Spatial-temporal similarity for trajectories with location noise and sporadic sampling

With the rapid advances and the penetration of the Internet of Things and sensors, a massive amount of trajectory data, given by discrete locations at certain timestamps, have been extracted or collected. Knowing the similarity between trajectories is fundamental to understanding their spatial-temporal correlation, with direct and far-reaching applications in contact tracing, companion detection, personalized marketing, etc. In this work, we consider the general and realistic sensing scenario that the locations of the trajectories may be noisy, and that these trajectories are sporadically sampled with randomness and asynchrony from the underlying continuous paths. Most of the prior work on trajectory similarity has not sufficiently considered the temporal dimension, or the issues of location noise and sporadic sampling, while others have limitations of strong assumptions such as a fixed known speed of users or the availability of a large amount of training data.We propose a novel and effective spatial-temporal measure termed STS (Spatial-Temporal Similarity) to evaluate the spatial-temporal overlap between any two trajectories. In order to account for the location noise and sporadic sampling, STS models each location in a trajectory as an observable outcome drawn from a probability distribution. With that, it efficiently reduces the need for training data by estimating a personalized spatial-temporal probability distribution of the object position from its own trajectory. Based on that, it subsequently computes the co-location probability and hence derives the similarity of any two trajectories. We have conducted extensive experiments to evaluate STS using real large-scale indoor (mall) and outdoor (taxi) datasets. Our results show that STS is substantially more accurate and robust than the state-of-the-art approaches, with an improvement of 63% on precision and 85% on mean rank.