger (e.g., uneven passenger flow distribution in different cross-sections of a metro network, the number of trips in same travel pattern of a trajectory, and so on). We evaluate GLTC based on real-world data, and the experimental result shows that GLTC outperforms other baselines.

Unsupervised hierarchical methodology of maritime traffic pattern extraction for knowledge discovery

Owing to the space–air–ground integrated networks (SAGIN), seaborne shipping has attracted increasing interest in the research on the motion behavior knowledge extraction and navigation pattern mining problems in the era of maritime big data for improving maritime traffic safety management. This study aims to develop a novel unsupervised methodology for feature extraction and knowledge discovery based on automatic identification system (AIS) data, allowing for seamless knowledge transfer to support trajectory data mining. The unsupervised hierarchical methodology is constructed from three parts: trajectory compression, trajectory similarity measure, and trajectory clustering. In the first part, an adaptive Douglas–Peucker with speed (ADPS) algorithm is created to preserve critical features, obtain useful information, and simplify trajectory information. Then, dynamic time warping (DTW) is utilized to measure the similarity between trajectories as the critical indicator in trajectory clustering. Finally, the improved spectral clustering with mapping (ISCM) is presented to extract vessel traffic behavior characteristics and mine movement patterns for enhancing marine safety and situational awareness. Comprehensive experiments are conducted and implemented in the Chengshan Jiao Promontory in China to verify the feasibility and effectiveness of the novel methodology. Experimental results show that the proposed methodology can effectively compress the trajectories, determine the number of clusters in advance, guarantee the clustering accuracy, and extract useful navigation knowledge while significantly reducing the computational cost. The clustering results are further explored and follow the Gaussian mixture distribution, which can help provide new discriminant criteria for trajectory clustering.

A comparative study on measurement of lane-changing trajectory similarities

Lane change (LC) represents an important driving behavior and significantly influences traffic efficiency and safety. Spatial LC behavior should be evaluated for vehicles in a transportation system, identifying vehicle movement patterns through similarities in LC trajectories. Contexts determine the trajectory of an objective. Therefore, it is necessary to deeply understand these contexts so that they could be incorporated into movement investigation. Both internal and external contexts pose direct/indirect impacts on movements and enable movement changes. As a result, contexts should be treated as distinct movement process dimensions, and the recording of data for trajectory evaluation based on spatiotemporal dimensions is inevitable. However, due to complicated inter-dimension associations, trajectory similarity measurement has rarely been studied in the literature. This paper focuses on contextualizing a similarity measure of LC trajectories using internal and external contexts and spatial footprints. A total of three models, including the longest common subsequence (LCSS), edit distance on real sequences (EDR), and dynamic time warping (DTW), are employed to examine multi-dimensional similarities between trajectories. The Next Generation Simulation (NGSIM) data were applied to evaluate these models. Contextual data were observed to be crucial parameters capable of increasing and decreasing movements. The similarities were found to be dependent on the thresholds in the EDR and LCSS models, and a change in the thresholds changed the outcome. To the best of the author’s knowledge, this paper is the first research on the use of several models for the similarity evaluation of LC trajectories.

A Clustering-based Approach for Predicting the Future Location of a Vessel

In recent years the number of vessel accidents has increased with the growing number of vessels in the Ocean. A substantial number of these accidents are due to human errors. However, a vessel could avoid some accidents if it knows future locations or trajectories of surrounding vessels. The future location (or trajectory) prediction of vessels is also valuable for maritime traffic management and planning. Existing approaches for predicting the future location are not vessel-specific, but the behavioural pattern of each type of vessel is different. On the other hand, clustering-based approaches are computationally expensive due to computing the similarity measures among vessel trajectories. In this paper, we propose a clustering-based framework that consists of three modules: dataset preparation, route clustering, and location prediction model. The main novelty of this proposal is that the prediction models are built using only trajectories of vessels of the same type, which we hypothesise will increase their accuracy. The other main contribution of our work is the evaluation of different strategies to improve computational efficiency, which can be critical for real-time vessel location prediction. We have used a density-based hierarchical clustering algorithm, HDBSCAN, where two fast implementations of trajectory similarity measures (Hausdorff Distance and Dynamic Time Warping) are evaluated for clustering route patterns. Also, the effect of using a trajectory compression algorithm (Ramer–Douglas–Peucker) to expedite the clustering process is analyzed. The performance of our approach is evaluated using real-world AIS data. We have compared our proposal against two baseline models. Evaluation results confirm the validity of the proposed approach for prediction of the future location of vessels