Measuring Similarity of Spatio-Temporal Trajectory Using Hausdorff Distance

The selection and robustness of similarity measure method is very important to the validity of the clustering results of spatial-temporal trajectory. In this paper, we propose a method for measuring the similarity of spatio-temporal trajectory using Hausdorff distance. Based on the multidimensional information of spatio-temporal trajectory data, this method selects spatial dimension and time dimension to measure the similarity of spatio-temporal trajectory. Firstly, based on the three characteristics of spatio-temporal trajectory, the spatio-temporal trajectory reconstruction strategy for similarity measurement is presented. Then, we transform the similarity measurement unit from point to trajectory segment, and propose a temporal synchronization distance measurement formula. Finally, considering the advantage of Hausdorff distance used on similarity measurement that takes into account the overall shape of spatio-temporal trajectory and the disadvantage that it is easy to be affected by the spatial distribution of spatio-temporal locus, we propose a measurement method of spatio-temporal trajectory similarity based on the average Hausdorff distance per unit time. The temporal and spatial clustering experiments were carried out using the microblog check-in trajectory data and taxi GPS trajectory data, and the spatio-temporal trajectory similarity measurement method proposed in this paper was compared with other existing methods. The experimental results show that this method can effectively calculate the similarity of space and time trajectories and meet the application needs of spatio-temporal trajectory clustering analysis.