Here Is Not There: Measuring Entailment-Based Trajectory Similarity for Location-Privacy Protection and Beyond (2312.01151v1)

Abstract: 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 geographic 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 geographic 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.

• The paper proposes a novel entailment-based framework that assesses trajectory similarity by inferring logical relationships in geographical contexts.
• It replaces traditional geometric metrics with semantic analysis, revealing how overlapping spatial relation facts capture contextual nuances.
• The approach demonstrates significant implications for location-privacy protections, highlighting potential misestimations in insurance and urban planning.

Assessing Trajectory Similarity Through Logical Entailment for Enhanced Location-Privacy

Introduction to Entailment-Based Trajectory Similarity

The assessment and comparison of human mobility patterns have traditionally been based on geometric or spatial-temporal approaches. Such assessments are pivotal across various sectors, including insurance, public safety, and urban planning. However, the reliance on abstract spatial representations often disregards the rich semantic context of geographical spaces. Zilong Liu and colleagues contribute to this discourse by proposing a novel approach to trajectory similarity, leveraging logical entailment—a form of inferential reasoning about the semantics of movement. Their work foregrounds the significance of the underlying geographical and societal context in assessing trajectory similarities, especially in applications concerning individual privacy and societal implications.

Logical Entailment as a Foundation for Comparing Trajectories

Unlike traditional measures, which predominantly focus on geometric properties, logical entailment emphasizes the inferred logical relationships within a geographical context. This method assesses trajectories based on the proportion of overlapping inferred facts—essentially spatial relation statements in the given paper. Such an approach enables a deeper understanding of trajectory similarities, considering the social and geographical implications of movement patterns.

Implications for Location-Privacy Protections

The discussion on location-privacy protections serves as a crucial application area for this entailment-based trajectory similarity measure. By evaluating a privacy-preserving trajectory-generation model, LSTM-TrajGAN, through this new lens, Liu et al. uncover the potential discrepancies that arise when geometrically similar but contextually diverse trajectories are treated equivalently. These discrepancies, illustrated through an insurance risk assessment example, highlight the practical implications of neglecting geographical context in trajectory analysis—potentially leading to significant misestimations in applications like insurance premium calculations.

Theoretical Advancements and Future Directions

This paper also advances the theoretical underpinnings of trajectory analysis by integrating logical entailment with trajectory similarity measures. Such integration encourages a more nuanced understanding of human mobility, emphasizing the importance of contextual semantics over mere geometric approximation. Looking ahead, the authors propose extending their framework to incorporate large-scale mobility datasets and exploring additional inferential calculi to further refine the semantic analysis of trajectories.

Conclusion

In sum, Liu et al.'s work presents a methodological shift towards incorporating logical entailment in trajectory similarity assessment. This shift not only enhances the accuracy of trajectory comparisons by factoring in the rich semantic context of geographical spaces but also underscores the broader societal implications of trajectory analysis. As we move toward an increasingly data-driven society, the need for nuanced, context-aware analytical tools becomes ever more critical, particularly in safeguarding individual privacy while ensuring the utility of mobility data. This paper marks a significant step in that direction, paving the way for future research and applications that balance the dual demands of privacy protection and data utility.