Trajectory similarity computation is critical to various spatial data-related applications. To date, many deep learning-based approaches have been proposed to approximate trajectory similarity. However, most of previous models focus on trajectories in Euclidean space, neglecting the information of road networks, which is an important prerequisite in many applications, such as traffic analytics, social recommendation. In this paper, we study the trajectory similarity learning over road networks. Different from previous task, trajectories over road networks contain richer and more complex information, e.g., the geographical and structure information of road networks. To this end, we propose SPGMT, a graph modeling based approach that leverages abundant structure and position information inherent in road networks for trajectory similarity learning. Particularly, our graph model learns informative node representations by simultaneously incorporating structure information of nodes from a local perspective and position information from a global perspective. This road network oriented module is the first proposal to learn from a broad context of graph topology. Afterwards, SPGMT designs a self-attention network and employs an LSTM to learn the sequential information from trajectories. We conduct experiments on real-life datasets to demonstrate the superiority of SPGMT in terms of effectiveness. Besides, additional study shows the flexibility and robustness of SPGMT.

The requirement for appropriate ways to measure the similarity between data objects is a common but vital task in various domains, such as data mining, machine learning and so on. Driven by abundant real-world applications, many well-known similarity (distance) metrics are proposed to measure the pairwise similarity of data pairs, e.g., graph edit distance for graphs and dynamic time warping for time series. However, many similarity metrics suffer from the high time complexity. More specifically, most of the well-known similarity metrics often need quadratic time or even much more time to compute the ground truth similarity and some of them are proven to be NP-hard. With the development of deep learning techniques, there is an emerging research trend on the learning for similarity computation on various data types in the field of database (DB) and data mining, which is quite different with the metric learning studies in the machine learning (ML) literature. Specifically, the studies in the ML focus on the learning for semantic similarity in specific tasks, which is implicitly indicated by the training data, on the data in the feature space. While the studies in the DB literature usually consider the learning for well-defined similarity metrics (e.g., graph edit distance) on the data objects (e.g., graphs), such that it can benefit the similarity computation on data in terms of multiple aspects, such as computation time, metric quality and search heuristic, and the learned representation of data can also be naturally fed to downstream tasks. This survey paper provides a comprehensive review of similarity computation learning on several data types, including set, sequence and graph. Moreover, we first classify the learning-based approaches in terms of their learning target into three categories, i.e., similarity learning, cost matrix learning and search heuristic learning. Then we detail some representative approaches for each category on every data type, and analyze some key features that are utilized by these approaches. Finally, we discuss some challenges and future directions towards the learning for similarity learning on these data types.

Trajectory similarity computation is the cornerstone of many applications in the field of trajectory data analysis. To cope with the high time complexity of calculating exact similarity between trajectories, learning-based models have been developed for a good trade-off between the similarity computing time and the accuracy of the learned similarity. As each trajectory can be represented by a fixed-length vector regardless of the size of the trajectory, the similarity computation among the trajectories is highly time-efficient. Nevertheless, we observe that these learning-based models are designed based on recurrent neural networks (RNN), which cannot properly capture the correlations among the trajectories. Moreover, these learning-based models simply use the similarity scores of the pairs of trajectories in the training for a specific similarity metric, while a vital piece of information is neglected: the mappings of the points between two trajectories are readily available when the similarity score is calculated. These motivate us to design a new learning-based model, named TMN, based on attention networks, aiming to significantly improve the accuracy such that a better trade-off between the similarity computing time and the accuracy can be achieved. The proposed matching mechanism associates points across trajectories by computing attention weights of point pairs so that TMN learns to simulate similarity computation between the trajectory pair. Apart from taking interactions between trajectories into consideration, the sequential information of each individual trajectory is also considered, thereby making full use of spatial features of a pair of trajectories. We evaluate various approaches on real-life datasets under extensive trajectory distance metrics. Experimental results demonstrate that TMN outperforms state-of-the-art methods in terms of accuracy. Besides, ablation studies prove the effectiveness of our novel matching mechanism.

Advances of the sensor and GPS techniques have motivated the proliferation of trajectory data in a wide spectrum of applications. Trajectory similarity computation is one of the most fundamental problems in trajectory analytics. Considering that the high complexity of similarity computation is usually a bottleneck for large-scale trajectory data analysis, there are many research efforts for reducing the complexity such as the approximate algorithms. However, most of them are proposed for only one or two specific similarity measures, and thus cannot support different similarity measures well. In this paper, we propose a deep learning based model, namely T3S, which embeds each trajectory (i.e., a sequence of points) into a vector (point) in a d-dimensional space, and hence can significantly accelerate the similarity computation between the trajectories. By applying recurrent and attention neural networks, T3S can capture various unique characteristics of the trajectories such as the ordering of the points, spatial and structural information. Furthermore, our learning based T3S can easily handle any trajectory similarity measures by adjusting its parameters through the training. Extensive experiments on two real-life datasets demonstrate the effectiveness and efficiency of T3S. T3S outperforms state-of-the-art deep learning based methods under four popular trajectories similarity measures.