Edit distance with Quasi Real Penalties: a hybrid distance for network-constrained trajectories

In this paper, we propose a new distance for network-constrained trajectories named Edit distance with Quasi Real Penalties (EQRP). Depending on the case, it can compare trajectories as non-ordered sets and as sequences while other distances only compare trajectories as non-ordered sets or as sequences. Moreover, it is parameter-free, manages local time shifting, and respects triangle inequality; three properties expected from a trajectory distance that are not satisfied simultaneously by any other distance to the best of our knowledge. To demonstrate the pertinence of our idea, we benchmark our distance against some state-of-the-art distances for network-constrained trajectories. Specifically, for each distance, we determine its capability to identify precisely similar trajectories. We also determine their respective performance for trajectory clustering. Our results show the predominance of EQRP over the existing edit distances and in some cases a more precise ability to evaluate the dissimilarity between network-constrained trajectories compared to other measures.