Comparative study on the effectiveness of trajectory similarity measurement algorithms

Many applications, e.g., Uber, collect large-scale trajectory data from moving vehicles on road network. Trajectory data analytics can benefit many real-world applications, such as route planning and transportation optimizations. Two core operations in trajectory data analytics are trajectory similarity search and join, and both of them rely on a trajectory similarity function to measure the similarity between two trajectories. However, existing similarity functions focus on trajectory points distance and neglect the fact the trajectories should be on road network. Obviously aligning trajectories on road network can remove the noise points introduced by system errors. Toward this goal, we define a road-network-aware trajectory similarity function to measure trajectory similarity. To support trajectory similarity search and join, we propose a filtering-refine framework. In the filtering step, we compute a signature of each trajectory such that if two trajectories are similar, they must share a common signature. We utilize the signatures to prune a huge number of dissimilar pairs. In the refine step, we design effective algorithms to verify the candidates that are not pruned in the filtering step. To support large-scale trajectories, we develop a system DISON for Distributed In-Memory Trajectory Similarity Search and Join on Road Network. DISON splits trajectories into disjoint partitions by considering load balance and locality, and designs effective global index to prune irrelevant partitions. Extensive experiments on real datasets showed that our method achieved high effectiveness, efficiency, and scalability and outperformed existing solutions significantly.

Under the background of big data era, massive trajectory data is constantly generated, which contains great value. The analysis and mining of spatiotemporal trajectory data is a research hotspot of spatial data, including trajectory retrieval, trajectory classification etc. In the process of analysis and mining, the similarity measurement between different trajectories is a key problem. Considering the amount of data, computational complexity, noise and other factors, different metrics need to be selected in different situations. In order to understand the performance of different similarity measurement algorithms, this paper selects the Longest Common Sub-Sequence Algorithm (LCSS), Fréchet Distance Algorithm and One Way Distance Algorithm (OWD) among the three kinds of trajectory similarity measurement algorithms and they were used for comparison. Experimental results show that LCSS algorithm can effectively resist the interference of noise points, Fréchet Distance Algorithm has strong robustness, and OWD Algorithm has low time complexity and short execution time.

In this paper, we present a high performance, coarse-to-fine scheme for image matching of infrared image and optical image. In order to eliminate the gray level difference and tolerance to distortion and noise existing in practice, this scheme uses the edge feature and combine a new similarity measures with modified Hausdorff distance to achieve the coarse-to-fine matching scheme. Our proposed method firstly extracts the feature points based on the method of Monte Carlo that reduce the computation load for the next matching, and then a new similarity measure is defined for coarse matching. Based on existing method of Monte Carlo evaluation the Huasdorff distance (MCHD), we define Monte Carlo modified Hausdorff distance (MCM-HD) to achieves the fine matching. Experiment are performed on a large test set and the result show that the fast search method diminishes the number of positions for calculate of Hausdorff distance, thus the computational load reduces and it is helpful to use Hausdorff distance in real time image matching. Compare with MCHD algorithm, our proposed method effectively improves the precision and reduces the execution time.

Tremendous growth of Location-based technologies resulted in the generation of a huge volume of spatial data, which needs to be analyzed to get potentially important patterns. The spatial patterns extracted can be used to design a better infrastructure ensuring reliable service coverage. Trajectory data is one variant of spatial data that are generated by moving objects travelling across. It is represented as a sequence of spatial coordinates (latitude, longitude) of a location. Trajectory clustering tries to group similar spatial data points to extract the most common movement behaviors. Trajectory data poses major challenges including uncertainty, sampling rate, representation, relationships, spatial autocorrelation, serialization, redundancy, and triviality, which makes it hard to apply traditional clustering algorithms over trajectory data. In this paper, K-Means and DBSCAN (Density-based spatial clustering of applications with noise) clustering algorithms are analyzed using different similarity measures like Euclidean, Hausdorff and Haversine distances with the help of index measures say Adjusted Rand Index (ARI) and Fowlkes-Mallows scores (FMS). Experiment is carried out over two different trajectory datasets and it is proved that usage of Haversine distance for clustering is efficient than Euclidean and Hausdorff distances in terms of spatial trajectory data.

The analysis of large-scale trajectory data has tremendous benefits for applications ranging from transportation planning to traffic management. A fundamental building block for the analysis of such data is the computation of similarity between trajectories. Existing work for similarity computation focuses mainly on the spatial aspects of trajectories, but more rarely takes into account time in conjunction with space. A key challenge when considering time is how to handle trajectories that are sampled asynchronously or at variable rates, which can lead to uncertainty. To tackle this problem, we quantify trajectory similarity as an interval, rather than a single value, to capture the uncertainty that can result from different sampling rates and asynchronous sampling. Based on this perspective, we develop a new trajectory similarity measure, Trajectory Interval Distance Estimation, which models similarity computation as a convex optimisation problem. Using two real datasets, we demonstrate that our proposed measure is extremely effective for assessing similarity in comparison to existing state of the art measures.

