Here is Not There: Measuring Entailment-based Trajectory Similarity for Location-Privacy Protection and Beyond

While the paths humans take play out in social as well as physical space, measures to describe and compare their trajectories are carried out in abstract, typically Euclidean, space. When these measures are applied to trajectories of actual individuals in an application area, alterations that are inconsequential in abstract space may suddenly become problematic once overlaid with geographical reality. In this work, we present a different view on trajectory similarity by introducing a measure that utilizes logical entailment. This is an inferential perspective that considers facts as triple statements deduced from the social and environmental context, in which the travel takes place, and their practical implications. We suggest a formalization of entailment-based trajectory similarity, measured as the overlapping proportion of facts, which are spatial relation statements in our case study. With the proposed measure, we evaluate LSTM-TrajGAN, a privacy-preserving trajectory-generation model. The entailment-based model evaluation reveals potential consequences of disregarding the rich structure of geographical space (e.g., miscalculated insurance risk due to regional shifts in our toy example). Our work highlights the advantage of applying logical entailment to trajectory-similarity reasoning for location-privacy protection and beyond.