## 2 Related Work  
Clustering is one of the most widely used data analysis and mining methods, conducted by measuring the similarity between objects and classifying those with a high degree of similarity into the same category. Clustering algorithms can be categorized into five main groups. The division-based clustering algorithms, such as K-means [8] and K-Medoids [11], use a few human-defined points as the initial centroids, and iteratively cluster until all data points are clustered based on heuristics. This class of algorithms is more sensitive to outlier points. The hierarchical-based clustering algorithms, such as BIRCH [12] and CURE [13], calculate the distance between the samples and combine the closest points until the clustering is completed. These algorithms have a high time complexity. The grid-based clustering algorithms divide the data space into grid cells, then map the data to the grid cells and calculate the density of each cell, and the neighboring dense cells form a cluster, such as STING [14] and CLIQUE [15]. But in general, they suffer from a lower accuracy. The model-based clustering algorithms mainly refer to probabilistic model-based methods and neural network model-based methods, such as GMM [16] and SOM [17]. They have a high computational complexity and poor clustering effect when the amount of data is small. In addition, the density-based clustering algorithms, such as DBSCAN [5] and OPTICS [18], check the continuity between samples in term of sample density and continuously expand the clusters based on connectable samples to obtain the final clustering results. Among them, the DBSCAN algorithm does not need to specify the number of clusters and can cluster datasets of arbitrary shapes, which is a classical clustering algorithm that has been widely used in many research fields, such as traffic flow mining, business center location selection, etc. However, existing clustering algorithms are not efficient to deal with the special properties of spatial-temporal trajectory data such as multi-dimensionality, large data volume, and high sparsity. For example, the classical DBSCAN algorithm is only applicable to spatial clustering, and the effect of clustering spatial-temporal trajectory data with multi-dimensional attribute information such as time is unsatisfactory. Recently, a number of research works have emerged to cluster spatial-temporal trajectory data. The ST-DBSCAN algorithm [8] processes and analyzes the data from the temporal and spatial dimensions, respectively. But the algorithm is more sensitive to the relevant parameters than the DBSCAN algorithm. And it fails to closely combine the temporal and spatial attributes of the trajectory data for clustering. The Quick Bundles clustering algorithm [19] can effectively process the spatial-temporal data and converge quickly. However, the selection of the clustering thresholds has a large impact on the final result of this algorithm, which relies heavily on manual experience setting. The MDST-DBSCAN algorithm [20] realizes the clustering of high-dimensional spatial-temporal data, but the selection of the initial point of clustering will have a great influence on the clustering results, so the stability of this algorithm is poor. In general, the existing spatial-temporal trajectory data clustering algorithms, especially the DBSCAN-based algorithms, have optimizable space in clustering efficiency when dealing with large-scale high-dimensional data. At the same time, such algorithms are sensitive to the _Eps_ and _MinPts_ parameters, and the clustering accuracy and efficiency are often limited by the optimization of clustering parameters. Parallelization is one of the most commonly used methods to accelerate the clustering speed of trajectory data. Parallel DBSCAN [21], the earliest distributed parallel version of the DBSCAN algorithm, realizes parallelization through the distributed spatial indexing data structure dR*-Tree to achieve an approximate linear speedup effect. But it is difficult to deal with large scale trajectory data.