In a cloud environment, resources should be acquired quickly and automatically released at runtime. Traditional trajectory data partitions, indexing and query processing techniques are extended, so that they can take advantage of the cloud of large clusters of highly parallel processing capabilities. There are ways with trajectory data in the cloud database query processing. The advanced sensing techniques available today caused the existence of many types of trajectory datasets whose study can form a strong basis for decision making regarding a data context. Trajectory data generally includes trajectory classification, trajectory clustering, and trajectory associations and so on. All these tools need trajectory similarity measures to get comparisons in trajectory data. Some of the popular existing methods of trajectory similarity include Euclidean distance, semantic distance and there near variants. Each variant of these techniques exhibits notable differences in measurement of similarity and computational difficulty. This paper targeted to deal with this situation with the goal of lower computational efforts in trajectory similarity computations. A two‐phase trajectory similarity measure is defined. The first phase does point level analysis of trajectory points representing all trajectories and the following phase use the analysis to find the similarities. Using a hybrid similarity framework, new means for trajectory clustering and trajectory query processing are developed. From trajectory analysis followed by trajectory clustering, evaluation of cluster quality and processing of trajectory query are undertaken in this paper in different ways from the existing methods. All the proposed developments are tested with trajectory datasets with multiple attributes and the results are more favour to proposed framework than the existing ones.

Analysis on spatial-temporal data has several benefits that range from an improved traffic network in a city to increased earnings for drivers and ridesharing companies. A common analysis technique is clustering. However, most clustering techniques consider a constrained representation of clusters that is limited to a single timestamp. Evolving clusters exist through several timestamps and interact with other spatial-temporal objects or clusters, having cluster relationships. When many evolving clusters exist for analysis, a graph can be used to represent cluster evolution. In this article, we propose a framework for graph-based cluster evolution representation and analysis. The framework represents cluster structure and relationships as well as provides a graph representation of cluster evolution for analysis. Evaluation is done in three case studies with spatial-temporal data about taxis that can identify important phenomena or trends in movements in a city for traffic improvement.

Remotely sensed data have been utilized for environmental change study over the past 30 years. Large collections of remote sensing imagery have made it possible for spatio‐temporal analyses of the environment and the impact of human activities. This research attempts to develop both conceptual framework and methodological implementation for land cover change detection based on medium and high spatial resolution imagery and temporal trajectory analysis. Multi‐temporal and multi‐scale remotely sensed data have been integrated from various sources with a monitoring time frame of 30 years, including historical and state‐of‐the‐art high‐resolution satellite imagery. Based on this, spatio‐temporal patterns of environmental change, which is largely represented by changes in land cover (e.g., vegetation and water), were analysed for the given timeframe. Multi‐scale and multi‐temporal remotely sensed data, including Landsat MSS, TM, ETM and SPOT HRV, were used to detect changes in land cover in the past 30 years in Tarim River, Xinjiang, China. The study shows that by using the auto‐classification approach an overall accuracy of 85–90% with a Kappa coefficient of 0.66–0.78 was achieved for the classification of individual images. The temporal trajectory of land‐use change was established and its spatial pattern was analysed to gain a better understanding of the human impact on the fragile ecosystem of China's arid environment.

The aim of this paper is to propose a new similarity measure between linguistic terms by using restricted equivalence functions. We formally define it and prove that it fulfills similarity conditions. We explain how this measure can be employed for improving approximate reasoning in expert system inference engines and for maximizing similarity measures between linguistic terms. Finally, an experimental comparison between similarity measures is performed.

The increasing amount of trajectory data facilitates a wide spectrum of practical applications. In many such applications, large numbers of trajectory range and similarity queries are issued continuously, which calls for high-throughput trajectory query processing. Traditional in-memory databases lack considerations of the unique features of trajectories, thus suffering from inferior performance. Existing trajectory query processing systems are typically designed for only one type of trajectory queries, i.e., either range or similarity query, but not for both. Inspired by the massive parallelism on GPUs, in this paper, we develop a GPU-accelerated framework, named GAT, to support both types of trajectory queries (i.e., both range and similarity queries) with high throughput. For similarity queries, we adopt the Edit Distance on Real sequence (EDR) as the similarity measure which is accurate and robust to noise in real-world trajectories. GAT employs a GPU-friendly index called GTIDX to effectively filter invalid trajectories for both range and similarity queries, and exploits the GPU to perform parallel verifications. To accelerate the verification process on the GPU, we apply the Morton-based encoding method to reorganize trajectory points and facilitate coalesced data accesses for individual point data in global memory, which reduces the global memory bandwidth requirement significantly. We also propose a technique of grouping size-varying cells into balanced blocks with similar numbers of trajectory points, to achieve load balancing among the Streaming Multiprocessors (SMs) of the GPU. We conduct extensive experiments to evaluate the performance of GAT using two real-life trajectory datasets. The results show that GAT is scalable and achieves high throughput with acceptable indexing cost.

