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 selfattention-based ones are the fastest and the most accurate. These results have implications for the use of trajectory similarity approaches given different application requirements. Code is available at https://github. com/changyanchuan/TrajSimiMeasures .