Spatial-temporal data refers to potentially massive amounts of data gathered across both space and time. Spatial-temporal data analysis helps uncover the value that this type of data holds to domains such as transportation operations, traffic management, service demand, and trip planning. Specifically, cluster analysis groups data into sets known as clusters such that elements inside a cluster are more similar to each other than elements in other clusters. Cluster analysis has been successfully applied in domains such as transportation, ecology, medicine, and astronomy. However, current cluster analysis techniques limit themselves to static cluster analysis, thereby missing the identification of interesting insights and patterns related to the evolution of clusters over time. In this paper, we clarify the concept of dynamic clusters and support new forms of cluster analyses by introducing, describing, and formalizing cluster relationships that represent important events, such as split or merge, that a cluster may go through from its start to its end. These relationships provide a foundation for investigating cluster evolution and providing novel insights for better operational and business decision making.

The article gives a general description and a detailed analysis of the divorce process of Volyn region population. The theoretical basis, demographic approaches to the study of divorce and divorce indicators in the region are analyzed. The importance of the divorces consequences and measures of demographic policy, which will be aimed at reducing them as a result of modernization of social and economic life in the current regime of reproduction: low birth rate and increasing life expectancy. Divorces peculiarities of Volyn region population are determined, the main of which are: sociological, psychological and demographic groups of risk factors for divorce. The main stages of family crises and their symptoms are described. The main negative consequences of divorce, which have an impact on the general demographic situation in the region are low birth rate (unrealized childbearing of divorced women); increase in the number of single-parent families in which the child is brought up by one parent; increasing the number of people who do not want to marry again after divorce; decrease of labor activity; deteriorating health, increased morbidity and death rate; increase suicides rate; increased risk of mental illness. It was found out the perspective psychological, legal forms and other assistance in marriage and family. The reasons for the low efficiency of the implementation of specific steps to overcome the processes of divorce in Volyn region are highlighted. Indicators for estimation of divorcing in the region have been calculated. Spatial-temporal data analysis of divorces for the period of 1995–2020 is carried out, regional features of their manifestation are singled out. The maps that reflect the spatial-temporal data differences of divorces in the regions were created. There were identified the main factors and preconditions for divorce in the region.

This study was conducted to test an automated method to identify unknown individuals. It relies on a previous radiographic file and uses an edge-based comparison of lumbar CT/PMCT reconstructions and radiographs. The living group was composed of 15 clinical lumbar spine CT scans and 15 paired radiographs belonging to the same patients. The deceased group consisted of 5 lumbar spine PMCT scans and 5 paired antemortem radiographs of deceased individuals plus the 15 unpaired radiographs belonging to the living. An automated method using image filtering (anisotropic diffusion) and edge detection (Canny filter) provided image contours. Cross comparisons of all the exams in each group were performed using similarity measurements under the affine registration hypothesis. The Dice coefficient and Hausdorff distance values were significantly linked (p < 0.001 and p = 0.001 respectively) to the matched examinations in the living group (p < 0.001; pseudo-R2 = 0.70). 12 of the 15 examinations were correctly paired, 2 were wrongly paired and 3 were not paired when they must have been. In the deceased group, the Hausdorff distance was significantly linked (p = 0.018) to the matched examinations (p < 0.001; pseudo-R2 = 0.62; Dice coefficient p = 0.138). The paired examinations were all correctly found, but one was wrongly paired. The negative predictive value was above 98% for both groups. We highlighted the feasibility of comparative radiological identification using automated edge detection in cross-modality (CT/PMCT scan and radiographs) examinations. This method could be of significant help to a radiologist or coroner in identifying unknown cadavers.

Hausdorff clustering of financial time series

This paper presents a new similarity measure for object recognition from large libraries of line-patterns. The measure draws its inspiration from both the Hausdorff distance and a recently reported Bayesian consistency measure that has been successfully used for graph-based correspondence matching. The measure uses robust error-kernels to gauge the similarity of pair-wise attribute relations defined on the edges of nearest neighbour graphs. We use the similarity measure in a recognition experiment which involves a library of over 1000 line-patterns. A sensitivity study reveals that the method is capable of delivering a recognition accuracy of 98%. A comparative study reveals that the method is most effective when a Gaussian kernel or Huber's robust kernel is used to weight the attribute relations. Moreover, the method consistently outperforms Rucklidge's median Hausdorff distance (1995).